From 110fdb48b12b83867bd6fce1efdfdad52518a4ba Mon Sep 17 00:00:00 2001
From: Guillaume Dalle <22795598+gdalle@users.noreply.github.com>
Date: Fri, 14 Jun 2024 10:53:38 +0200
Subject: [PATCH 1/3] Individual indexing

---
 src/ADNLPProblems/britgas.jl | 2698 ++++++++++++----------------------
 1 file changed, 900 insertions(+), 1798 deletions(-)

diff --git a/src/ADNLPProblems/britgas.jl b/src/ADNLPProblems/britgas.jl
index 8ade774a..5857c9b1 100644
--- a/src/ADNLPProblems/britgas.jl
+++ b/src/ADNLPProblems/britgas.jl
@@ -20,905 +20,456 @@ function britgas(; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) wh
   h = T(0.01)
 
   function f(x)
-    p1_0,
-    p2_0,
-    p3_0,
-    p4_0,
-    p5_0,
-    p6_0,
-    p7_0,
-    p8_0,
-    p9_0,
-    p10_0,
-    p11_0,
-    p12_0,
-    p13_0,
-    p14_0,
-    p15_0,
-    p16_0,
-    p17_0,
-    p18_0,
-    p19_0,
-    p20_0,
-    p21_0,
-    p22_0,
-    p23_0,
-    p1_1,
-    p2_1,
-    p3_1,
-    p4_1,
-    p5_1,
-    p6_1,
-    p7_1,
-    p8_1,
-    p9_1,
-    p10_1,
-    p11_1,
-    p12_1,
-    p13_1,
-    p14_1,
-    p15_1,
-    p16_1,
-    p17_1,
-    p18_1,
-    p19_1,
-    p20_1,
-    p21_1,
-    p22_1,
-    p23_1,
-    p1_2,
-    p2_2,
-    p3_2,
-    p4_2,
-    p5_2,
-    p6_2,
-    p7_2,
-    p8_2,
-    p9_2,
-    p10_2,
-    p11_2,
-    p12_2,
-    p13_2,
-    p14_2,
-    p15_2,
-    p16_2,
-    p17_2,
-    p18_2,
-    p19_2,
-    p20_2,
-    p21_2,
-    p22_2,
-    p23_2,
-    p1_3,
-    p2_3,
-    p3_3,
-    p4_3,
-    p5_3,
-    p6_3,
-    p7_3,
-    p8_3,
-    p9_3,
-    p10_3,
-    p11_3,
-    p12_3,
-    p13_3,
-    p14_3,
-    p15_3,
-    p16_3,
-    p17_3,
-    p18_3,
-    p19_3,
-    p20_3,
-    p21_3,
-    p22_3,
-    p23_3,
-    p1_4,
-    p2_4,
-    p3_4,
-    p4_4,
-    p5_4,
-    p6_4,
-    p7_4,
-    p8_4,
-    p9_4,
-    p10_4,
-    p11_4,
-    p12_4,
-    p13_4,
-    p14_4,
-    p15_4,
-    p16_4,
-    p17_4,
-    p18_4,
-    p19_4,
-    p20_4,
-    p21_4,
-    p22_4,
-    p23_4,
-    p1_5,
-    p2_5,
-    p3_5,
-    p4_5,
-    p5_5,
-    p6_5,
-    p7_5,
-    p8_5,
-    p9_5,
-    p10_5,
-    p11_5,
-    p12_5,
-    p13_5,
-    p14_5,
-    p15_5,
-    p16_5,
-    p17_5,
-    p18_5,
-    p19_5,
-    p20_5,
-    p21_5,
-    p22_5,
-    p23_5,
-    p1_6,
-    p2_6,
-    p3_6,
-    p4_6,
-    p5_6,
-    p6_6,
-    p7_6,
-    p8_6,
-    p9_6,
-    p10_6,
-    p11_6,
-    p12_6,
-    p13_6,
-    p14_6,
-    p15_6,
-    p16_6,
-    p17_6,
-    p18_6,
-    p19_6,
-    p20_6,
-    p21_6,
-    p22_6,
-    p23_6,
-    p1_7,
-    p2_7,
-    p3_7,
-    p4_7,
-    p5_7,
-    p6_7,
-    p7_7,
-    p8_7,
-    p9_7,
-    p10_7,
-    p11_7,
-    p12_7,
-    p13_7,
-    p14_7,
-    p15_7,
-    p16_7,
-    p17_7,
-    p18_7,
-    p19_7,
-    p20_7,
-    p21_7,
-    p22_7,
-    p23_7,
-    p1_8,
-    p2_8,
-    p3_8,
-    p4_8,
-    p5_8,
-    p6_8,
-    p7_8,
-    p8_8,
-    p9_8,
-    p10_8,
-    p11_8,
-    p12_8,
-    p13_8,
-    p14_8,
-    p15_8,
-    p16_8,
-    p17_8,
-    p18_8,
-    p19_8,
-    p20_8,
-    p21_8,
-    p22_8,
-    p23_8,
-    q1_2_0,
-    q1_17_0,
-    q2_3_0,
-    q4_5_0,
-    q5_6_0,
-    q7_8_0,
-    q8_9_0,
-    q8_10_0,
-    q8_11_0,
-    q11_12_0,
-    q12_13_0,
-    q13_14_0,
-    q13_15_0,
-    q15_16_0,
-    q17_18_0,
-    q18_19_0,
-    q20_21_0,
-    q21_22_0,
-    q22_23_0,
-    q1_2_1,
-    q1_17_1,
-    q2_3_1,
-    q4_5_1,
-    q5_6_1,
-    q7_8_1,
-    q8_9_1,
-    q8_10_1,
-    q8_11_1,
-    q11_12_1,
-    q12_13_1,
-    q13_14_1,
-    q13_15_1,
-    q15_16_1,
-    q17_18_1,
-    q18_19_1,
-    q20_21_1,
-    q21_22_1,
-    q22_23_1,
-    q1_2_2,
-    q1_17_2,
-    q2_3_2,
-    q4_5_2,
-    q5_6_2,
-    q7_8_2,
-    q8_9_2,
-    q8_10_2,
-    q8_11_2,
-    q11_12_2,
-    q12_13_2,
-    q13_14_2,
-    q13_15_2,
-    q15_16_2,
-    q17_18_2,
-    q18_19_2,
-    q20_21_2,
-    q21_22_2,
-    q22_23_2,
-    q1_2_3,
-    q1_17_3,
-    q2_3_3,
-    q4_5_3,
-    q5_6_3,
-    q7_8_3,
-    q8_9_3,
-    q8_10_3,
-    q8_11_3,
-    q11_12_3,
-    q12_13_3,
-    q13_14_3,
-    q13_15_3,
-    q15_16_3,
-    q17_18_3,
-    q18_19_3,
-    q20_21_3,
-    q21_22_3,
-    q22_23_3,
-    q1_2_4,
-    q1_17_4,
-    q2_3_4,
-    q4_5_4,
-    q5_6_4,
-    q7_8_4,
-    q8_9_4,
-    q8_10_4,
-    q8_11_4,
-    q11_12_4,
-    q12_13_4,
-    q13_14_4,
-    q13_15_4,
-    q15_16_4,
-    q17_18_4,
-    q18_19_4,
-    q20_21_4,
-    q21_22_4,
-    q22_23_4,
-    q1_2_5,
-    q1_17_5,
-    q2_3_5,
-    q4_5_5,
-    q5_6_5,
-    q7_8_5,
-    q8_9_5,
-    q8_10_5,
-    q8_11_5,
-    q11_12_5,
-    q12_13_5,
-    q13_14_5,
-    q13_15_5,
-    q15_16_5,
-    q17_18_5,
-    q18_19_5,
-    q20_21_5,
-    q21_22_5,
-    q22_23_5,
-    q1_2_6,
-    q1_17_6,
-    q2_3_6,
-    q4_5_6,
-    q5_6_6,
-    q7_8_6,
-    q8_9_6,
-    q8_10_6,
-    q8_11_6,
-    q11_12_6,
-    q12_13_6,
-    q13_14_6,
-    q13_15_6,
-    q15_16_6,
-    q17_18_6,
-    q18_19_6,
-    q20_21_6,
-    q21_22_6,
-    q22_23_6,
-    q1_2_7,
-    q1_17_7,
-    q2_3_7,
-    q4_5_7,
-    q5_6_7,
-    q7_8_7,
-    q8_9_7,
-    q8_10_7,
-    q8_11_7,
-    q11_12_7,
-    q12_13_7,
-    q13_14_7,
-    q13_15_7,
-    q15_16_7,
-    q17_18_7,
-    q18_19_7,
-    q20_21_7,
-    q21_22_7,
-    q22_23_7,
-    q1_2_8,
-    q1_17_8,
-    q2_3_8,
-    q4_5_8,
-    q5_6_8,
-    q7_8_8,
-    q8_9_8,
-    q8_10_8,
-    q8_11_8,
-    q11_12_8,
-    q12_13_8,
-    q13_14_8,
-    q13_15_8,
-    q15_16_8,
-    q17_18_8,
-    q18_19_8,
-    q20_21_8,
-    q21_22_8,
-    q22_23_8,
-    f3_4_1,
-    f5_7_1,
-    f19_20_1,
-    r3_4_1,
-    r5_7_1,
-    r19_20_1,
-    f3_4_2,
-    f5_7_2,
-    f19_20_2,
-    r3_4_2,
-    r5_7_2,
-    r19_20_2,
-    f3_4_3,
-    f5_7_3,
-    f19_20_3,
-    r3_4_3,
-    r5_7_3,
-    r19_20_3,
-    f3_4_4,
-    f5_7_4,
-    f19_20_4,
-    r3_4_4,
-    r5_7_4,
-    r19_20_4,
-    f3_4_5,
-    f5_7_5,
-    f19_20_5,
-    r3_4_5,
-    r5_7_5,
-    r19_20_5,
-    f3_4_6,
-    f5_7_6,
-    f19_20_6,
-    r3_4_6,
-    r5_7_6,
-    r19_20_6,
-    f3_4_7,
-    f5_7_7,
-    f19_20_7,
-    r3_4_7,
-    r5_7_7,
-    r19_20_7,
-    f3_4_8,
-    f5_7_8,
-    f19_20_8,
-    r3_4_8,
-    r5_7_8,
-    r19_20_8,
-    in1_1,
-    out16_1,
-    out23_1,
-    in1_2,
-    out16_2,
-    out23_2,
-    in1_3,
-    out16_3,
-    out23_3,
-    in1_4,
-    out16_4,
-    out23_4,
-    in1_5,
-    out16_5,
-    out23_5,
-    in1_6,
-    out16_6,
-    out23_6,
-    in1_7,
-    out16_7,
-    out23_7,
-    in1_8,
-    out16_8,
-    out23_8 = x[1],
-    x[2],
-    x[3],
-    x[4],
-    x[5],
-    x[6],
-    x[7],
-    x[8],
-    x[9],
-    x[10],
-    x[11],
-    x[12],
-    x[13],
-    x[14],
-    x[15],
-    x[16],
-    x[17],
-    x[18],
-    x[19],
-    x[20],
-    x[21],
-    x[22],
-    x[23],
-    x[24],
-    x[25],
-    x[26],
-    x[27],
-    x[28],
-    x[29],
-    x[30],
-    x[31],
-    x[32],
-    x[33],
-    x[34],
-    x[35],
-    x[36],
-    x[37],
-    x[38],
-    x[39],
-    x[40],
-    x[41],
-    x[42],
-    x[43],
-    x[44],
-    x[45],
-    x[46],
-    x[47],
-    x[48],
-    x[49],
-    x[50],
-    x[51],
-    x[52],
-    x[53],
-    x[54],
-    x[55],
-    x[56],
-    x[57],
-    x[58],
-    x[59],
-    x[60],
-    x[61],
-    x[62],
-    x[63],
-    x[64],
-    x[65],
-    x[66],
-    x[67],
-    x[68],
-    x[69],
-    x[70],
-    x[71],
-    x[72],
-    x[73],
-    x[74],
-    x[75],
-    x[76],
-    x[77],
-    x[78],
-    x[79],
-    x[80],
-    x[81],
-    x[82],
-    x[83],
-    x[84],
-    x[85],
-    x[86],
-    x[87],
-    x[88],
-    x[89],
-    x[90],
-    x[91],
-    x[92],
-    x[93],
-    x[94],
-    x[95],
-    x[96],
-    x[97],
-    x[98],
-    x[99],
-    x[100],
-    x[101],
-    x[102],
-    x[103],
-    x[104],
-    x[105],
-    x[106],
-    x[107],
-    x[108],
-    x[109],
-    x[110],
-    x[111],
-    x[112],
-    x[113],
-    x[114],
-    x[115],
-    x[116],
-    x[117],
-    x[118],
-    x[119],
-    x[120],
-    x[121],
-    x[122],
-    x[123],
-    x[124],
-    x[125],
-    x[126],
-    x[127],
-    x[128],
-    x[129],
-    x[130],
-    x[131],
-    x[132],
-    x[133],
-    x[134],
-    x[135],
-    x[136],
-    x[137],
-    x[138],
-    x[139],
-    x[140],
-    x[141],
-    x[142],
-    x[143],
-    x[144],
-    x[145],
-    x[146],
-    x[147],
-    x[148],
-    x[149],
-    x[150],
-    x[151],
-    x[152],
-    x[153],
-    x[154],
-    x[155],
-    x[156],
-    x[157],
-    x[158],
-    x[159],
-    x[160],
-    x[161],
-    x[162],
-    x[163],
-    x[164],
-    x[165],
-    x[166],
-    x[167],
-    x[168],
-    x[169],
-    x[170],
-    x[171],
-    x[172],
-    x[173],
-    x[174],
-    x[175],
-    x[176],
-    x[177],
-    x[178],
-    x[179],
-    x[180],
-    x[181],
-    x[182],
-    x[183],
-    x[184],
-    x[185],
-    x[186],
-    x[187],
-    x[188],
-    x[189],
-    x[190],
-    x[191],
-    x[192],
-    x[193],
-    x[194],
-    x[195],
-    x[196],
-    x[197],
-    x[198],
-    x[199],
-    x[200],
-    x[201],
-    x[202],
-    x[203],
-    x[204],
-    x[205],
-    x[206],
-    x[207],
-    x[208],
-    x[209],
-    x[210],
-    x[211],
-    x[212],
-    x[213],
-    x[214],
-    x[215],
-    x[216],
-    x[217],
-    x[218],
-    x[219],
-    x[220],
-    x[221],
-    x[222],
-    x[223],
-    x[224],
-    x[225],
-    x[226],
-    x[227],
-    x[228],
-    x[229],
-    x[230],
-    x[231],
-    x[232],
-    x[233],
-    x[234],
-    x[235],
-    x[236],
-    x[237],
-    x[238],
-    x[239],
-    x[240],
-    x[241],
-    x[242],
-    x[243],
-    x[244],
-    x[245],
-    x[246],
-    x[247],
-    x[248],
-    x[249],
-    x[250],
-    x[251],
-    x[252],
-    x[253],
-    x[254],
-    x[255],
-    x[256],
-    x[257],
-    x[258],
-    x[259],
-    x[260],
-    x[261],
-    x[262],
-    x[263],
-    x[264],
-    x[265],
-    x[266],
-    x[267],
-    x[268],
-    x[269],
-    x[270],
-    x[271],
-    x[272],
-    x[273],
-    x[274],
-    x[275],
-    x[276],
-    x[277],
-    x[278],
-    x[279],
-    x[280],
-    x[281],
-    x[282],
-    x[283],
-    x[284],
-    x[285],
-    x[286],
-    x[287],
-    x[288],
-    x[289],
-    x[290],
-    x[291],
-    x[292],
-    x[293],
-    x[294],
-    x[295],
-    x[296],
-    x[297],
-    x[298],
-    x[299],
-    x[300],
-    x[301],
-    x[302],
-    x[303],
-    x[304],
-    x[305],
-    x[306],
-    x[307],
-    x[308],
-    x[309],
-    x[310],
-    x[311],
-    x[312],
-    x[313],
-    x[314],
-    x[315],
-    x[316],
-    x[317],
-    x[318],
-    x[319],
-    x[320],
-    x[321],
-    x[322],
-    x[323],
-    x[324],
-    x[325],
-    x[326],
-    x[327],
-    x[328],
-    x[329],
-    x[330],
-    x[331],
-    x[332],
-    x[333],
-    x[334],
-    x[335],
-    x[336],
-    x[337],
-    x[338],
-    x[339],
-    x[340],
-    x[341],
-    x[342],
-    x[343],
-    x[344],
-    x[345],
-    x[346],
-    x[347],
-    x[348],
-    x[349],
-    x[350],
-    x[351],
-    x[352],
-    x[353],
-    x[354],
-    x[355],
-    x[356],
-    x[357],
-    x[358],
-    x[359],
-    x[360],
-    x[361],
-    x[362],
-    x[363],
-    x[364],
-    x[365],
-    x[366],
-    x[367],
-    x[368],
-    x[369],
-    x[370],
-    x[371],
-    x[372],
-    x[373],
-    x[374],
-    x[375],
-    x[376],
-    x[377],
-    x[378],
-    x[379],
-    x[380],
-    x[381],
-    x[382],
-    x[383],
-    x[384],
-    x[385],
-    x[386],
-    x[387],
-    x[388],
-    x[389],
-    x[390],
-    x[391],
-    x[392],
-    x[393],
-    x[394],
-    x[395],
-    x[396],
-    x[397],
-    x[398],
-    x[399],
-    x[400],
-    x[401],
-    x[402],
-    x[403],
-    x[404],
-    x[405],
-    x[406],
-    x[407],
-    x[408],
-    x[409],
-    x[410],
-    x[411],
-    x[412],
-    x[413],
-    x[414],
-    x[415],
-    x[416],
-    x[417],
-    x[418],
-    x[419],
-    x[420],
-    x[421],
-    x[422],
-    x[423],
-    x[424],
-    x[425],
-    x[426],
-    x[427],
-    x[428],
-    x[429],
-    x[430],
-    x[431],
-    x[432],
-    x[433],
-    x[434],
-    x[435],
-    x[436],
-    x[437],
-    x[438],
-    x[439],
-    x[440],
-    x[441],
-    x[442],
-    x[443],
-    x[444],
-    x[445],
-    x[446],
-    x[447],
-    x[448],
-    x[449],
-    x[450]
+    p1_0 = x[1]
+    p2_0 = x[2]
+    p3_0 = x[3]
+    p4_0 = x[4]
+    p5_0 = x[5]
+    p6_0 = x[6]
+    p7_0 = x[7]
+    p8_0 = x[8]
+    p9_0 = x[9]
+    p10_0 = x[10]
+    p11_0 = x[11]
+    p12_0 = x[12]
+    p13_0 = x[13]
+    p14_0 = x[14]
+    p15_0 = x[15]
+    p16_0 = x[16]
+    p17_0 = x[17]
+    p18_0 = x[18]
+    p19_0 = x[19]
+    p20_0 = x[20]
+    p21_0 = x[21]
+    p22_0 = x[22]
+    p23_0 = x[23]
+    p1_1 = x[24]
+    p2_1 = x[25]
+    p3_1 = x[26]
+    p4_1 = x[27]
+    p5_1 = x[28]
+    p6_1 = x[29]
+    p7_1 = x[30]
+    p8_1 = x[31]
+    p9_1 = x[32]
+    p10_1 = x[33]
+    p11_1 = x[34]
+    p12_1 = x[35]
+    p13_1 = x[36]
+    p14_1 = x[37]
+    p15_1 = x[38]
+    p16_1 = x[39]
+    p17_1 = x[40]
+    p18_1 = x[41]
+    p19_1 = x[42]
+    p20_1 = x[43]
+    p21_1 = x[44]
+    p22_1 = x[45]
+    p23_1 = x[46]
+    p1_2 = x[47]
+    p2_2 = x[48]
+    p3_2 = x[49]
+    p4_2 = x[50]
+    p5_2 = x[51]
+    p6_2 = x[52]
+    p7_2 = x[53]
+    p8_2 = x[54]
+    p9_2 = x[55]
+    p10_2 = x[56]
+    p11_2 = x[57]
+    p12_2 = x[58]
+    p13_2 = x[59]
+    p14_2 = x[60]
+    p15_2 = x[61]
+    p16_2 = x[62]
+    p17_2 = x[63]
+    p18_2 = x[64]
+    p19_2 = x[65]
+    p20_2 = x[66]
+    p21_2 = x[67]
+    p22_2 = x[68]
+    p23_2 = x[69]
+    p1_3 = x[70]
+    p2_3 = x[71]
+    p3_3 = x[72]
+    p4_3 = x[73]
+    p5_3 = x[74]
+    p6_3 = x[75]
+    p7_3 = x[76]
+    p8_3 = x[77]
+    p9_3 = x[78]
+    p10_3 = x[79]
+    p11_3 = x[80]
+    p12_3 = x[81]
+    p13_3 = x[82]
+    p14_3 = x[83]
+    p15_3 = x[84]
+    p16_3 = x[85]
+    p17_3 = x[86]
+    p18_3 = x[87]
+    p19_3 = x[88]
+    p20_3 = x[89]
+    p21_3 = x[90]
+    p22_3 = x[91]
+    p23_3 = x[92]
+    p1_4 = x[93]
+    p2_4 = x[94]
+    p3_4 = x[95]
+    p4_4 = x[96]
+    p5_4 = x[97]
+    p6_4 = x[98]
+    p7_4 = x[99]
+    p8_4 = x[100]
+    p9_4 = x[101]
+    p10_4 = x[102]
+    p11_4 = x[103]
+    p12_4 = x[104]
+    p13_4 = x[105]
+    p14_4 = x[106]
+    p15_4 = x[107]
+    p16_4 = x[108]
+    p17_4 = x[109]
+    p18_4 = x[110]
+    p19_4 = x[111]
+    p20_4 = x[112]
+    p21_4 = x[113]
+    p22_4 = x[114]
+    p23_4 = x[115]
+    p1_5 = x[116]
+    p2_5 = x[117]
+    p3_5 = x[118]
+    p4_5 = x[119]
+    p5_5 = x[120]
+    p6_5 = x[121]
+    p7_5 = x[122]
+    p8_5 = x[123]
+    p9_5 = x[124]
+    p10_5 = x[125]
+    p11_5 = x[126]
+    p12_5 = x[127]
+    p13_5 = x[128]
+    p14_5 = x[129]
+    p15_5 = x[130]
+    p16_5 = x[131]
+    p17_5 = x[132]
+    p18_5 = x[133]
+    p19_5 = x[134]
+    p20_5 = x[135]
+    p21_5 = x[136]
+    p22_5 = x[137]
+    p23_5 = x[138]
+    p1_6 = x[139]
+    p2_6 = x[140]
+    p3_6 = x[141]
+    p4_6 = x[142]
+    p5_6 = x[143]
+    p6_6 = x[144]
+    p7_6 = x[145]
+    p8_6 = x[146]
+    p9_6 = x[147]
+    p10_6 = x[148]
+    p11_6 = x[149]
+    p12_6 = x[150]
+    p13_6 = x[151]
+    p14_6 = x[152]
+    p15_6 = x[153]
+    p16_6 = x[154]
+    p17_6 = x[155]
+    p18_6 = x[156]
+    p19_6 = x[157]
+    p20_6 = x[158]
+    p21_6 = x[159]
+    p22_6 = x[160]
+    p23_6 = x[161]
+    p1_7 = x[162]
+    p2_7 = x[163]
+    p3_7 = x[164]
+    p4_7 = x[165]
+    p5_7 = x[166]
+    p6_7 = x[167]
+    p7_7 = x[168]
+    p8_7 = x[169]
+    p9_7 = x[170]
+    p10_7 = x[171]
+    p11_7 = x[172]
+    p12_7 = x[173]
+    p13_7 = x[174]
+    p14_7 = x[175]
+    p15_7 = x[176]
+    p16_7 = x[177]
+    p17_7 = x[178]
+    p18_7 = x[179]
+    p19_7 = x[180]
+    p20_7 = x[181]
+    p21_7 = x[182]
+    p22_7 = x[183]
+    p23_7 = x[184]
+    p1_8 = x[185]
+    p2_8 = x[186]
+    p3_8 = x[187]
+    p4_8 = x[188]
+    p5_8 = x[189]
+    p6_8 = x[190]
+    p7_8 = x[191]
+    p8_8 = x[192]
+    p9_8 = x[193]
+    p10_8 = x[194]
+    p11_8 = x[195]
+    p12_8 = x[196]
+    p13_8 = x[197]
+    p14_8 = x[198]
+    p15_8 = x[199]
+    p16_8 = x[200]
+    p17_8 = x[201]
+    p18_8 = x[202]
+    p19_8 = x[203]
+    p20_8 = x[204]
+    p21_8 = x[205]
+    p22_8 = x[206]
+    p23_8 = x[207]
+    q1_2_0 = x[208]
+    q1_17_0 = x[209]
+    q2_3_0 = x[210]
+    q4_5_0 = x[211]
+    q5_6_0 = x[212]
+    q7_8_0 = x[213]
+    q8_9_0 = x[214]
+    q8_10_0 = x[215]
+    q8_11_0 = x[216]
+    q11_12_0 = x[217]
+    q12_13_0 = x[218]
+    q13_14_0 = x[219]
+    q13_15_0 = x[220]
+    q15_16_0 = x[221]
+    q17_18_0 = x[222]
+    q18_19_0 = x[223]
+    q20_21_0 = x[224]
+    q21_22_0 = x[225]
+    q22_23_0 = x[226]
+    q1_2_1 = x[227]
+    q1_17_1 = x[228]
+    q2_3_1 = x[229]
+    q4_5_1 = x[230]
+    q5_6_1 = x[231]
+    q7_8_1 = x[232]
+    q8_9_1 = x[233]
+    q8_10_1 = x[234]
+    q8_11_1 = x[235]
+    q11_12_1 = x[236]
+    q12_13_1 = x[237]
+    q13_14_1 = x[238]
+    q13_15_1 = x[239]
+    q15_16_1 = x[240]
+    q17_18_1 = x[241]
+    q18_19_1 = x[242]
+    q20_21_1 = x[243]
+    q21_22_1 = x[244]
+    q22_23_1 = x[245]
+    q1_2_2 = x[246]
+    q1_17_2 = x[247]
+    q2_3_2 = x[248]
+    q4_5_2 = x[249]
+    q5_6_2 = x[250]
+    q7_8_2 = x[251]
+    q8_9_2 = x[252]
+    q8_10_2 = x[253]
+    q8_11_2 = x[254]
+    q11_12_2 = x[255]
+    q12_13_2 = x[256]
+    q13_14_2 = x[257]
+    q13_15_2 = x[258]
+    q15_16_2 = x[259]
+    q17_18_2 = x[260]
+    q18_19_2 = x[261]
+    q20_21_2 = x[262]
+    q21_22_2 = x[263]
+    q22_23_2 = x[264]
+    q1_2_3 = x[265]
+    q1_17_3 = x[266]
+    q2_3_3 = x[267]
+    q4_5_3 = x[268]
+    q5_6_3 = x[269]
+    q7_8_3 = x[270]
+    q8_9_3 = x[271]
+    q8_10_3 = x[272]
+    q8_11_3 = x[273]
+    q11_12_3 = x[274]
+    q12_13_3 = x[275]
+    q13_14_3 = x[276]
+    q13_15_3 = x[277]
+    q15_16_3 = x[278]
+    q17_18_3 = x[279]
+    q18_19_3 = x[280]
+    q20_21_3 = x[281]
+    q21_22_3 = x[282]
+    q22_23_3 = x[283]
+    q1_2_4 = x[284]
+    q1_17_4 = x[285]
+    q2_3_4 = x[286]
+    q4_5_4 = x[287]
+    q5_6_4 = x[288]
+    q7_8_4 = x[289]
+    q8_9_4 = x[290]
+    q8_10_4 = x[291]
+    q8_11_4 = x[292]
+    q11_12_4 = x[293]
+    q12_13_4 = x[294]
+    q13_14_4 = x[295]
+    q13_15_4 = x[296]
+    q15_16_4 = x[297]
+    q17_18_4 = x[298]
+    q18_19_4 = x[299]
+    q20_21_4 = x[300]
+    q21_22_4 = x[301]
+    q22_23_4 = x[302]
+    q1_2_5 = x[303]
+    q1_17_5 = x[304]
+    q2_3_5 = x[305]
+    q4_5_5 = x[306]
+    q5_6_5 = x[307]
+    q7_8_5 = x[308]
+    q8_9_5 = x[309]
+    q8_10_5 = x[310]
+    q8_11_5 = x[311]
+    q11_12_5 = x[312]
+    q12_13_5 = x[313]
+    q13_14_5 = x[314]
+    q13_15_5 = x[315]
+    q15_16_5 = x[316]
+    q17_18_5 = x[317]
+    q18_19_5 = x[318]
+    q20_21_5 = x[319]
+    q21_22_5 = x[320]
+    q22_23_5 = x[321]
+    q1_2_6 = x[322]
+    q1_17_6 = x[323]
+    q2_3_6 = x[324]
+    q4_5_6 = x[325]
+    q5_6_6 = x[326]
+    q7_8_6 = x[327]
+    q8_9_6 = x[328]
+    q8_10_6 = x[329]
+    q8_11_6 = x[330]
+    q11_12_6 = x[331]
+    q12_13_6 = x[332]
+    q13_14_6 = x[333]
+    q13_15_6 = x[334]
+    q15_16_6 = x[335]
+    q17_18_6 = x[336]
+    q18_19_6 = x[337]
+    q20_21_6 = x[338]
+    q21_22_6 = x[339]
+    q22_23_6 = x[340]
+    q1_2_7 = x[341]
+    q1_17_7 = x[342]
+    q2_3_7 = x[343]
+    q4_5_7 = x[344]
+    q5_6_7 = x[345]
+    q7_8_7 = x[346]
+    q8_9_7 = x[347]
+    q8_10_7 = x[348]
+    q8_11_7 = x[349]
+    q11_12_7 = x[350]
+    q12_13_7 = x[351]
+    q13_14_7 = x[352]
+    q13_15_7 = x[353]
+    q15_16_7 = x[354]
+    q17_18_7 = x[355]
+    q18_19_7 = x[356]
+    q20_21_7 = x[357]
+    q21_22_7 = x[358]
+    q22_23_7 = x[359]
+    q1_2_8 = x[360]
+    q1_17_8 = x[361]
+    q2_3_8 = x[362]
+    q4_5_8 = x[363]
+    q5_6_8 = x[364]
+    q7_8_8 = x[365]
+    q8_9_8 = x[366]
+    q8_10_8 = x[367]
+    q8_11_8 = x[368]
+    q11_12_8 = x[369]
+    q12_13_8 = x[370]
+    q13_14_8 = x[371]
+    q13_15_8 = x[372]
+    q15_16_8 = x[373]
+    q17_18_8 = x[374]
+    q18_19_8 = x[375]
+    q20_21_8 = x[376]
+    q21_22_8 = x[377]
+    q22_23_8 = x[378]
+    f3_4_1 = x[379]
+    f5_7_1 = x[380]
+    f19_20_1 = x[381]
+    r3_4_1 = x[382]
+    r5_7_1 = x[383]
+    r19_20_1 = x[384]
+    f3_4_2 = x[385]
+    f5_7_2 = x[386]
+    f19_20_2 = x[387]
+    r3_4_2 = x[388]
+    r5_7_2 = x[389]
+    r19_20_2 = x[390]
+    f3_4_3 = x[391]
+    f5_7_3 = x[392]
+    f19_20_3 = x[393]
+    r3_4_3 = x[394]
+    r5_7_3 = x[395]
+    r19_20_3 = x[396]
+    f3_4_4 = x[397]
+    f5_7_4 = x[398]
+    f19_20_4 = x[399]
+    r3_4_4 = x[400]
+    r5_7_4 = x[401]
+    r19_20_4 = x[402]
+    f3_4_5 = x[403]
+    f5_7_5 = x[404]
+    f19_20_5 = x[405]
+    r3_4_5 = x[406]
+    r5_7_5 = x[407]
+    r19_20_5 = x[408]
+    f3_4_6 = x[409]
+    f5_7_6 = x[410]
+    f19_20_6 = x[411]
+    r3_4_6 = x[412]
+    r5_7_6 = x[413]
+    r19_20_6 = x[414]
+    f3_4_7 = x[415]
+    f5_7_7 = x[416]
+    f19_20_7 = x[417]
+    r3_4_7 = x[418]
+    r5_7_7 = x[419]
+    r19_20_7 = x[420]
+    f3_4_8 = x[421]
+    f5_7_8 = x[422]
+    f19_20_8 = x[423]
+    r3_4_8 = x[424]
+    r5_7_8 = x[425]
+    r19_20_8 = x[426]
+    in1_1 = x[427]
+    out16_1 = x[428]
+    out23_1 = x[429]
+    in1_2 = x[430]
+    out16_2 = x[431]
+    out23_2 = x[432]
+    in1_3 = x[433]
+    out16_3 = x[434]
+    out23_3 = x[435]
+    in1_4 = x[436]
+    out16_4 = x[437]
+    out23_4 = x[438]
+    in1_5 = x[439]
+    out16_5 = x[440]
+    out23_5 = x[441]
+    in1_6 = x[442]
+    out16_6 = x[443]
+    out23_6 = x[444]
+    in1_7 = x[445]
+    out16_7 = x[446]
+    out23_7 = x[447]
+    in1_8 = x[448]
+    out16_8 = x[449]
+    out23_8 = x[450]
     return f3_4_1 * ((abs(r3_4_1)^(22 // 100)) - 1) +
            f5_7_1 * ((abs(r5_7_1)^(22 // 100)) - 1) +
            f19_20_1 * ((abs(r19_20_1)^(22 // 100)) - 1) +
@@ -1397,905 +948,456 @@ function britgas(; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) wh
     1.0,
   ]
   function c!(cx, x)
-    p1_0,
-    p2_0,
-    p3_0,
-    p4_0,
-    p5_0,
-    p6_0,
-    p7_0,
-    p8_0,
-    p9_0,
-    p10_0,
-    p11_0,
-    p12_0,
-    p13_0,
-    p14_0,
-    p15_0,
-    p16_0,
-    p17_0,
-    p18_0,
-    p19_0,
-    p20_0,
-    p21_0,
-    p22_0,
-    p23_0,
-    p1_1,
-    p2_1,
-    p3_1,
-    p4_1,
-    p5_1,
-    p6_1,
-    p7_1,
-    p8_1,
-    p9_1,
-    p10_1,
-    p11_1,
-    p12_1,
-    p13_1,
-    p14_1,
-    p15_1,
-    p16_1,
-    p17_1,
-    p18_1,
-    p19_1,
-    p20_1,
-    p21_1,
-    p22_1,
-    p23_1,
-    p1_2,
-    p2_2,
-    p3_2,
-    p4_2,
-    p5_2,
-    p6_2,
-    p7_2,
-    p8_2,
-    p9_2,
-    p10_2,
-    p11_2,
-    p12_2,
-    p13_2,
-    p14_2,
-    p15_2,
-    p16_2,
-    p17_2,
-    p18_2,
-    p19_2,
-    p20_2,
-    p21_2,
-    p22_2,
-    p23_2,
-    p1_3,
-    p2_3,
-    p3_3,
-    p4_3,
-    p5_3,
-    p6_3,
-    p7_3,
-    p8_3,
-    p9_3,
-    p10_3,
-    p11_3,
-    p12_3,
-    p13_3,
-    p14_3,
-    p15_3,
-    p16_3,
-    p17_3,
-    p18_3,
-    p19_3,
-    p20_3,
-    p21_3,
-    p22_3,
-    p23_3,
-    p1_4,
-    p2_4,
-    p3_4,
-    p4_4,
-    p5_4,
-    p6_4,
-    p7_4,
-    p8_4,
-    p9_4,
-    p10_4,
-    p11_4,
-    p12_4,
-    p13_4,
-    p14_4,
-    p15_4,
-    p16_4,
-    p17_4,
-    p18_4,
-    p19_4,
-    p20_4,
-    p21_4,
-    p22_4,
-    p23_4,
-    p1_5,
-    p2_5,
-    p3_5,
-    p4_5,
-    p5_5,
-    p6_5,
-    p7_5,
-    p8_5,
-    p9_5,
-    p10_5,
-    p11_5,
-    p12_5,
-    p13_5,
-    p14_5,
-    p15_5,
-    p16_5,
-    p17_5,
-    p18_5,
-    p19_5,
-    p20_5,
-    p21_5,
-    p22_5,
-    p23_5,
-    p1_6,
-    p2_6,
-    p3_6,
-    p4_6,
-    p5_6,
-    p6_6,
-    p7_6,
-    p8_6,
-    p9_6,
-    p10_6,
-    p11_6,
-    p12_6,
-    p13_6,
-    p14_6,
-    p15_6,
-    p16_6,
-    p17_6,
-    p18_6,
-    p19_6,
-    p20_6,
-    p21_6,
-    p22_6,
-    p23_6,
-    p1_7,
-    p2_7,
-    p3_7,
-    p4_7,
-    p5_7,
-    p6_7,
-    p7_7,
-    p8_7,
-    p9_7,
-    p10_7,
-    p11_7,
-    p12_7,
-    p13_7,
-    p14_7,
-    p15_7,
-    p16_7,
-    p17_7,
-    p18_7,
-    p19_7,
-    p20_7,
-    p21_7,
-    p22_7,
-    p23_7,
-    p1_8,
-    p2_8,
-    p3_8,
-    p4_8,
-    p5_8,
-    p6_8,
-    p7_8,
-    p8_8,
-    p9_8,
-    p10_8,
-    p11_8,
-    p12_8,
-    p13_8,
-    p14_8,
-    p15_8,
-    p16_8,
-    p17_8,
-    p18_8,
-    p19_8,
-    p20_8,
-    p21_8,
-    p22_8,
-    p23_8,
-    q1_2_0,
-    q1_17_0,
-    q2_3_0,
-    q4_5_0,
-    q5_6_0,
-    q7_8_0,
-    q8_9_0,
-    q8_10_0,
-    q8_11_0,
-    q11_12_0,
-    q12_13_0,
-    q13_14_0,
-    q13_15_0,
-    q15_16_0,
-    q17_18_0,
-    q18_19_0,
-    q20_21_0,
-    q21_22_0,
-    q22_23_0,
-    q1_2_1,
-    q1_17_1,
-    q2_3_1,
-    q4_5_1,
-    q5_6_1,
-    q7_8_1,
-    q8_9_1,
-    q8_10_1,
-    q8_11_1,
-    q11_12_1,
-    q12_13_1,
-    q13_14_1,
-    q13_15_1,
-    q15_16_1,
-    q17_18_1,
-    q18_19_1,
-    q20_21_1,
-    q21_22_1,
-    q22_23_1,
-    q1_2_2,
-    q1_17_2,
-    q2_3_2,
-    q4_5_2,
-    q5_6_2,
-    q7_8_2,
-    q8_9_2,
-    q8_10_2,
-    q8_11_2,
-    q11_12_2,
-    q12_13_2,
-    q13_14_2,
-    q13_15_2,
-    q15_16_2,
-    q17_18_2,
-    q18_19_2,
-    q20_21_2,
-    q21_22_2,
-    q22_23_2,
-    q1_2_3,
-    q1_17_3,
-    q2_3_3,
-    q4_5_3,
-    q5_6_3,
-    q7_8_3,
-    q8_9_3,
-    q8_10_3,
-    q8_11_3,
-    q11_12_3,
-    q12_13_3,
-    q13_14_3,
-    q13_15_3,
-    q15_16_3,
-    q17_18_3,
-    q18_19_3,
-    q20_21_3,
-    q21_22_3,
-    q22_23_3,
-    q1_2_4,
-    q1_17_4,
-    q2_3_4,
-    q4_5_4,
-    q5_6_4,
-    q7_8_4,
-    q8_9_4,
-    q8_10_4,
-    q8_11_4,
-    q11_12_4,
-    q12_13_4,
-    q13_14_4,
-    q13_15_4,
-    q15_16_4,
-    q17_18_4,
-    q18_19_4,
-    q20_21_4,
-    q21_22_4,
-    q22_23_4,
-    q1_2_5,
-    q1_17_5,
-    q2_3_5,
-    q4_5_5,
-    q5_6_5,
-    q7_8_5,
-    q8_9_5,
-    q8_10_5,
-    q8_11_5,
-    q11_12_5,
-    q12_13_5,
-    q13_14_5,
-    q13_15_5,
-    q15_16_5,
-    q17_18_5,
-    q18_19_5,
-    q20_21_5,
-    q21_22_5,
-    q22_23_5,
-    q1_2_6,
-    q1_17_6,
-    q2_3_6,
-    q4_5_6,
-    q5_6_6,
-    q7_8_6,
-    q8_9_6,
-    q8_10_6,
-    q8_11_6,
-    q11_12_6,
-    q12_13_6,
-    q13_14_6,
-    q13_15_6,
-    q15_16_6,
-    q17_18_6,
-    q18_19_6,
-    q20_21_6,
-    q21_22_6,
-    q22_23_6,
-    q1_2_7,
-    q1_17_7,
-    q2_3_7,
-    q4_5_7,
-    q5_6_7,
-    q7_8_7,
-    q8_9_7,
-    q8_10_7,
-    q8_11_7,
-    q11_12_7,
-    q12_13_7,
-    q13_14_7,
-    q13_15_7,
-    q15_16_7,
-    q17_18_7,
-    q18_19_7,
-    q20_21_7,
-    q21_22_7,
-    q22_23_7,
-    q1_2_8,
-    q1_17_8,
-    q2_3_8,
-    q4_5_8,
-    q5_6_8,
-    q7_8_8,
-    q8_9_8,
-    q8_10_8,
-    q8_11_8,
-    q11_12_8,
-    q12_13_8,
-    q13_14_8,
-    q13_15_8,
-    q15_16_8,
-    q17_18_8,
-    q18_19_8,
-    q20_21_8,
-    q21_22_8,
-    q22_23_8,
-    f3_4_1,
-    f5_7_1,
-    f19_20_1,
-    r3_4_1,
-    r5_7_1,
-    r19_20_1,
-    f3_4_2,
-    f5_7_2,
-    f19_20_2,
-    r3_4_2,
-    r5_7_2,
-    r19_20_2,
-    f3_4_3,
-    f5_7_3,
-    f19_20_3,
-    r3_4_3,
-    r5_7_3,
-    r19_20_3,
-    f3_4_4,
-    f5_7_4,
-    f19_20_4,
-    r3_4_4,
-    r5_7_4,
-    r19_20_4,
-    f3_4_5,
-    f5_7_5,
-    f19_20_5,
-    r3_4_5,
-    r5_7_5,
-    r19_20_5,
-    f3_4_6,
-    f5_7_6,
-    f19_20_6,
-    r3_4_6,
-    r5_7_6,
-    r19_20_6,
-    f3_4_7,
-    f5_7_7,
-    f19_20_7,
-    r3_4_7,
-    r5_7_7,
-    r19_20_7,
-    f3_4_8,
-    f5_7_8,
-    f19_20_8,
-    r3_4_8,
-    r5_7_8,
-    r19_20_8,
-    in1_1,
-    out16_1,
-    out23_1,
-    in1_2,
-    out16_2,
-    out23_2,
-    in1_3,
-    out16_3,
-    out23_3,
-    in1_4,
-    out16_4,
-    out23_4,
-    in1_5,
-    out16_5,
-    out23_5,
-    in1_6,
-    out16_6,
-    out23_6,
-    in1_7,
-    out16_7,
-    out23_7,
-    in1_8,
-    out16_8,
-    out23_8 = x[1],
-    x[2],
-    x[3],
-    x[4],
-    x[5],
-    x[6],
-    x[7],
-    x[8],
-    x[9],
-    x[10],
-    x[11],
-    x[12],
-    x[13],
-    x[14],
-    x[15],
-    x[16],
-    x[17],
-    x[18],
-    x[19],
-    x[20],
-    x[21],
-    x[22],
-    x[23],
-    x[24],
-    x[25],
-    x[26],
-    x[27],
-    x[28],
-    x[29],
-    x[30],
-    x[31],
-    x[32],
-    x[33],
-    x[34],
-    x[35],
-    x[36],
-    x[37],
-    x[38],
-    x[39],
-    x[40],
-    x[41],
-    x[42],
-    x[43],
-    x[44],
-    x[45],
-    x[46],
-    x[47],
-    x[48],
-    x[49],
-    x[50],
-    x[51],
-    x[52],
-    x[53],
-    x[54],
-    x[55],
-    x[56],
-    x[57],
-    x[58],
-    x[59],
-    x[60],
-    x[61],
-    x[62],
-    x[63],
-    x[64],
-    x[65],
-    x[66],
-    x[67],
-    x[68],
-    x[69],
-    x[70],
-    x[71],
-    x[72],
-    x[73],
-    x[74],
-    x[75],
-    x[76],
-    x[77],
-    x[78],
-    x[79],
-    x[80],
-    x[81],
-    x[82],
-    x[83],
-    x[84],
-    x[85],
-    x[86],
-    x[87],
-    x[88],
-    x[89],
-    x[90],
-    x[91],
-    x[92],
-    x[93],
-    x[94],
-    x[95],
-    x[96],
-    x[97],
-    x[98],
-    x[99],
-    x[100],
-    x[101],
-    x[102],
-    x[103],
-    x[104],
-    x[105],
-    x[106],
-    x[107],
-    x[108],
-    x[109],
-    x[110],
-    x[111],
-    x[112],
-    x[113],
-    x[114],
-    x[115],
-    x[116],
-    x[117],
-    x[118],
-    x[119],
-    x[120],
-    x[121],
-    x[122],
-    x[123],
-    x[124],
-    x[125],
-    x[126],
-    x[127],
-    x[128],
-    x[129],
-    x[130],
-    x[131],
-    x[132],
-    x[133],
-    x[134],
-    x[135],
-    x[136],
-    x[137],
-    x[138],
-    x[139],
-    x[140],
-    x[141],
-    x[142],
-    x[143],
-    x[144],
-    x[145],
-    x[146],
-    x[147],
-    x[148],
-    x[149],
-    x[150],
-    x[151],
-    x[152],
-    x[153],
-    x[154],
-    x[155],
-    x[156],
-    x[157],
-    x[158],
-    x[159],
-    x[160],
-    x[161],
-    x[162],
-    x[163],
-    x[164],
-    x[165],
-    x[166],
-    x[167],
-    x[168],
-    x[169],
-    x[170],
-    x[171],
-    x[172],
-    x[173],
-    x[174],
-    x[175],
-    x[176],
-    x[177],
-    x[178],
-    x[179],
-    x[180],
-    x[181],
-    x[182],
-    x[183],
-    x[184],
-    x[185],
-    x[186],
-    x[187],
-    x[188],
-    x[189],
-    x[190],
-    x[191],
-    x[192],
-    x[193],
-    x[194],
-    x[195],
-    x[196],
-    x[197],
-    x[198],
-    x[199],
-    x[200],
-    x[201],
-    x[202],
-    x[203],
-    x[204],
-    x[205],
-    x[206],
-    x[207],
-    x[208],
-    x[209],
-    x[210],
-    x[211],
-    x[212],
-    x[213],
-    x[214],
-    x[215],
-    x[216],
-    x[217],
-    x[218],
-    x[219],
-    x[220],
-    x[221],
-    x[222],
-    x[223],
-    x[224],
-    x[225],
-    x[226],
-    x[227],
-    x[228],
-    x[229],
-    x[230],
-    x[231],
-    x[232],
-    x[233],
-    x[234],
-    x[235],
-    x[236],
-    x[237],
-    x[238],
-    x[239],
-    x[240],
-    x[241],
-    x[242],
-    x[243],
-    x[244],
-    x[245],
-    x[246],
-    x[247],
-    x[248],
-    x[249],
-    x[250],
-    x[251],
-    x[252],
-    x[253],
-    x[254],
-    x[255],
-    x[256],
-    x[257],
-    x[258],
-    x[259],
-    x[260],
-    x[261],
-    x[262],
-    x[263],
-    x[264],
-    x[265],
-    x[266],
-    x[267],
-    x[268],
-    x[269],
-    x[270],
-    x[271],
-    x[272],
-    x[273],
-    x[274],
-    x[275],
-    x[276],
-    x[277],
-    x[278],
-    x[279],
-    x[280],
-    x[281],
-    x[282],
-    x[283],
-    x[284],
-    x[285],
-    x[286],
-    x[287],
-    x[288],
-    x[289],
-    x[290],
-    x[291],
-    x[292],
-    x[293],
-    x[294],
-    x[295],
-    x[296],
-    x[297],
-    x[298],
-    x[299],
-    x[300],
-    x[301],
-    x[302],
-    x[303],
-    x[304],
-    x[305],
-    x[306],
-    x[307],
-    x[308],
-    x[309],
-    x[310],
-    x[311],
-    x[312],
-    x[313],
-    x[314],
-    x[315],
-    x[316],
-    x[317],
-    x[318],
-    x[319],
-    x[320],
-    x[321],
-    x[322],
-    x[323],
-    x[324],
-    x[325],
-    x[326],
-    x[327],
-    x[328],
-    x[329],
-    x[330],
-    x[331],
-    x[332],
-    x[333],
-    x[334],
-    x[335],
-    x[336],
-    x[337],
-    x[338],
-    x[339],
-    x[340],
-    x[341],
-    x[342],
-    x[343],
-    x[344],
-    x[345],
-    x[346],
-    x[347],
-    x[348],
-    x[349],
-    x[350],
-    x[351],
-    x[352],
-    x[353],
-    x[354],
-    x[355],
-    x[356],
-    x[357],
-    x[358],
-    x[359],
-    x[360],
-    x[361],
-    x[362],
-    x[363],
-    x[364],
-    x[365],
-    x[366],
-    x[367],
-    x[368],
-    x[369],
-    x[370],
-    x[371],
-    x[372],
-    x[373],
-    x[374],
-    x[375],
-    x[376],
-    x[377],
-    x[378],
-    x[379],
-    x[380],
-    x[381],
-    x[382],
-    x[383],
-    x[384],
-    x[385],
-    x[386],
-    x[387],
-    x[388],
-    x[389],
-    x[390],
-    x[391],
-    x[392],
-    x[393],
-    x[394],
-    x[395],
-    x[396],
-    x[397],
-    x[398],
-    x[399],
-    x[400],
-    x[401],
-    x[402],
-    x[403],
-    x[404],
-    x[405],
-    x[406],
-    x[407],
-    x[408],
-    x[409],
-    x[410],
-    x[411],
-    x[412],
-    x[413],
-    x[414],
-    x[415],
-    x[416],
-    x[417],
-    x[418],
-    x[419],
-    x[420],
-    x[421],
-    x[422],
-    x[423],
-    x[424],
-    x[425],
-    x[426],
-    x[427],
-    x[428],
-    x[429],
-    x[430],
-    x[431],
-    x[432],
-    x[433],
-    x[434],
-    x[435],
-    x[436],
-    x[437],
-    x[438],
-    x[439],
-    x[440],
-    x[441],
-    x[442],
-    x[443],
-    x[444],
-    x[445],
-    x[446],
-    x[447],
-    x[448],
-    x[449],
-    x[450]
+    p1_0 = x[1]
+    p2_0 = x[2]
+    p3_0 = x[3]
+    p4_0 = x[4]
+    p5_0 = x[5]
+    p6_0 = x[6]
+    p7_0 = x[7]
+    p8_0 = x[8]
+    p9_0 = x[9]
+    p10_0 = x[10]
+    p11_0 = x[11]
+    p12_0 = x[12]
+    p13_0 = x[13]
+    p14_0 = x[14]
+    p15_0 = x[15]
+    p16_0 = x[16]
+    p17_0 = x[17]
+    p18_0 = x[18]
+    p19_0 = x[19]
+    p20_0 = x[20]
+    p21_0 = x[21]
+    p22_0 = x[22]
+    p23_0 = x[23]
+    p1_1 = x[24]
+    p2_1 = x[25]
+    p3_1 = x[26]
+    p4_1 = x[27]
+    p5_1 = x[28]
+    p6_1 = x[29]
+    p7_1 = x[30]
+    p8_1 = x[31]
+    p9_1 = x[32]
+    p10_1 = x[33]
+    p11_1 = x[34]
+    p12_1 = x[35]
+    p13_1 = x[36]
+    p14_1 = x[37]
+    p15_1 = x[38]
+    p16_1 = x[39]
+    p17_1 = x[40]
+    p18_1 = x[41]
+    p19_1 = x[42]
+    p20_1 = x[43]
+    p21_1 = x[44]
+    p22_1 = x[45]
+    p23_1 = x[46]
+    p1_2 = x[47]
+    p2_2 = x[48]
+    p3_2 = x[49]
+    p4_2 = x[50]
+    p5_2 = x[51]
+    p6_2 = x[52]
+    p7_2 = x[53]
+    p8_2 = x[54]
+    p9_2 = x[55]
+    p10_2 = x[56]
+    p11_2 = x[57]
+    p12_2 = x[58]
+    p13_2 = x[59]
+    p14_2 = x[60]
+    p15_2 = x[61]
+    p16_2 = x[62]
+    p17_2 = x[63]
+    p18_2 = x[64]
+    p19_2 = x[65]
+    p20_2 = x[66]
+    p21_2 = x[67]
+    p22_2 = x[68]
+    p23_2 = x[69]
+    p1_3 = x[70]
+    p2_3 = x[71]
+    p3_3 = x[72]
+    p4_3 = x[73]
+    p5_3 = x[74]
+    p6_3 = x[75]
+    p7_3 = x[76]
+    p8_3 = x[77]
+    p9_3 = x[78]
+    p10_3 = x[79]
+    p11_3 = x[80]
+    p12_3 = x[81]
+    p13_3 = x[82]
+    p14_3 = x[83]
+    p15_3 = x[84]
+    p16_3 = x[85]
+    p17_3 = x[86]
+    p18_3 = x[87]
+    p19_3 = x[88]
+    p20_3 = x[89]
+    p21_3 = x[90]
+    p22_3 = x[91]
+    p23_3 = x[92]
+    p1_4 = x[93]
+    p2_4 = x[94]
+    p3_4 = x[95]
+    p4_4 = x[96]
+    p5_4 = x[97]
+    p6_4 = x[98]
+    p7_4 = x[99]
+    p8_4 = x[100]
+    p9_4 = x[101]
+    p10_4 = x[102]
+    p11_4 = x[103]
+    p12_4 = x[104]
+    p13_4 = x[105]
+    p14_4 = x[106]
+    p15_4 = x[107]
+    p16_4 = x[108]
+    p17_4 = x[109]
+    p18_4 = x[110]
+    p19_4 = x[111]
+    p20_4 = x[112]
+    p21_4 = x[113]
+    p22_4 = x[114]
+    p23_4 = x[115]
+    p1_5 = x[116]
+    p2_5 = x[117]
+    p3_5 = x[118]
+    p4_5 = x[119]
+    p5_5 = x[120]
+    p6_5 = x[121]
+    p7_5 = x[122]
+    p8_5 = x[123]
+    p9_5 = x[124]
+    p10_5 = x[125]
+    p11_5 = x[126]
+    p12_5 = x[127]
+    p13_5 = x[128]
+    p14_5 = x[129]
+    p15_5 = x[130]
+    p16_5 = x[131]
+    p17_5 = x[132]
+    p18_5 = x[133]
+    p19_5 = x[134]
+    p20_5 = x[135]
+    p21_5 = x[136]
+    p22_5 = x[137]
+    p23_5 = x[138]
+    p1_6 = x[139]
+    p2_6 = x[140]
+    p3_6 = x[141]
+    p4_6 = x[142]
+    p5_6 = x[143]
+    p6_6 = x[144]
+    p7_6 = x[145]
+    p8_6 = x[146]
+    p9_6 = x[147]
+    p10_6 = x[148]
+    p11_6 = x[149]
+    p12_6 = x[150]
+    p13_6 = x[151]
+    p14_6 = x[152]
+    p15_6 = x[153]
+    p16_6 = x[154]
+    p17_6 = x[155]
+    p18_6 = x[156]
+    p19_6 = x[157]
+    p20_6 = x[158]
+    p21_6 = x[159]
+    p22_6 = x[160]
+    p23_6 = x[161]
+    p1_7 = x[162]
+    p2_7 = x[163]
+    p3_7 = x[164]
+    p4_7 = x[165]
+    p5_7 = x[166]
+    p6_7 = x[167]
+    p7_7 = x[168]
+    p8_7 = x[169]
+    p9_7 = x[170]
+    p10_7 = x[171]
+    p11_7 = x[172]
+    p12_7 = x[173]
+    p13_7 = x[174]
+    p14_7 = x[175]
+    p15_7 = x[176]
+    p16_7 = x[177]
+    p17_7 = x[178]
+    p18_7 = x[179]
+    p19_7 = x[180]
+    p20_7 = x[181]
+    p21_7 = x[182]
+    p22_7 = x[183]
+    p23_7 = x[184]
+    p1_8 = x[185]
+    p2_8 = x[186]
+    p3_8 = x[187]
+    p4_8 = x[188]
+    p5_8 = x[189]
+    p6_8 = x[190]
+    p7_8 = x[191]
+    p8_8 = x[192]
+    p9_8 = x[193]
+    p10_8 = x[194]
+    p11_8 = x[195]
+    p12_8 = x[196]
+    p13_8 = x[197]
+    p14_8 = x[198]
+    p15_8 = x[199]
+    p16_8 = x[200]
+    p17_8 = x[201]
+    p18_8 = x[202]
+    p19_8 = x[203]
+    p20_8 = x[204]
+    p21_8 = x[205]
+    p22_8 = x[206]
+    p23_8 = x[207]
+    q1_2_0 = x[208]
+    q1_17_0 = x[209]
+    q2_3_0 = x[210]
+    q4_5_0 = x[211]
+    q5_6_0 = x[212]
+    q7_8_0 = x[213]
+    q8_9_0 = x[214]
+    q8_10_0 = x[215]
+    q8_11_0 = x[216]
+    q11_12_0 = x[217]
+    q12_13_0 = x[218]
+    q13_14_0 = x[219]
+    q13_15_0 = x[220]
+    q15_16_0 = x[221]
+    q17_18_0 = x[222]
+    q18_19_0 = x[223]
+    q20_21_0 = x[224]
+    q21_22_0 = x[225]
+    q22_23_0 = x[226]
+    q1_2_1 = x[227]
+    q1_17_1 = x[228]
+    q2_3_1 = x[229]
+    q4_5_1 = x[230]
+    q5_6_1 = x[231]
+    q7_8_1 = x[232]
+    q8_9_1 = x[233]
+    q8_10_1 = x[234]
+    q8_11_1 = x[235]
+    q11_12_1 = x[236]
+    q12_13_1 = x[237]
+    q13_14_1 = x[238]
+    q13_15_1 = x[239]
+    q15_16_1 = x[240]
+    q17_18_1 = x[241]
+    q18_19_1 = x[242]
+    q20_21_1 = x[243]
+    q21_22_1 = x[244]
+    q22_23_1 = x[245]
+    q1_2_2 = x[246]
+    q1_17_2 = x[247]
+    q2_3_2 = x[248]
+    q4_5_2 = x[249]
+    q5_6_2 = x[250]
+    q7_8_2 = x[251]
+    q8_9_2 = x[252]
+    q8_10_2 = x[253]
+    q8_11_2 = x[254]
+    q11_12_2 = x[255]
+    q12_13_2 = x[256]
+    q13_14_2 = x[257]
+    q13_15_2 = x[258]
+    q15_16_2 = x[259]
+    q17_18_2 = x[260]
+    q18_19_2 = x[261]
+    q20_21_2 = x[262]
+    q21_22_2 = x[263]
+    q22_23_2 = x[264]
+    q1_2_3 = x[265]
+    q1_17_3 = x[266]
+    q2_3_3 = x[267]
+    q4_5_3 = x[268]
+    q5_6_3 = x[269]
+    q7_8_3 = x[270]
+    q8_9_3 = x[271]
+    q8_10_3 = x[272]
+    q8_11_3 = x[273]
+    q11_12_3 = x[274]
+    q12_13_3 = x[275]
+    q13_14_3 = x[276]
+    q13_15_3 = x[277]
+    q15_16_3 = x[278]
+    q17_18_3 = x[279]
+    q18_19_3 = x[280]
+    q20_21_3 = x[281]
+    q21_22_3 = x[282]
+    q22_23_3 = x[283]
+    q1_2_4 = x[284]
+    q1_17_4 = x[285]
+    q2_3_4 = x[286]
+    q4_5_4 = x[287]
+    q5_6_4 = x[288]
+    q7_8_4 = x[289]
+    q8_9_4 = x[290]
+    q8_10_4 = x[291]
+    q8_11_4 = x[292]
+    q11_12_4 = x[293]
+    q12_13_4 = x[294]
+    q13_14_4 = x[295]
+    q13_15_4 = x[296]
+    q15_16_4 = x[297]
+    q17_18_4 = x[298]
+    q18_19_4 = x[299]
+    q20_21_4 = x[300]
+    q21_22_4 = x[301]
+    q22_23_4 = x[302]
+    q1_2_5 = x[303]
+    q1_17_5 = x[304]
+    q2_3_5 = x[305]
+    q4_5_5 = x[306]
+    q5_6_5 = x[307]
+    q7_8_5 = x[308]
+    q8_9_5 = x[309]
+    q8_10_5 = x[310]
+    q8_11_5 = x[311]
+    q11_12_5 = x[312]
+    q12_13_5 = x[313]
+    q13_14_5 = x[314]
+    q13_15_5 = x[315]
+    q15_16_5 = x[316]
+    q17_18_5 = x[317]
+    q18_19_5 = x[318]
+    q20_21_5 = x[319]
+    q21_22_5 = x[320]
+    q22_23_5 = x[321]
+    q1_2_6 = x[322]
+    q1_17_6 = x[323]
+    q2_3_6 = x[324]
+    q4_5_6 = x[325]
+    q5_6_6 = x[326]
+    q7_8_6 = x[327]
+    q8_9_6 = x[328]
+    q8_10_6 = x[329]
+    q8_11_6 = x[330]
+    q11_12_6 = x[331]
+    q12_13_6 = x[332]
+    q13_14_6 = x[333]
+    q13_15_6 = x[334]
+    q15_16_6 = x[335]
+    q17_18_6 = x[336]
+    q18_19_6 = x[337]
+    q20_21_6 = x[338]
+    q21_22_6 = x[339]
+    q22_23_6 = x[340]
+    q1_2_7 = x[341]
+    q1_17_7 = x[342]
+    q2_3_7 = x[343]
+    q4_5_7 = x[344]
+    q5_6_7 = x[345]
+    q7_8_7 = x[346]
+    q8_9_7 = x[347]
+    q8_10_7 = x[348]
+    q8_11_7 = x[349]
+    q11_12_7 = x[350]
+    q12_13_7 = x[351]
+    q13_14_7 = x[352]
+    q13_15_7 = x[353]
+    q15_16_7 = x[354]
+    q17_18_7 = x[355]
+    q18_19_7 = x[356]
+    q20_21_7 = x[357]
+    q21_22_7 = x[358]
+    q22_23_7 = x[359]
+    q1_2_8 = x[360]
+    q1_17_8 = x[361]
+    q2_3_8 = x[362]
+    q4_5_8 = x[363]
+    q5_6_8 = x[364]
+    q7_8_8 = x[365]
+    q8_9_8 = x[366]
+    q8_10_8 = x[367]
+    q8_11_8 = x[368]
+    q11_12_8 = x[369]
+    q12_13_8 = x[370]
+    q13_14_8 = x[371]
+    q13_15_8 = x[372]
+    q15_16_8 = x[373]
+    q17_18_8 = x[374]
+    q18_19_8 = x[375]
+    q20_21_8 = x[376]
+    q21_22_8 = x[377]
+    q22_23_8 = x[378]
+    f3_4_1 = x[379]
+    f5_7_1 = x[380]
+    f19_20_1 = x[381]
+    r3_4_1 = x[382]
+    r5_7_1 = x[383]
+    r19_20_1 = x[384]
+    f3_4_2 = x[385]
+    f5_7_2 = x[386]
+    f19_20_2 = x[387]
+    r3_4_2 = x[388]
+    r5_7_2 = x[389]
+    r19_20_2 = x[390]
+    f3_4_3 = x[391]
+    f5_7_3 = x[392]
+    f19_20_3 = x[393]
+    r3_4_3 = x[394]
+    r5_7_3 = x[395]
+    r19_20_3 = x[396]
+    f3_4_4 = x[397]
+    f5_7_4 = x[398]
+    f19_20_4 = x[399]
+    r3_4_4 = x[400]
+    r5_7_4 = x[401]
+    r19_20_4 = x[402]
+    f3_4_5 = x[403]
+    f5_7_5 = x[404]
+    f19_20_5 = x[405]
+    r3_4_5 = x[406]
+    r5_7_5 = x[407]
+    r19_20_5 = x[408]
+    f3_4_6 = x[409]
+    f5_7_6 = x[410]
+    f19_20_6 = x[411]
+    r3_4_6 = x[412]
+    r5_7_6 = x[413]
+    r19_20_6 = x[414]
+    f3_4_7 = x[415]
+    f5_7_7 = x[416]
+    f19_20_7 = x[417]
+    r3_4_7 = x[418]
+    r5_7_7 = x[419]
+    r19_20_7 = x[420]
+    f3_4_8 = x[421]
+    f5_7_8 = x[422]
+    f19_20_8 = x[423]
+    r3_4_8 = x[424]
+    r5_7_8 = x[425]
+    r19_20_8 = x[426]
+    in1_1 = x[427]
+    out16_1 = x[428]
+    out23_1 = x[429]
+    in1_2 = x[430]
+    out16_2 = x[431]
+    out23_2 = x[432]
+    in1_3 = x[433]
+    out16_3 = x[434]
+    out23_3 = x[435]
+    in1_4 = x[436]
+    out16_4 = x[437]
+    out23_4 = x[438]
+    in1_5 = x[439]
+    out16_5 = x[440]
+    out23_5 = x[441]
+    in1_6 = x[442]
+    out16_6 = x[443]
+    out23_6 = x[444]
+    in1_7 = x[445]
+    out16_7 = x[446]
+    out23_7 = x[447]
+    in1_8 = x[448]
+    out16_8 = x[449]
+    out23_8 = x[450]
     cx[1] =
       p1_1 / ((1) + (1) * p1_1) - p1_0 / ((1) + (1) * p1_0) - T(0.75) * q1_17_1 - T(0.75) * q1_2_1 +
       in1_1 - T(0.25) * q1_17_0 - T(0.25) * q1_2_0

From e95daf92ac1754e7009f775720c4352c8b76295b Mon Sep 17 00:00:00 2001
From: Guillaume Dalle <22795598+gdalle@users.noreply.github.com>
Date: Fri, 14 Jun 2024 12:08:11 +0200
Subject: [PATCH 2/3] Compress

---
 src/ADNLPProblems/britgas.jl | 2464 ++++++++--------------------------
 1 file changed, 597 insertions(+), 1867 deletions(-)

diff --git a/src/ADNLPProblems/britgas.jl b/src/ADNLPProblems/britgas.jl
index 5857c9b1..82452d1d 100644
--- a/src/ADNLPProblems/britgas.jl
+++ b/src/ADNLPProblems/britgas.jl
@@ -1,15 +1,17 @@
 export britgas
 
+_britgas_obj(fi, ri) = fi * (abs(ri)^(22 // 100) - 1)
+
 function britgas(; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) where {T}
   hours = T(8)
   nodes = T(23)
-  theta = T(0.75)
+  θ = T(0.75)
   a = T(1.0)
   b = T(1.0)
-  alpha = T(1.8539)
+  α = T(1.8539)
   dt = T(1.0)
   one = T(1.0)
-  omega = T(1.0) + (-1.0 * (T(0.75)))
+  omega = T(1.0) + (-1.0 * T(0.75))
   s = -1 + (T(8))
   crmax = 10
   k = T(1.0)
@@ -19,481 +21,77 @@ function britgas(; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) wh
   vddt = (T(1.0)) * ((T(1.0)) / (T(1.0)))
   h = T(0.01)
 
+  # newly introduced
+
+  γ = T(0.5)
+
+  # q variables are indexed with some pairs from 1:23 × 1:23
+  q_ind = [
+    (1, 2),
+    (1, 17),
+    (2, 3),
+    (4, 5),
+    (5, 6),
+    (7, 8),
+    (8, 9),
+    (8, 10),
+    (8, 11),
+    (11, 12),
+    (12, 13),
+    (13, 14),
+    (13, 15),
+    (15, 16),
+    (17, 18),
+    (18, 19),
+    (20, 21),
+    (21, 22),
+    (22, 23),
+  ]
+  q_outneighbors = [i => Int[] for i = 1:23]
+  q_inneighbors = [i => Int[] for i = 1:23]
+  for (i, j) in q_ind
+    push!(q_outneighbors[i], j)
+    push!(q_inneighbors[j], i)
+  end
+  q_neighbors = [vcat(q_inneighbors[i], q_outneighbors[i]) for i in 1:23]
+
+  # f and r variables are indexed with some pairs from 1:23 × 1:23
+  fr_ind = [(3, 4), (5, 7), (19, 20)]
+  fr_outneighbors = [i => Int[] for i = 1:23]
+  fr_inneighbors = [i => Int[] for i = 1:23]
+  for (i, j) in fr_ind
+    push!(fr_outneighbors[i], j)
+    push!(fr_inneighbors[j], i)
+  end
+  fr_neighbors = [vcat(fr_inneighbors[i], outneighbors[i]) for i in 1:23]
+
+  # in and out variables are indexed with some indices from 1:23
+  in_ind = [1]
+  out_ind = [16, 23]
+
   function f(x)
-    p1_0 = x[1]
-    p2_0 = x[2]
-    p3_0 = x[3]
-    p4_0 = x[4]
-    p5_0 = x[5]
-    p6_0 = x[6]
-    p7_0 = x[7]
-    p8_0 = x[8]
-    p9_0 = x[9]
-    p10_0 = x[10]
-    p11_0 = x[11]
-    p12_0 = x[12]
-    p13_0 = x[13]
-    p14_0 = x[14]
-    p15_0 = x[15]
-    p16_0 = x[16]
-    p17_0 = x[17]
-    p18_0 = x[18]
-    p19_0 = x[19]
-    p20_0 = x[20]
-    p21_0 = x[21]
-    p22_0 = x[22]
-    p23_0 = x[23]
-    p1_1 = x[24]
-    p2_1 = x[25]
-    p3_1 = x[26]
-    p4_1 = x[27]
-    p5_1 = x[28]
-    p6_1 = x[29]
-    p7_1 = x[30]
-    p8_1 = x[31]
-    p9_1 = x[32]
-    p10_1 = x[33]
-    p11_1 = x[34]
-    p12_1 = x[35]
-    p13_1 = x[36]
-    p14_1 = x[37]
-    p15_1 = x[38]
-    p16_1 = x[39]
-    p17_1 = x[40]
-    p18_1 = x[41]
-    p19_1 = x[42]
-    p20_1 = x[43]
-    p21_1 = x[44]
-    p22_1 = x[45]
-    p23_1 = x[46]
-    p1_2 = x[47]
-    p2_2 = x[48]
-    p3_2 = x[49]
-    p4_2 = x[50]
-    p5_2 = x[51]
-    p6_2 = x[52]
-    p7_2 = x[53]
-    p8_2 = x[54]
-    p9_2 = x[55]
-    p10_2 = x[56]
-    p11_2 = x[57]
-    p12_2 = x[58]
-    p13_2 = x[59]
-    p14_2 = x[60]
-    p15_2 = x[61]
-    p16_2 = x[62]
-    p17_2 = x[63]
-    p18_2 = x[64]
-    p19_2 = x[65]
-    p20_2 = x[66]
-    p21_2 = x[67]
-    p22_2 = x[68]
-    p23_2 = x[69]
-    p1_3 = x[70]
-    p2_3 = x[71]
-    p3_3 = x[72]
-    p4_3 = x[73]
-    p5_3 = x[74]
-    p6_3 = x[75]
-    p7_3 = x[76]
-    p8_3 = x[77]
-    p9_3 = x[78]
-    p10_3 = x[79]
-    p11_3 = x[80]
-    p12_3 = x[81]
-    p13_3 = x[82]
-    p14_3 = x[83]
-    p15_3 = x[84]
-    p16_3 = x[85]
-    p17_3 = x[86]
-    p18_3 = x[87]
-    p19_3 = x[88]
-    p20_3 = x[89]
-    p21_3 = x[90]
-    p22_3 = x[91]
-    p23_3 = x[92]
-    p1_4 = x[93]
-    p2_4 = x[94]
-    p3_4 = x[95]
-    p4_4 = x[96]
-    p5_4 = x[97]
-    p6_4 = x[98]
-    p7_4 = x[99]
-    p8_4 = x[100]
-    p9_4 = x[101]
-    p10_4 = x[102]
-    p11_4 = x[103]
-    p12_4 = x[104]
-    p13_4 = x[105]
-    p14_4 = x[106]
-    p15_4 = x[107]
-    p16_4 = x[108]
-    p17_4 = x[109]
-    p18_4 = x[110]
-    p19_4 = x[111]
-    p20_4 = x[112]
-    p21_4 = x[113]
-    p22_4 = x[114]
-    p23_4 = x[115]
-    p1_5 = x[116]
-    p2_5 = x[117]
-    p3_5 = x[118]
-    p4_5 = x[119]
-    p5_5 = x[120]
-    p6_5 = x[121]
-    p7_5 = x[122]
-    p8_5 = x[123]
-    p9_5 = x[124]
-    p10_5 = x[125]
-    p11_5 = x[126]
-    p12_5 = x[127]
-    p13_5 = x[128]
-    p14_5 = x[129]
-    p15_5 = x[130]
-    p16_5 = x[131]
-    p17_5 = x[132]
-    p18_5 = x[133]
-    p19_5 = x[134]
-    p20_5 = x[135]
-    p21_5 = x[136]
-    p22_5 = x[137]
-    p23_5 = x[138]
-    p1_6 = x[139]
-    p2_6 = x[140]
-    p3_6 = x[141]
-    p4_6 = x[142]
-    p5_6 = x[143]
-    p6_6 = x[144]
-    p7_6 = x[145]
-    p8_6 = x[146]
-    p9_6 = x[147]
-    p10_6 = x[148]
-    p11_6 = x[149]
-    p12_6 = x[150]
-    p13_6 = x[151]
-    p14_6 = x[152]
-    p15_6 = x[153]
-    p16_6 = x[154]
-    p17_6 = x[155]
-    p18_6 = x[156]
-    p19_6 = x[157]
-    p20_6 = x[158]
-    p21_6 = x[159]
-    p22_6 = x[160]
-    p23_6 = x[161]
-    p1_7 = x[162]
-    p2_7 = x[163]
-    p3_7 = x[164]
-    p4_7 = x[165]
-    p5_7 = x[166]
-    p6_7 = x[167]
-    p7_7 = x[168]
-    p8_7 = x[169]
-    p9_7 = x[170]
-    p10_7 = x[171]
-    p11_7 = x[172]
-    p12_7 = x[173]
-    p13_7 = x[174]
-    p14_7 = x[175]
-    p15_7 = x[176]
-    p16_7 = x[177]
-    p17_7 = x[178]
-    p18_7 = x[179]
-    p19_7 = x[180]
-    p20_7 = x[181]
-    p21_7 = x[182]
-    p22_7 = x[183]
-    p23_7 = x[184]
-    p1_8 = x[185]
-    p2_8 = x[186]
-    p3_8 = x[187]
-    p4_8 = x[188]
-    p5_8 = x[189]
-    p6_8 = x[190]
-    p7_8 = x[191]
-    p8_8 = x[192]
-    p9_8 = x[193]
-    p10_8 = x[194]
-    p11_8 = x[195]
-    p12_8 = x[196]
-    p13_8 = x[197]
-    p14_8 = x[198]
-    p15_8 = x[199]
-    p16_8 = x[200]
-    p17_8 = x[201]
-    p18_8 = x[202]
-    p19_8 = x[203]
-    p20_8 = x[204]
-    p21_8 = x[205]
-    p22_8 = x[206]
-    p23_8 = x[207]
-    q1_2_0 = x[208]
-    q1_17_0 = x[209]
-    q2_3_0 = x[210]
-    q4_5_0 = x[211]
-    q5_6_0 = x[212]
-    q7_8_0 = x[213]
-    q8_9_0 = x[214]
-    q8_10_0 = x[215]
-    q8_11_0 = x[216]
-    q11_12_0 = x[217]
-    q12_13_0 = x[218]
-    q13_14_0 = x[219]
-    q13_15_0 = x[220]
-    q15_16_0 = x[221]
-    q17_18_0 = x[222]
-    q18_19_0 = x[223]
-    q20_21_0 = x[224]
-    q21_22_0 = x[225]
-    q22_23_0 = x[226]
-    q1_2_1 = x[227]
-    q1_17_1 = x[228]
-    q2_3_1 = x[229]
-    q4_5_1 = x[230]
-    q5_6_1 = x[231]
-    q7_8_1 = x[232]
-    q8_9_1 = x[233]
-    q8_10_1 = x[234]
-    q8_11_1 = x[235]
-    q11_12_1 = x[236]
-    q12_13_1 = x[237]
-    q13_14_1 = x[238]
-    q13_15_1 = x[239]
-    q15_16_1 = x[240]
-    q17_18_1 = x[241]
-    q18_19_1 = x[242]
-    q20_21_1 = x[243]
-    q21_22_1 = x[244]
-    q22_23_1 = x[245]
-    q1_2_2 = x[246]
-    q1_17_2 = x[247]
-    q2_3_2 = x[248]
-    q4_5_2 = x[249]
-    q5_6_2 = x[250]
-    q7_8_2 = x[251]
-    q8_9_2 = x[252]
-    q8_10_2 = x[253]
-    q8_11_2 = x[254]
-    q11_12_2 = x[255]
-    q12_13_2 = x[256]
-    q13_14_2 = x[257]
-    q13_15_2 = x[258]
-    q15_16_2 = x[259]
-    q17_18_2 = x[260]
-    q18_19_2 = x[261]
-    q20_21_2 = x[262]
-    q21_22_2 = x[263]
-    q22_23_2 = x[264]
-    q1_2_3 = x[265]
-    q1_17_3 = x[266]
-    q2_3_3 = x[267]
-    q4_5_3 = x[268]
-    q5_6_3 = x[269]
-    q7_8_3 = x[270]
-    q8_9_3 = x[271]
-    q8_10_3 = x[272]
-    q8_11_3 = x[273]
-    q11_12_3 = x[274]
-    q12_13_3 = x[275]
-    q13_14_3 = x[276]
-    q13_15_3 = x[277]
-    q15_16_3 = x[278]
-    q17_18_3 = x[279]
-    q18_19_3 = x[280]
-    q20_21_3 = x[281]
-    q21_22_3 = x[282]
-    q22_23_3 = x[283]
-    q1_2_4 = x[284]
-    q1_17_4 = x[285]
-    q2_3_4 = x[286]
-    q4_5_4 = x[287]
-    q5_6_4 = x[288]
-    q7_8_4 = x[289]
-    q8_9_4 = x[290]
-    q8_10_4 = x[291]
-    q8_11_4 = x[292]
-    q11_12_4 = x[293]
-    q12_13_4 = x[294]
-    q13_14_4 = x[295]
-    q13_15_4 = x[296]
-    q15_16_4 = x[297]
-    q17_18_4 = x[298]
-    q18_19_4 = x[299]
-    q20_21_4 = x[300]
-    q21_22_4 = x[301]
-    q22_23_4 = x[302]
-    q1_2_5 = x[303]
-    q1_17_5 = x[304]
-    q2_3_5 = x[305]
-    q4_5_5 = x[306]
-    q5_6_5 = x[307]
-    q7_8_5 = x[308]
-    q8_9_5 = x[309]
-    q8_10_5 = x[310]
-    q8_11_5 = x[311]
-    q11_12_5 = x[312]
-    q12_13_5 = x[313]
-    q13_14_5 = x[314]
-    q13_15_5 = x[315]
-    q15_16_5 = x[316]
-    q17_18_5 = x[317]
-    q18_19_5 = x[318]
-    q20_21_5 = x[319]
-    q21_22_5 = x[320]
-    q22_23_5 = x[321]
-    q1_2_6 = x[322]
-    q1_17_6 = x[323]
-    q2_3_6 = x[324]
-    q4_5_6 = x[325]
-    q5_6_6 = x[326]
-    q7_8_6 = x[327]
-    q8_9_6 = x[328]
-    q8_10_6 = x[329]
-    q8_11_6 = x[330]
-    q11_12_6 = x[331]
-    q12_13_6 = x[332]
-    q13_14_6 = x[333]
-    q13_15_6 = x[334]
-    q15_16_6 = x[335]
-    q17_18_6 = x[336]
-    q18_19_6 = x[337]
-    q20_21_6 = x[338]
-    q21_22_6 = x[339]
-    q22_23_6 = x[340]
-    q1_2_7 = x[341]
-    q1_17_7 = x[342]
-    q2_3_7 = x[343]
-    q4_5_7 = x[344]
-    q5_6_7 = x[345]
-    q7_8_7 = x[346]
-    q8_9_7 = x[347]
-    q8_10_7 = x[348]
-    q8_11_7 = x[349]
-    q11_12_7 = x[350]
-    q12_13_7 = x[351]
-    q13_14_7 = x[352]
-    q13_15_7 = x[353]
-    q15_16_7 = x[354]
-    q17_18_7 = x[355]
-    q18_19_7 = x[356]
-    q20_21_7 = x[357]
-    q21_22_7 = x[358]
-    q22_23_7 = x[359]
-    q1_2_8 = x[360]
-    q1_17_8 = x[361]
-    q2_3_8 = x[362]
-    q4_5_8 = x[363]
-    q5_6_8 = x[364]
-    q7_8_8 = x[365]
-    q8_9_8 = x[366]
-    q8_10_8 = x[367]
-    q8_11_8 = x[368]
-    q11_12_8 = x[369]
-    q12_13_8 = x[370]
-    q13_14_8 = x[371]
-    q13_15_8 = x[372]
-    q15_16_8 = x[373]
-    q17_18_8 = x[374]
-    q18_19_8 = x[375]
-    q20_21_8 = x[376]
-    q21_22_8 = x[377]
-    q22_23_8 = x[378]
-    f3_4_1 = x[379]
-    f5_7_1 = x[380]
-    f19_20_1 = x[381]
-    r3_4_1 = x[382]
-    r5_7_1 = x[383]
-    r19_20_1 = x[384]
-    f3_4_2 = x[385]
-    f5_7_2 = x[386]
-    f19_20_2 = x[387]
-    r3_4_2 = x[388]
-    r5_7_2 = x[389]
-    r19_20_2 = x[390]
-    f3_4_3 = x[391]
-    f5_7_3 = x[392]
-    f19_20_3 = x[393]
-    r3_4_3 = x[394]
-    r5_7_3 = x[395]
-    r19_20_3 = x[396]
-    f3_4_4 = x[397]
-    f5_7_4 = x[398]
-    f19_20_4 = x[399]
-    r3_4_4 = x[400]
-    r5_7_4 = x[401]
-    r19_20_4 = x[402]
-    f3_4_5 = x[403]
-    f5_7_5 = x[404]
-    f19_20_5 = x[405]
-    r3_4_5 = x[406]
-    r5_7_5 = x[407]
-    r19_20_5 = x[408]
-    f3_4_6 = x[409]
-    f5_7_6 = x[410]
-    f19_20_6 = x[411]
-    r3_4_6 = x[412]
-    r5_7_6 = x[413]
-    r19_20_6 = x[414]
-    f3_4_7 = x[415]
-    f5_7_7 = x[416]
-    f19_20_7 = x[417]
-    r3_4_7 = x[418]
-    r5_7_7 = x[419]
-    r19_20_7 = x[420]
-    f3_4_8 = x[421]
-    f5_7_8 = x[422]
-    f19_20_8 = x[423]
-    r3_4_8 = x[424]
-    r5_7_8 = x[425]
-    r19_20_8 = x[426]
-    in1_1 = x[427]
-    out16_1 = x[428]
-    out23_1 = x[429]
-    in1_2 = x[430]
-    out16_2 = x[431]
-    out23_2 = x[432]
-    in1_3 = x[433]
-    out16_3 = x[434]
-    out23_3 = x[435]
-    in1_4 = x[436]
-    out16_4 = x[437]
-    out23_4 = x[438]
-    in1_5 = x[439]
-    out16_5 = x[440]
-    out23_5 = x[441]
-    in1_6 = x[442]
-    out16_6 = x[443]
-    out23_6 = x[444]
-    in1_7 = x[445]
-    out16_7 = x[446]
-    out23_7 = x[447]
-    in1_8 = x[448]
-    out16_8 = x[449]
-    out23_8 = x[450]
-    return f3_4_1 * ((abs(r3_4_1)^(22 // 100)) - 1) +
-           f5_7_1 * ((abs(r5_7_1)^(22 // 100)) - 1) +
-           f19_20_1 * ((abs(r19_20_1)^(22 // 100)) - 1) +
-           f3_4_2 * ((abs(r3_4_2)^(22 // 100)) - 1) +
-           f5_7_2 * ((abs(r5_7_2)^(22 // 100)) - 1) +
-           f19_20_2 * ((abs(r19_20_2)^(22 // 100)) - 1) +
-           f3_4_3 * ((abs(r3_4_3)^(22 // 100)) - 1) +
-           f5_7_3 * ((abs(r5_7_3)^(22 // 100)) - 1) +
-           f19_20_3 * ((abs(r19_20_3)^(22 // 100)) - 1) +
-           f3_4_4 * ((abs(r3_4_4)^(22 // 100)) - 1) +
-           f5_7_4 * ((abs(r5_7_4)^(22 // 100)) - 1) +
-           f19_20_4 * ((abs(r19_20_4)^(22 // 100)) - 1) +
-           f3_4_5 * ((abs(r3_4_5)^(22 // 100)) - 1) +
-           f5_7_5 * ((abs(r5_7_5)^(22 // 100)) - 1) +
-           f19_20_5 * ((abs(r19_20_5)^(22 // 100)) - 1) +
-           f3_4_6 * ((abs(r3_4_6)^(22 // 100)) - 1) +
-           f5_7_6 * ((abs(r5_7_6)^(22 // 100)) - 1) +
-           f19_20_6 * ((abs(r19_20_6)^(22 // 100)) - 1) +
-           f3_4_7 * ((abs(r3_4_7)^(22 // 100)) - 1) +
-           f5_7_7 * ((abs(r5_7_7)^(22 // 100)) - 1) +
-           f19_20_7 * ((abs(r19_20_7)^(22 // 100)) - 1) +
-           f3_4_8 * ((abs(r3_4_8)^(22 // 100)) - 1) +
-           f5_7_8 * ((abs(r5_7_8)^(22 // 100)) - 1) +
-           f19_20_8 * ((abs(r19_20_8)^(22 // 100)) - 1)
+    f_1 = view(x, 379:381)
+    r_1 = view(x, 382:384)
+    f_2 = view(x, 385:387)
+    r_2 = view(x, 388:390)
+    f_3 = view(x, 391:393)
+    r_3 = view(x, 394:396)
+    f_4 = view(x, 397:399)
+    r_4 = view(x, 400:402)
+    f_5 = view(x, 403:405)
+    r_5 = view(x, 406:408)
+    f_6 = view(x, 409:411)
+    r_6 = view(x, 412:414)
+    f_7 = view(x, 415:417)
+    r_7 = view(x, 418:420)
+    f_8 = view(x, 421:423)
+    r_8 = view(x, 424:426)
+
+    f_ = [f_1, f_2, f_3, f_4, f_5, f_6, f_7, f_8]
+    r_ = [r_1, r_2, r_3, r_4, r_5, r_6, r_7, r_8]
+
+    o = sum(mapreduce(_britgas_obj, +, f_[t], r_[t]) for t = 1:8)
+    return o
   end
   x0 = T[
     1.0,
@@ -948,1544 +546,676 @@ function britgas(; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) wh
     1.0,
   ]
   function c!(cx, x)
-    p1_0 = x[1]
-    p2_0 = x[2]
-    p3_0 = x[3]
-    p4_0 = x[4]
-    p5_0 = x[5]
-    p6_0 = x[6]
-    p7_0 = x[7]
-    p8_0 = x[8]
-    p9_0 = x[9]
-    p10_0 = x[10]
-    p11_0 = x[11]
-    p12_0 = x[12]
-    p13_0 = x[13]
-    p14_0 = x[14]
-    p15_0 = x[15]
-    p16_0 = x[16]
-    p17_0 = x[17]
-    p18_0 = x[18]
-    p19_0 = x[19]
-    p20_0 = x[20]
-    p21_0 = x[21]
-    p22_0 = x[22]
-    p23_0 = x[23]
-    p1_1 = x[24]
-    p2_1 = x[25]
-    p3_1 = x[26]
-    p4_1 = x[27]
-    p5_1 = x[28]
-    p6_1 = x[29]
-    p7_1 = x[30]
-    p8_1 = x[31]
-    p9_1 = x[32]
-    p10_1 = x[33]
-    p11_1 = x[34]
-    p12_1 = x[35]
-    p13_1 = x[36]
-    p14_1 = x[37]
-    p15_1 = x[38]
-    p16_1 = x[39]
-    p17_1 = x[40]
-    p18_1 = x[41]
-    p19_1 = x[42]
-    p20_1 = x[43]
-    p21_1 = x[44]
-    p22_1 = x[45]
-    p23_1 = x[46]
-    p1_2 = x[47]
-    p2_2 = x[48]
-    p3_2 = x[49]
-    p4_2 = x[50]
-    p5_2 = x[51]
-    p6_2 = x[52]
-    p7_2 = x[53]
-    p8_2 = x[54]
-    p9_2 = x[55]
-    p10_2 = x[56]
-    p11_2 = x[57]
-    p12_2 = x[58]
-    p13_2 = x[59]
-    p14_2 = x[60]
-    p15_2 = x[61]
-    p16_2 = x[62]
-    p17_2 = x[63]
-    p18_2 = x[64]
-    p19_2 = x[65]
-    p20_2 = x[66]
-    p21_2 = x[67]
-    p22_2 = x[68]
-    p23_2 = x[69]
-    p1_3 = x[70]
-    p2_3 = x[71]
-    p3_3 = x[72]
-    p4_3 = x[73]
-    p5_3 = x[74]
-    p6_3 = x[75]
-    p7_3 = x[76]
-    p8_3 = x[77]
-    p9_3 = x[78]
-    p10_3 = x[79]
-    p11_3 = x[80]
-    p12_3 = x[81]
-    p13_3 = x[82]
-    p14_3 = x[83]
-    p15_3 = x[84]
-    p16_3 = x[85]
-    p17_3 = x[86]
-    p18_3 = x[87]
-    p19_3 = x[88]
-    p20_3 = x[89]
-    p21_3 = x[90]
-    p22_3 = x[91]
-    p23_3 = x[92]
-    p1_4 = x[93]
-    p2_4 = x[94]
-    p3_4 = x[95]
-    p4_4 = x[96]
-    p5_4 = x[97]
-    p6_4 = x[98]
-    p7_4 = x[99]
-    p8_4 = x[100]
-    p9_4 = x[101]
-    p10_4 = x[102]
-    p11_4 = x[103]
-    p12_4 = x[104]
-    p13_4 = x[105]
-    p14_4 = x[106]
-    p15_4 = x[107]
-    p16_4 = x[108]
-    p17_4 = x[109]
-    p18_4 = x[110]
-    p19_4 = x[111]
-    p20_4 = x[112]
-    p21_4 = x[113]
-    p22_4 = x[114]
-    p23_4 = x[115]
-    p1_5 = x[116]
-    p2_5 = x[117]
-    p3_5 = x[118]
-    p4_5 = x[119]
-    p5_5 = x[120]
-    p6_5 = x[121]
-    p7_5 = x[122]
-    p8_5 = x[123]
-    p9_5 = x[124]
-    p10_5 = x[125]
-    p11_5 = x[126]
-    p12_5 = x[127]
-    p13_5 = x[128]
-    p14_5 = x[129]
-    p15_5 = x[130]
-    p16_5 = x[131]
-    p17_5 = x[132]
-    p18_5 = x[133]
-    p19_5 = x[134]
-    p20_5 = x[135]
-    p21_5 = x[136]
-    p22_5 = x[137]
-    p23_5 = x[138]
-    p1_6 = x[139]
-    p2_6 = x[140]
-    p3_6 = x[141]
-    p4_6 = x[142]
-    p5_6 = x[143]
-    p6_6 = x[144]
-    p7_6 = x[145]
-    p8_6 = x[146]
-    p9_6 = x[147]
-    p10_6 = x[148]
-    p11_6 = x[149]
-    p12_6 = x[150]
-    p13_6 = x[151]
-    p14_6 = x[152]
-    p15_6 = x[153]
-    p16_6 = x[154]
-    p17_6 = x[155]
-    p18_6 = x[156]
-    p19_6 = x[157]
-    p20_6 = x[158]
-    p21_6 = x[159]
-    p22_6 = x[160]
-    p23_6 = x[161]
-    p1_7 = x[162]
-    p2_7 = x[163]
-    p3_7 = x[164]
-    p4_7 = x[165]
-    p5_7 = x[166]
-    p6_7 = x[167]
-    p7_7 = x[168]
-    p8_7 = x[169]
-    p9_7 = x[170]
-    p10_7 = x[171]
-    p11_7 = x[172]
-    p12_7 = x[173]
-    p13_7 = x[174]
-    p14_7 = x[175]
-    p15_7 = x[176]
-    p16_7 = x[177]
-    p17_7 = x[178]
-    p18_7 = x[179]
-    p19_7 = x[180]
-    p20_7 = x[181]
-    p21_7 = x[182]
-    p22_7 = x[183]
-    p23_7 = x[184]
-    p1_8 = x[185]
-    p2_8 = x[186]
-    p3_8 = x[187]
-    p4_8 = x[188]
-    p5_8 = x[189]
-    p6_8 = x[190]
-    p7_8 = x[191]
-    p8_8 = x[192]
-    p9_8 = x[193]
-    p10_8 = x[194]
-    p11_8 = x[195]
-    p12_8 = x[196]
-    p13_8 = x[197]
-    p14_8 = x[198]
-    p15_8 = x[199]
-    p16_8 = x[200]
-    p17_8 = x[201]
-    p18_8 = x[202]
-    p19_8 = x[203]
-    p20_8 = x[204]
-    p21_8 = x[205]
-    p22_8 = x[206]
-    p23_8 = x[207]
-    q1_2_0 = x[208]
-    q1_17_0 = x[209]
-    q2_3_0 = x[210]
-    q4_5_0 = x[211]
-    q5_6_0 = x[212]
-    q7_8_0 = x[213]
-    q8_9_0 = x[214]
-    q8_10_0 = x[215]
-    q8_11_0 = x[216]
-    q11_12_0 = x[217]
-    q12_13_0 = x[218]
-    q13_14_0 = x[219]
-    q13_15_0 = x[220]
-    q15_16_0 = x[221]
-    q17_18_0 = x[222]
-    q18_19_0 = x[223]
-    q20_21_0 = x[224]
-    q21_22_0 = x[225]
-    q22_23_0 = x[226]
-    q1_2_1 = x[227]
-    q1_17_1 = x[228]
-    q2_3_1 = x[229]
-    q4_5_1 = x[230]
-    q5_6_1 = x[231]
-    q7_8_1 = x[232]
-    q8_9_1 = x[233]
-    q8_10_1 = x[234]
-    q8_11_1 = x[235]
-    q11_12_1 = x[236]
-    q12_13_1 = x[237]
-    q13_14_1 = x[238]
-    q13_15_1 = x[239]
-    q15_16_1 = x[240]
-    q17_18_1 = x[241]
-    q18_19_1 = x[242]
-    q20_21_1 = x[243]
-    q21_22_1 = x[244]
-    q22_23_1 = x[245]
-    q1_2_2 = x[246]
-    q1_17_2 = x[247]
-    q2_3_2 = x[248]
-    q4_5_2 = x[249]
-    q5_6_2 = x[250]
-    q7_8_2 = x[251]
-    q8_9_2 = x[252]
-    q8_10_2 = x[253]
-    q8_11_2 = x[254]
-    q11_12_2 = x[255]
-    q12_13_2 = x[256]
-    q13_14_2 = x[257]
-    q13_15_2 = x[258]
-    q15_16_2 = x[259]
-    q17_18_2 = x[260]
-    q18_19_2 = x[261]
-    q20_21_2 = x[262]
-    q21_22_2 = x[263]
-    q22_23_2 = x[264]
-    q1_2_3 = x[265]
-    q1_17_3 = x[266]
-    q2_3_3 = x[267]
-    q4_5_3 = x[268]
-    q5_6_3 = x[269]
-    q7_8_3 = x[270]
-    q8_9_3 = x[271]
-    q8_10_3 = x[272]
-    q8_11_3 = x[273]
-    q11_12_3 = x[274]
-    q12_13_3 = x[275]
-    q13_14_3 = x[276]
-    q13_15_3 = x[277]
-    q15_16_3 = x[278]
-    q17_18_3 = x[279]
-    q18_19_3 = x[280]
-    q20_21_3 = x[281]
-    q21_22_3 = x[282]
-    q22_23_3 = x[283]
-    q1_2_4 = x[284]
-    q1_17_4 = x[285]
-    q2_3_4 = x[286]
-    q4_5_4 = x[287]
-    q5_6_4 = x[288]
-    q7_8_4 = x[289]
-    q8_9_4 = x[290]
-    q8_10_4 = x[291]
-    q8_11_4 = x[292]
-    q11_12_4 = x[293]
-    q12_13_4 = x[294]
-    q13_14_4 = x[295]
-    q13_15_4 = x[296]
-    q15_16_4 = x[297]
-    q17_18_4 = x[298]
-    q18_19_4 = x[299]
-    q20_21_4 = x[300]
-    q21_22_4 = x[301]
-    q22_23_4 = x[302]
-    q1_2_5 = x[303]
-    q1_17_5 = x[304]
-    q2_3_5 = x[305]
-    q4_5_5 = x[306]
-    q5_6_5 = x[307]
-    q7_8_5 = x[308]
-    q8_9_5 = x[309]
-    q8_10_5 = x[310]
-    q8_11_5 = x[311]
-    q11_12_5 = x[312]
-    q12_13_5 = x[313]
-    q13_14_5 = x[314]
-    q13_15_5 = x[315]
-    q15_16_5 = x[316]
-    q17_18_5 = x[317]
-    q18_19_5 = x[318]
-    q20_21_5 = x[319]
-    q21_22_5 = x[320]
-    q22_23_5 = x[321]
-    q1_2_6 = x[322]
-    q1_17_6 = x[323]
-    q2_3_6 = x[324]
-    q4_5_6 = x[325]
-    q5_6_6 = x[326]
-    q7_8_6 = x[327]
-    q8_9_6 = x[328]
-    q8_10_6 = x[329]
-    q8_11_6 = x[330]
-    q11_12_6 = x[331]
-    q12_13_6 = x[332]
-    q13_14_6 = x[333]
-    q13_15_6 = x[334]
-    q15_16_6 = x[335]
-    q17_18_6 = x[336]
-    q18_19_6 = x[337]
-    q20_21_6 = x[338]
-    q21_22_6 = x[339]
-    q22_23_6 = x[340]
-    q1_2_7 = x[341]
-    q1_17_7 = x[342]
-    q2_3_7 = x[343]
-    q4_5_7 = x[344]
-    q5_6_7 = x[345]
-    q7_8_7 = x[346]
-    q8_9_7 = x[347]
-    q8_10_7 = x[348]
-    q8_11_7 = x[349]
-    q11_12_7 = x[350]
-    q12_13_7 = x[351]
-    q13_14_7 = x[352]
-    q13_15_7 = x[353]
-    q15_16_7 = x[354]
-    q17_18_7 = x[355]
-    q18_19_7 = x[356]
-    q20_21_7 = x[357]
-    q21_22_7 = x[358]
-    q22_23_7 = x[359]
-    q1_2_8 = x[360]
-    q1_17_8 = x[361]
-    q2_3_8 = x[362]
-    q4_5_8 = x[363]
-    q5_6_8 = x[364]
-    q7_8_8 = x[365]
-    q8_9_8 = x[366]
-    q8_10_8 = x[367]
-    q8_11_8 = x[368]
-    q11_12_8 = x[369]
-    q12_13_8 = x[370]
-    q13_14_8 = x[371]
-    q13_15_8 = x[372]
-    q15_16_8 = x[373]
-    q17_18_8 = x[374]
-    q18_19_8 = x[375]
-    q20_21_8 = x[376]
-    q21_22_8 = x[377]
-    q22_23_8 = x[378]
-    f3_4_1 = x[379]
-    f5_7_1 = x[380]
-    f19_20_1 = x[381]
-    r3_4_1 = x[382]
-    r5_7_1 = x[383]
-    r19_20_1 = x[384]
-    f3_4_2 = x[385]
-    f5_7_2 = x[386]
-    f19_20_2 = x[387]
-    r3_4_2 = x[388]
-    r5_7_2 = x[389]
-    r19_20_2 = x[390]
-    f3_4_3 = x[391]
-    f5_7_3 = x[392]
-    f19_20_3 = x[393]
-    r3_4_3 = x[394]
-    r5_7_3 = x[395]
-    r19_20_3 = x[396]
-    f3_4_4 = x[397]
-    f5_7_4 = x[398]
-    f19_20_4 = x[399]
-    r3_4_4 = x[400]
-    r5_7_4 = x[401]
-    r19_20_4 = x[402]
-    f3_4_5 = x[403]
-    f5_7_5 = x[404]
-    f19_20_5 = x[405]
-    r3_4_5 = x[406]
-    r5_7_5 = x[407]
-    r19_20_5 = x[408]
-    f3_4_6 = x[409]
-    f5_7_6 = x[410]
-    f19_20_6 = x[411]
-    r3_4_6 = x[412]
-    r5_7_6 = x[413]
-    r19_20_6 = x[414]
-    f3_4_7 = x[415]
-    f5_7_7 = x[416]
-    f19_20_7 = x[417]
-    r3_4_7 = x[418]
-    r5_7_7 = x[419]
-    r19_20_7 = x[420]
-    f3_4_8 = x[421]
-    f5_7_8 = x[422]
-    f19_20_8 = x[423]
-    r3_4_8 = x[424]
-    r5_7_8 = x[425]
-    r19_20_8 = x[426]
-    in1_1 = x[427]
-    out16_1 = x[428]
-    out23_1 = x[429]
-    in1_2 = x[430]
-    out16_2 = x[431]
-    out23_2 = x[432]
-    in1_3 = x[433]
-    out16_3 = x[434]
-    out23_3 = x[435]
-    in1_4 = x[436]
-    out16_4 = x[437]
-    out23_4 = x[438]
-    in1_5 = x[439]
-    out16_5 = x[440]
-    out23_5 = x[441]
-    in1_6 = x[442]
-    out16_6 = x[443]
-    out23_6 = x[444]
-    in1_7 = x[445]
-    out16_7 = x[446]
-    out23_7 = x[447]
-    in1_8 = x[448]
-    out16_8 = x[449]
-    out23_8 = x[450]
+    p_0 = view(x, 1:23)
+    p_1 = view(x, 24:46)
+    p_2 = view(x, 47:69)
+    p_3 = view(x, 70:92)
+    p_4 = view(x, 93:115)
+    p_5 = view(x, 116:138)
+    p_6 = view(x, 139:161)
+    p_7 = view(x, 162:184)
+    p_8 = view(x, 185:207)
+
+    q_0 = Dict(q_ind .=> view(x, 208:226))
+    q_1 = Dict(q_ind .=> view(x, 227:245))
+    q_2 = Dict(q_ind .=> view(x, 246:264))
+    q_3 = Dict(q_ind .=> view(x, 265:283))
+    q_4 = Dict(q_ind .=> view(x, 284:302))
+    q_5 = Dict(q_ind .=> view(x, 303:321))
+    q_6 = Dict(q_ind .=> view(x, 322:340))
+    q_7 = Dict(q_ind .=> view(x, 341:359))
+    q_8 = Dict(q_ind .=> view(x, 360:378))
+
+    f_1 = Dict(fr_ind .=> view(x, 379:381))
+    r_1 = Dict(fr_ind .=> view(x, 382:384))
+    f_2 = Dict(fr_ind .=> view(x, 385:387))
+    r_2 = Dict(fr_ind .=> view(x, 388:390))
+    f_3 = Dict(fr_ind .=> view(x, 391:393))
+    r_3 = Dict(fr_ind .=> view(x, 394:396))
+    f_4 = Dict(fr_ind .=> view(x, 397:399))
+    r_4 = Dict(fr_ind .=> view(x, 400:402))
+    f_5 = Dict(fr_ind .=> view(x, 403:405))
+    r_5 = Dict(fr_ind .=> view(x, 406:408))
+    f_6 = Dict(fr_ind .=> view(x, 409:411))
+    r_6 = Dict(fr_ind .=> view(x, 412:414))
+    f_7 = Dict(fr_ind .=> view(x, 415:417))
+    r_7 = Dict(fr_ind .=> view(x, 418:420))
+    f_8 = Dict(fr_ind .=> view(x, 421:423))
+    r_8 = Dict(fr_ind .=> view(x, 424:426))
+
+    in_1 = Dict.(in_ind .=> view(x, 427:427))
+    out_1 = Dict(out_ind .=> view(x, 428:429))
+    in_2 = Dict.(in_ind .=> view(x, 430:430))
+    out_2 = Dict(out_ind .=> view(x, 431:432))
+    in_3 = Dict.(in_ind .=> view(x, 433:433))
+    out_3 = Dict(out_ind .=> view(x, 434:435))
+    in_4 = Dict.(in_ind .=> view(x, 436:436))
+    out_4 = Dict(out_ind .=> view(x, 437:438))
+    in_5 = Dict.(in_ind .=> view(x, 439:439))
+    out_5 = Dict(out_ind .=> view(x, 440:441))
+    in_6 = Dict.(in_ind .=> view(x, 442:442))
+    out_6 = Dict(out_ind .=> view(x, 443:444))
+    in_7 = Dict.(in_ind .=> view(x, 445:445))
+    out_7 = Dict(out_ind .=> view(x, 446:447))
+    in_8 = Dict.(in_ind .=> view(x, 448:448))
+    out_8 = Dict(out_ind .=> view(x, 449:450))
+
+    # multi-step variables
+    p_ = [p_1, p_2, p_3, p_4, p_5, p_6, p_7, p_8]
+    q_ = [q_1, q_2, q_3, q_4, q_5, q_6, q_7, q_8]
+    f_ = [f_1, f_2, f_3, f_4, f_5, f_6, f_7, f_8]
+    r_ = [r_1, r_2, r_3, r_4, r_5, r_6, r_7, r_8]
+    in_ = [in_1, in_2, in_3, in_4, in_5, in_6, in_7, in_8]
+    out_ = [out_1, out_2, out_3, out_4, out_5, out_6, out_7, out_8]
+
+    # time step 1
+
     cx[1] =
-      p1_1 / ((1) + (1) * p1_1) - p1_0 / ((1) + (1) * p1_0) - T(0.75) * q1_17_1 - T(0.75) * q1_2_1 +
-      in1_1 - T(0.25) * q1_17_0 - T(0.25) * q1_2_0
+      p_1[1] / (1 + p_1[1]) - p_0[1] / (1 + p_0[1]) - θ * q1_17_1 - θ * q1_2_1 + in_1[1] -
+      (1 - θ) * q1_17_0 - (1 - θ) * q1_2_0
+
+    cx[1] =
+      p1_1 / (1 + p1_1) - p1_0 / (1 + p1_0) - θ * q1_17_1 - θ * q1_2_1 + in1_1 - (1 - θ) * q1_17_0 -
+      (1 - θ) * q1_2_0
     cx[2] =
-      p2_1 / ((1) + (1) * p2_1) - p2_0 / ((1) + (1) * p2_0) - T(0.75) * q2_3_1 + T(0.75) * q1_2_1 -
-      T(0.25) * q2_3_0 + T(0.25) * q1_2_0 - 1
-    cx[3] =
-      p3_1 / ((1) + (1) * p3_1) - p3_0 / ((1) + (1) * p3_0) - f3_4_1 +
-      T(0.75) * q2_3_1 +
-      T(0.25) * q2_3_0
-    cx[4] =
-      p4_1 / ((1) + (1) * p4_1) - p4_0 / ((1) + (1) * p4_0) - T(0.75) * q4_5_1 + f3_4_1 -
-      T(0.25) * q4_5_0
+      p2_1 / (1 + p2_1) - p2_0 / (1 + p2_0) - θ * q2_3_1 + θ * q1_2_1 - (1 - θ) * q2_3_0 +
+      (1 - θ) * q1_2_0 - 1
+    cx[3] = p3_1 / (1 + p3_1) - p3_0 / (1 + p3_0) - f3_4_1 + θ * q2_3_1 + (1 - θ) * q2_3_0
+    cx[4] = p4_1 / (1 + p4_1) - p4_0 / (1 + p4_0) - θ * q4_5_1 + f3_4_1 - (1 - θ) * q4_5_0
     cx[5] =
-      p5_1 / ((1) + (1) * p5_1) - p5_0 / ((1) + (1) * p5_0) - T(0.75) * q5_6_1 - f5_7_1 +
-      T(0.75) * q4_5_1 - T(0.25) * q5_6_0 + T(0.25) * q4_5_0
-    cx[6] =
-      p6_1 / ((1) + (1) * p6_1) - p6_0 / ((1) + (1) * p6_0) + T(0.75) * q5_6_1 + T(0.25) * q5_6_0 -
-      1
-    cx[7] =
-      p7_1 / ((1) + (1) * p7_1) - p7_0 / ((1) + (1) * p7_0) - T(0.75) * q7_8_1 + f5_7_1 -
-      T(0.25) * q7_8_0
+      p5_1 / (1 + p5_1) - p5_0 / (1 + p5_0) - θ * q5_6_1 - f5_7_1 + θ * q4_5_1 - (1 - θ) * q5_6_0 +
+      (1 - θ) * q4_5_0
+    cx[6] = p6_1 / (1 + p6_1) - p6_0 / (1 + p6_0) + θ * q5_6_1 + (1 - θ) * q5_6_0 - 1
+    cx[7] = p7_1 / (1 + p7_1) - p7_0 / (1 + p7_0) - θ * q7_8_1 + f5_7_1 - (1 - θ) * q7_8_0
     cx[8] =
-      p8_1 / ((1) + (1) * p8_1) - p8_0 / ((1) + (1) * p8_0) - T(0.75) * q8_9_1 - T(0.75) * q8_10_1 -
-      T(0.75) * q8_11_1 + T(0.75) * q7_8_1 - T(0.25) * q8_9_0 - T(0.25) * q8_10_0 -
-      T(0.25) * q8_11_0 + T(0.25) * q7_8_0
-    cx[9] =
-      p9_1 / ((1) + (1) * p9_1) - p9_0 / ((1) + (1) * p9_0) + T(0.75) * q8_9_1 + T(0.25) * q8_9_0
-    cx[10] =
-      p10_1 / ((1) + (1) * p10_1) - p10_0 / ((1) + (1) * p10_0) +
-      T(0.75) * q8_10_1 +
-      T(0.25) * q8_10_0 - 1
+      p8_1 / (1 + p8_1) - p8_0 / (1 + p8_0) - θ * q8_9_1 - θ * q8_10_1 - θ * q8_11_1 + θ * q7_8_1 -
+      (1 - θ) * q8_9_0 - (1 - θ) * q8_10_0 - (1 - θ) * q8_11_0 + (1 - θ) * q7_8_0
+    cx[9] = p9_1 / (1 + p9_1) - p9_0 / (1 + p9_0) + θ * q8_9_1 + (1 - θ) * q8_9_0
+    cx[10] = p10_1 / (1 + p10_1) - p10_0 / (1 + p10_0) + θ * q8_10_1 + (1 - θ) * q8_10_0 - 1
     cx[11] =
-      p11_1 / ((1) + (1) * p11_1) - p11_0 / ((1) + (1) * p11_0) - T(0.75) * q11_12_1 +
-      T(0.75) * q8_11_1 - T(0.25) * q11_12_0 + T(0.25) * q8_11_0
+      p11_1 / (1 + p11_1) - p11_0 / (1 + p11_0) - θ * q11_12_1 + θ * q8_11_1 - (1 - θ) * q11_12_0 +
+      (1 - θ) * q8_11_0
     cx[12] =
-      p12_1 / ((1) + (1) * p12_1) - p12_0 / ((1) + (1) * p12_0) - T(0.75) * q12_13_1 +
-      T(0.75) * q11_12_1 - T(0.25) * q12_13_0 + T(0.25) * q11_12_0
+      p12_1 / (1 + p12_1) - p12_0 / (1 + p12_0) - θ * q12_13_1 + θ * q11_12_1 - (1 - θ) * q12_13_0 +
+      (1 - θ) * q11_12_0
     cx[13] =
-      p13_1 / ((1) + (1) * p13_1) - p13_0 / ((1) + (1) * p13_0) - T(0.75) * q13_14_1 -
-      T(0.75) * q13_15_1 + T(0.75) * q12_13_1 - T(0.25) * q13_14_0 - T(0.25) * q13_15_0 +
-      T(0.25) * q12_13_0 - 1
-    cx[14] =
-      p14_1 / ((1) + (1) * p14_1) - p14_0 / ((1) + (1) * p14_0) +
-      T(0.75) * q13_14_1 +
-      T(0.25) * q13_14_0
+      p13_1 / (1 + p13_1) - p13_0 / (1 + p13_0) - θ * q13_14_1 - θ * q13_15_1 + θ * q12_13_1 -
+      (1 - θ) * q13_14_0 - (1 - θ) * q13_15_0 + (1 - θ) * q12_13_0 - 1
+    cx[14] = p14_1 / (1 + p14_1) - p14_0 / (1 + p14_0) + θ * q13_14_1 + (1 - θ) * q13_14_0
     cx[15] =
-      p15_1 / ((1) + (1) * p15_1) - p15_0 / ((1) + (1) * p15_0) - T(0.75) * q15_16_1 +
-      T(0.75) * q13_15_1 - T(0.25) * q15_16_0 + T(0.25) * q13_15_0 - 1
-    cx[16] =
-      p16_1 / ((1) + (1) * p16_1) - p16_0 / ((1) + (1) * p16_0) +
-      T(0.75) * q15_16_1 +
-      T(0.25) * q15_16_0 - out16_1
+      p15_1 / (1 + p15_1) - p15_0 / (1 + p15_0) - θ * q15_16_1 + θ * q13_15_1 - (1 - θ) * q15_16_0 +
+      (1 - θ) * q13_15_0 - 1
+    cx[16] = p16_1 / (1 + p16_1) - p16_0 / (1 + p16_0) + θ * q15_16_1 + (1 - θ) * q15_16_0 - out16_1
     cx[17] =
-      p17_1 / ((1) + (1) * p17_1) - p17_0 / ((1) + (1) * p17_0) - T(0.75) * q17_18_1 +
-      T(0.75) * q1_17_1 - T(0.25) * q17_18_0 + T(0.25) * q1_17_0 - 1
+      p17_1 / (1 + p17_1) - p17_0 / (1 + p17_0) - θ * q17_18_1 + θ * q1_17_1 - (1 - θ) * q17_18_0 +
+      (1 - θ) * q1_17_0 - 1
     cx[18] =
-      p18_1 / ((1) + (1) * p18_1) - p18_0 / ((1) + (1) * p18_0) - T(0.75) * q18_19_1 +
-      T(0.75) * q17_18_1 - T(0.25) * q18_19_0 + T(0.25) * q17_18_0 - 1
+      p18_1 / (1 + p18_1) - p18_0 / (1 + p18_0) - θ * q18_19_1 + θ * q17_18_1 - (1 - θ) * q18_19_0 +
+      (1 - θ) * q17_18_0 - 1
     cx[19] =
-      p19_1 / ((1) + (1) * p19_1) - p19_0 / ((1) + (1) * p19_0) - f19_20_1 +
-      T(0.75) * q18_19_1 +
-      T(0.25) * q18_19_0
+      p19_1 / (1 + p19_1) - p19_0 / (1 + p19_0) - f19_20_1 + θ * q18_19_1 + (1 - θ) * q18_19_0
     cx[20] =
-      p20_1 / ((1) + (1) * p20_1) - p20_0 / ((1) + (1) * p20_0) - T(0.75) * q20_21_1 + f19_20_1 -
-      T(0.25) * q20_21_0
+      p20_1 / (1 + p20_1) - p20_0 / (1 + p20_0) - θ * q20_21_1 + f19_20_1 - (1 - θ) * q20_21_0
     cx[21] =
-      p21_1 / ((1) + (1) * p21_1) - p21_0 / ((1) + (1) * p21_0) - T(0.75) * q21_22_1 +
-      T(0.75) * q20_21_1 - T(0.25) * q21_22_0 + T(0.25) * q20_21_0 - 1
+      p21_1 / (1 + p21_1) - p21_0 / (1 + p21_0) - θ * q21_22_1 + θ * q20_21_1 - (1 - θ) * q21_22_0 +
+      (1 - θ) * q20_21_0 - 1
     cx[22] =
-      p22_1 / ((1) + (1) * p22_1) - p22_0 / ((1) + (1) * p22_0) - T(0.75) * q22_23_1 +
-      T(0.75) * q21_22_1 - T(0.25) * q22_23_0 + T(0.25) * q21_22_0 - 1
-    cx[23] =
-      p23_1 / ((1) + (1) * p23_1) - p23_0 / ((1) + (1) * p23_0) +
-      T(0.75) * q22_23_1 +
-      T(0.25) * q22_23_0 - out23_1
+      p22_1 / (1 + p22_1) - p22_0 / (1 + p22_0) - θ * q22_23_1 + θ * q21_22_1 - (1 - θ) * q22_23_0 +
+      (1 - θ) * q21_22_0 - 1
+    cx[23] = p23_1 / (1 + p23_1) - p23_0 / (1 + p23_0) + θ * q22_23_1 + (1 - θ) * q22_23_0 - out23_1
     cx[24] = p3_1 * r3_4_1 - p4_1
     cx[25] = p5_1 * r5_7_1 - p7_1
     cx[26] = p19_1 * r19_20_1 - p20_1
-    cx[27] =
-      p1_1 * p1_1 - p2_1 * p2_1 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p1_1 + p2_1)) * ((abs(q1_2_1))^T(1.8539))
-    cx[28] =
-      p1_1 * p1_1 - p17_1 * p17_1 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p1_1 + p17_1)) * ((abs(q1_17_1))^T(1.8539))
-    cx[29] =
-      p2_1 * p2_1 - p3_1 * p3_1 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p2_1 + p3_1)) * ((abs(q2_3_1))^T(1.8539))
-    cx[30] =
-      p4_1 * p4_1 - p5_1 * p5_1 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p4_1 + p5_1)) * ((abs(q4_5_1))^T(1.8539))
-    cx[31] =
-      p5_1 * p5_1 - p6_1 * p6_1 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p5_1 + p6_1)) * ((abs(q5_6_1))^T(1.8539))
-    cx[32] =
-      p7_1 * p7_1 - p8_1 * p8_1 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p7_1 + p8_1)) * ((abs(q7_8_1))^T(1.8539))
-    cx[33] =
-      p8_1 * p8_1 - p9_1 * p9_1 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p8_1 + p9_1)) * ((abs(q8_9_1))^T(1.8539))
-    cx[34] =
-      p8_1 * p8_1 - p10_1 * p10_1 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p8_1 + p10_1)) * ((abs(q8_10_1))^T(1.8539))
-    cx[35] =
-      p8_1 * p8_1 - p11_1 * p11_1 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p8_1 + p11_1)) * ((abs(q8_11_1))^T(1.8539))
-    cx[36] =
-      p11_1 * p11_1 - p12_1 * p12_1 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p11_1 + p12_1)) * ((abs(q11_12_1))^T(1.8539))
-    cx[37] =
-      p12_1 * p12_1 - p13_1 * p13_1 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p12_1 + p13_1)) * ((abs(q12_13_1))^T(1.8539))
-    cx[38] =
-      p13_1 * p13_1 - p14_1 * p14_1 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p13_1 + p14_1)) * ((abs(q13_14_1))^T(1.8539))
-    cx[39] =
-      p13_1 * p13_1 - p15_1 * p15_1 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p13_1 + p15_1)) * ((abs(q13_15_1))^T(1.8539))
-    cx[40] =
-      p15_1 * p15_1 - p16_1 * p16_1 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p15_1 + p16_1)) * ((abs(q15_16_1))^T(1.8539))
-    cx[41] =
-      p17_1 * p17_1 - p18_1 * p18_1 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p17_1 + p18_1)) * ((abs(q17_18_1))^T(1.8539))
-    cx[42] =
-      p18_1 * p18_1 - p19_1 * p19_1 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p18_1 + p19_1)) * ((abs(q18_19_1))^T(1.8539))
-    cx[43] =
-      p20_1 * p20_1 - p21_1 * p21_1 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p20_1 + p21_1)) * ((abs(q20_21_1))^T(1.8539))
-    cx[44] =
-      p21_1 * p21_1 - p22_1 * p22_1 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p21_1 + p22_1)) * ((abs(q21_22_1))^T(1.8539))
-    cx[45] =
-      p22_1 * p22_1 - p23_1 * p23_1 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p22_1 + p23_1)) * ((abs(q22_23_1))^T(1.8539))
+    cx[27] = p1_1 * p1_1 - p2_1 * p2_1 - h * (1 + γ * (p1_1 + p2_1)) * (abs(q1_2_1)^α)
+    cx[28] = p1_1 * p1_1 - p17_1 * p17_1 - h * (1 + γ * (p1_1 + p17_1)) * (abs(q1_17_1)^α)
+    cx[29] = p2_1 * p2_1 - p3_1 * p3_1 - h * (1 + γ * (p2_1 + p3_1)) * (abs(q2_3_1)^α)
+    cx[30] = p4_1 * p4_1 - p5_1 * p5_1 - h * (1 + γ * (p4_1 + p5_1)) * (abs(q4_5_1)^α)
+    cx[31] = p5_1 * p5_1 - p6_1 * p6_1 - h * (1 + γ * (p5_1 + p6_1)) * (abs(q5_6_1)^α)
+    cx[32] = p7_1 * p7_1 - p8_1 * p8_1 - h * (1 + γ * (p7_1 + p8_1)) * (abs(q7_8_1)^α)
+    cx[33] = p8_1 * p8_1 - p9_1 * p9_1 - h * (1 + γ * (p8_1 + p9_1)) * (abs(q8_9_1)^α)
+    cx[34] = p8_1 * p8_1 - p10_1 * p10_1 - h * (1 + γ * (p8_1 + p10_1)) * (abs(q8_10_1)^α)
+    cx[35] = p8_1 * p8_1 - p11_1 * p11_1 - h * (1 + γ * (p8_1 + p11_1)) * (abs(q8_11_1)^α)
+    cx[36] = p11_1 * p11_1 - p12_1 * p12_1 - h * (1 + γ * (p11_1 + p12_1)) * (abs(q11_12_1)^α)
+    cx[37] = p12_1 * p12_1 - p13_1 * p13_1 - h * (1 + γ * (p12_1 + p13_1)) * (abs(q12_13_1)^α)
+    cx[38] = p13_1 * p13_1 - p14_1 * p14_1 - h * (1 + γ * (p13_1 + p14_1)) * (abs(q13_14_1)^α)
+    cx[39] = p13_1 * p13_1 - p15_1 * p15_1 - h * (1 + γ * (p13_1 + p15_1)) * (abs(q13_15_1)^α)
+    cx[40] = p15_1 * p15_1 - p16_1 * p16_1 - h * (1 + γ * (p15_1 + p16_1)) * (abs(q15_16_1)^α)
+    cx[41] = p17_1 * p17_1 - p18_1 * p18_1 - h * (1 + γ * (p17_1 + p18_1)) * (abs(q17_18_1)^α)
+    cx[42] = p18_1 * p18_1 - p19_1 * p19_1 - h * (1 + γ * (p18_1 + p19_1)) * (abs(q18_19_1)^α)
+    cx[43] = p20_1 * p20_1 - p21_1 * p21_1 - h * (1 + γ * (p20_1 + p21_1)) * (abs(q20_21_1)^α)
+    cx[44] = p21_1 * p21_1 - p22_1 * p22_1 - h * (1 + γ * (p21_1 + p22_1)) * (abs(q21_22_1)^α)
+    cx[45] = p22_1 * p22_1 - p23_1 * p23_1 - h * (1 + γ * (p22_1 + p23_1)) * (abs(q22_23_1)^α)
+
+    # time step 2
+
     cx[46] =
-      p1_2 / ((1) + (1) * p1_2) - p1_1 / ((1) + (1) * p1_1) - T(0.75) * q1_17_2 - T(0.75) * q1_2_2 +
-      in1_2 - T(0.25) * q1_17_1 - T(0.25) * q1_2_1
+      p1_2 / (1 + p1_2) - p1_1 / (1 + p1_1) - θ * q1_17_2 - θ * q1_2_2 + in1_2 - (1 - θ) * q1_17_1 -
+      (1 - θ) * q1_2_1
     cx[47] =
-      p2_2 / ((1) + (1) * p2_2) - p2_1 / ((1) + (1) * p2_1) - T(0.75) * q2_3_2 + T(0.75) * q1_2_2 -
-      T(0.25) * q2_3_1 + T(0.25) * q1_2_1 - 1
-    cx[48] =
-      p3_2 / ((1) + (1) * p3_2) - p3_1 / ((1) + (1) * p3_1) - f3_4_2 +
-      T(0.75) * q2_3_2 +
-      T(0.25) * q2_3_1
-    cx[49] =
-      p4_2 / ((1) + (1) * p4_2) - p4_1 / ((1) + (1) * p4_1) - T(0.75) * q4_5_2 + f3_4_2 -
-      T(0.25) * q4_5_1
+      p2_2 / (1 + p2_2) - p2_1 / (1 + p2_1) - θ * q2_3_2 + θ * q1_2_2 - (1 - θ) * q2_3_1 +
+      (1 - θ) * q1_2_1 - 1
+    cx[48] = p3_2 / (1 + p3_2) - p3_1 / (1 + p3_1) - f3_4_2 + θ * q2_3_2 + (1 - θ) * q2_3_1
+    cx[49] = p4_2 / (1 + p4_2) - p4_1 / (1 + p4_1) - θ * q4_5_2 + f3_4_2 - (1 - θ) * q4_5_1
     cx[50] =
-      p5_2 / ((1) + (1) * p5_2) - p5_1 / ((1) + (1) * p5_1) - T(0.75) * q5_6_2 - f5_7_2 +
-      T(0.75) * q4_5_2 - T(0.25) * q5_6_1 + T(0.25) * q4_5_1
-    cx[51] =
-      p6_2 / ((1) + (1) * p6_2) - p6_1 / ((1) + (1) * p6_1) + T(0.75) * q5_6_2 + T(0.25) * q5_6_1 -
-      1
-    cx[52] =
-      p7_2 / ((1) + (1) * p7_2) - p7_1 / ((1) + (1) * p7_1) - T(0.75) * q7_8_2 + f5_7_2 -
-      T(0.25) * q7_8_1
+      p5_2 / (1 + p5_2) - p5_1 / (1 + p5_1) - θ * q5_6_2 - f5_7_2 + θ * q4_5_2 - (1 - θ) * q5_6_1 +
+      (1 - θ) * q4_5_1
+    cx[51] = p6_2 / (1 + p6_2) - p6_1 / (1 + p6_1) + θ * q5_6_2 + (1 - θ) * q5_6_1 - 1
+    cx[52] = p7_2 / (1 + p7_2) - p7_1 / (1 + p7_1) - θ * q7_8_2 + f5_7_2 - (1 - θ) * q7_8_1
     cx[53] =
-      p8_2 / ((1) + (1) * p8_2) - p8_1 / ((1) + (1) * p8_1) - T(0.75) * q8_9_2 - T(0.75) * q8_10_2 -
-      T(0.75) * q8_11_2 + T(0.75) * q7_8_2 - T(0.25) * q8_9_1 - T(0.25) * q8_10_1 -
-      T(0.25) * q8_11_1 + T(0.25) * q7_8_1
-    cx[54] =
-      p9_2 / ((1) + (1) * p9_2) - p9_1 / ((1) + (1) * p9_1) + T(0.75) * q8_9_2 + T(0.25) * q8_9_1
-    cx[55] =
-      p10_2 / ((1) + (1) * p10_2) - p10_1 / ((1) + (1) * p10_1) +
-      T(0.75) * q8_10_2 +
-      T(0.25) * q8_10_1 - 1
+      p8_2 / (1 + p8_2) - p8_1 / (1 + p8_1) - θ * q8_9_2 - θ * q8_10_2 - θ * q8_11_2 + θ * q7_8_2 -
+      (1 - θ) * q8_9_1 - (1 - θ) * q8_10_1 - (1 - θ) * q8_11_1 + (1 - θ) * q7_8_1
+    cx[54] = p9_2 / (1 + p9_2) - p9_1 / (1 + p9_1) + θ * q8_9_2 + (1 - θ) * q8_9_1
+    cx[55] = p10_2 / (1 + p10_2) - p10_1 / (1 + p10_1) + θ * q8_10_2 + (1 - θ) * q8_10_1 - 1
     cx[56] =
-      p11_2 / ((1) + (1) * p11_2) - p11_1 / ((1) + (1) * p11_1) - T(0.75) * q11_12_2 +
-      T(0.75) * q8_11_2 - T(0.25) * q11_12_1 + T(0.25) * q8_11_1
+      p11_2 / (1 + p11_2) - p11_1 / (1 + p11_1) - θ * q11_12_2 + θ * q8_11_2 - (1 - θ) * q11_12_1 +
+      (1 - θ) * q8_11_1
     cx[57] =
-      p12_2 / ((1) + (1) * p12_2) - p12_1 / ((1) + (1) * p12_1) - T(0.75) * q12_13_2 +
-      T(0.75) * q11_12_2 - T(0.25) * q12_13_1 + T(0.25) * q11_12_1
+      p12_2 / (1 + p12_2) - p12_1 / (1 + p12_1) - θ * q12_13_2 + θ * q11_12_2 - (1 - θ) * q12_13_1 +
+      (1 - θ) * q11_12_1
     cx[58] =
-      p13_2 / ((1) + (1) * p13_2) - p13_1 / ((1) + (1) * p13_1) - T(0.75) * q13_14_2 -
-      T(0.75) * q13_15_2 + T(0.75) * q12_13_2 - T(0.25) * q13_14_1 - T(0.25) * q13_15_1 +
-      T(0.25) * q12_13_1 - 1
-    cx[59] =
-      p14_2 / ((1) + (1) * p14_2) - p14_1 / ((1) + (1) * p14_1) +
-      T(0.75) * q13_14_2 +
-      T(0.25) * q13_14_1
+      p13_2 / (1 + p13_2) - p13_1 / (1 + p13_1) - θ * q13_14_2 - θ * q13_15_2 + θ * q12_13_2 -
+      (1 - θ) * q13_14_1 - (1 - θ) * q13_15_1 + (1 - θ) * q12_13_1 - 1
+    cx[59] = p14_2 / (1 + p14_2) - p14_1 / (1 + p14_1) + θ * q13_14_2 + (1 - θ) * q13_14_1
     cx[60] =
-      p15_2 / ((1) + (1) * p15_2) - p15_1 / ((1) + (1) * p15_1) - T(0.75) * q15_16_2 +
-      T(0.75) * q13_15_2 - T(0.25) * q15_16_1 + T(0.25) * q13_15_1 - 1
-    cx[61] =
-      p16_2 / ((1) + (1) * p16_2) - p16_1 / ((1) + (1) * p16_1) +
-      T(0.75) * q15_16_2 +
-      T(0.25) * q15_16_1 - out16_2
+      p15_2 / (1 + p15_2) - p15_1 / (1 + p15_1) - θ * q15_16_2 + θ * q13_15_2 - (1 - θ) * q15_16_1 +
+      (1 - θ) * q13_15_1 - 1
+    cx[61] = p16_2 / (1 + p16_2) - p16_1 / (1 + p16_1) + θ * q15_16_2 + (1 - θ) * q15_16_1 - out16_2
     cx[62] =
-      p17_2 / ((1) + (1) * p17_2) - p17_1 / ((1) + (1) * p17_1) - T(0.75) * q17_18_2 +
-      T(0.75) * q1_17_2 - T(0.25) * q17_18_1 + T(0.25) * q1_17_1 - 1
+      p17_2 / (1 + p17_2) - p17_1 / (1 + p17_1) - θ * q17_18_2 + θ * q1_17_2 - (1 - θ) * q17_18_1 +
+      (1 - θ) * q1_17_1 - 1
     cx[63] =
-      p18_2 / ((1) + (1) * p18_2) - p18_1 / ((1) + (1) * p18_1) - T(0.75) * q18_19_2 +
-      T(0.75) * q17_18_2 - T(0.25) * q18_19_1 + T(0.25) * q17_18_1 - 1
+      p18_2 / (1 + p18_2) - p18_1 / (1 + p18_1) - θ * q18_19_2 + θ * q17_18_2 - (1 - θ) * q18_19_1 +
+      (1 - θ) * q17_18_1 - 1
     cx[64] =
-      p19_2 / ((1) + (1) * p19_2) - p19_1 / ((1) + (1) * p19_1) - f19_20_2 +
-      T(0.75) * q18_19_2 +
-      T(0.25) * q18_19_1
+      p19_2 / (1 + p19_2) - p19_1 / (1 + p19_1) - f19_20_2 + θ * q18_19_2 + (1 - θ) * q18_19_1
     cx[65] =
-      p20_2 / ((1) + (1) * p20_2) - p20_1 / ((1) + (1) * p20_1) - T(0.75) * q20_21_2 + f19_20_2 -
-      T(0.25) * q20_21_1
+      p20_2 / (1 + p20_2) - p20_1 / (1 + p20_1) - θ * q20_21_2 + f19_20_2 - (1 - θ) * q20_21_1
     cx[66] =
-      p21_2 / ((1) + (1) * p21_2) - p21_1 / ((1) + (1) * p21_1) - T(0.75) * q21_22_2 +
-      T(0.75) * q20_21_2 - T(0.25) * q21_22_1 + T(0.25) * q20_21_1 - 1
+      p21_2 / (1 + p21_2) - p21_1 / (1 + p21_1) - θ * q21_22_2 + θ * q20_21_2 - (1 - θ) * q21_22_1 +
+      (1 - θ) * q20_21_1 - 1
     cx[67] =
-      p22_2 / ((1) + (1) * p22_2) - p22_1 / ((1) + (1) * p22_1) - T(0.75) * q22_23_2 +
-      T(0.75) * q21_22_2 - T(0.25) * q22_23_1 + T(0.25) * q21_22_1 - 1
-    cx[68] =
-      p23_2 / ((1) + (1) * p23_2) - p23_1 / ((1) + (1) * p23_1) +
-      T(0.75) * q22_23_2 +
-      T(0.25) * q22_23_1 - out23_2
+      p22_2 / (1 + p22_2) - p22_1 / (1 + p22_1) - θ * q22_23_2 + θ * q21_22_2 - (1 - θ) * q22_23_1 +
+      (1 - θ) * q21_22_1 - 1
+    cx[68] = p23_2 / (1 + p23_2) - p23_1 / (1 + p23_1) + θ * q22_23_2 + (1 - θ) * q22_23_1 - out23_2
     cx[69] = p3_2 * r3_4_2 - p4_2
     cx[70] = p5_2 * r5_7_2 - p7_2
     cx[71] = p19_2 * r19_20_2 - p20_2
-    cx[72] =
-      p1_2 * p1_2 - p2_2 * p2_2 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p1_2 + p2_2)) * ((abs(q1_2_2))^T(1.8539))
-    cx[73] =
-      p1_2 * p1_2 - p17_2 * p17_2 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p1_2 + p17_2)) * ((abs(q1_17_2))^T(1.8539))
-    cx[74] =
-      p2_2 * p2_2 - p3_2 * p3_2 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p2_2 + p3_2)) * ((abs(q2_3_2))^T(1.8539))
-    cx[75] =
-      p4_2 * p4_2 - p5_2 * p5_2 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p4_2 + p5_2)) * ((abs(q4_5_2))^T(1.8539))
-    cx[76] =
-      p5_2 * p5_2 - p6_2 * p6_2 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p5_2 + p6_2)) * ((abs(q5_6_2))^T(1.8539))
-    cx[77] =
-      p7_2 * p7_2 - p8_2 * p8_2 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p7_2 + p8_2)) * ((abs(q7_8_2))^T(1.8539))
-    cx[78] =
-      p8_2 * p8_2 - p9_2 * p9_2 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p8_2 + p9_2)) * ((abs(q8_9_2))^T(1.8539))
-    cx[79] =
-      p8_2 * p8_2 - p10_2 * p10_2 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p8_2 + p10_2)) * ((abs(q8_10_2))^T(1.8539))
-    cx[80] =
-      p8_2 * p8_2 - p11_2 * p11_2 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p8_2 + p11_2)) * ((abs(q8_11_2))^T(1.8539))
-    cx[81] =
-      p11_2 * p11_2 - p12_2 * p12_2 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p11_2 + p12_2)) * ((abs(q11_12_2))^T(1.8539))
-    cx[82] =
-      p12_2 * p12_2 - p13_2 * p13_2 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p12_2 + p13_2)) * ((abs(q12_13_2))^T(1.8539))
-    cx[83] =
-      p13_2 * p13_2 - p14_2 * p14_2 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p13_2 + p14_2)) * ((abs(q13_14_2))^T(1.8539))
-    cx[84] =
-      p13_2 * p13_2 - p15_2 * p15_2 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p13_2 + p15_2)) * ((abs(q13_15_2))^T(1.8539))
-    cx[85] =
-      p15_2 * p15_2 - p16_2 * p16_2 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p15_2 + p16_2)) * ((abs(q15_16_2))^T(1.8539))
-    cx[86] =
-      p17_2 * p17_2 - p18_2 * p18_2 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p17_2 + p18_2)) * ((abs(q17_18_2))^T(1.8539))
-    cx[87] =
-      p18_2 * p18_2 - p19_2 * p19_2 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p18_2 + p19_2)) * ((abs(q18_19_2))^T(1.8539))
-    cx[88] =
-      p20_2 * p20_2 - p21_2 * p21_2 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p20_2 + p21_2)) * ((abs(q20_21_2))^T(1.8539))
-    cx[89] =
-      p21_2 * p21_2 - p22_2 * p22_2 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p21_2 + p22_2)) * ((abs(q21_22_2))^T(1.8539))
-    cx[90] =
-      p22_2 * p22_2 - p23_2 * p23_2 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p22_2 + p23_2)) * ((abs(q22_23_2))^T(1.8539))
+    cx[72] = p1_2 * p1_2 - p2_2 * p2_2 - h * (1 + γ * (p1_2 + p2_2)) * (abs(q1_2_2)^α)
+    cx[73] = p1_2 * p1_2 - p17_2 * p17_2 - h * (1 + γ * (p1_2 + p17_2)) * (abs(q1_17_2)^α)
+    cx[74] = p2_2 * p2_2 - p3_2 * p3_2 - h * (1 + γ * (p2_2 + p3_2)) * (abs(q2_3_2)^α)
+    cx[75] = p4_2 * p4_2 - p5_2 * p5_2 - h * (1 + γ * (p4_2 + p5_2)) * (abs(q4_5_2)^α)
+    cx[76] = p5_2 * p5_2 - p6_2 * p6_2 - h * (1 + γ * (p5_2 + p6_2)) * (abs(q5_6_2)^α)
+    cx[77] = p7_2 * p7_2 - p8_2 * p8_2 - h * (1 + γ * (p7_2 + p8_2)) * (abs(q7_8_2)^α)
+    cx[78] = p8_2 * p8_2 - p9_2 * p9_2 - h * (1 + γ * (p8_2 + p9_2)) * (abs(q8_9_2)^α)
+    cx[79] = p8_2 * p8_2 - p10_2 * p10_2 - h * (1 + γ * (p8_2 + p10_2)) * (abs(q8_10_2)^α)
+    cx[80] = p8_2 * p8_2 - p11_2 * p11_2 - h * (1 + γ * (p8_2 + p11_2)) * (abs(q8_11_2)^α)
+    cx[81] = p11_2 * p11_2 - p12_2 * p12_2 - h * (1 + γ * (p11_2 + p12_2)) * (abs(q11_12_2)^α)
+    cx[82] = p12_2 * p12_2 - p13_2 * p13_2 - h * (1 + γ * (p12_2 + p13_2)) * (abs(q12_13_2)^α)
+    cx[83] = p13_2 * p13_2 - p14_2 * p14_2 - h * (1 + γ * (p13_2 + p14_2)) * (abs(q13_14_2)^α)
+    cx[84] = p13_2 * p13_2 - p15_2 * p15_2 - h * (1 + γ * (p13_2 + p15_2)) * (abs(q13_15_2)^α)
+    cx[85] = p15_2 * p15_2 - p16_2 * p16_2 - h * (1 + γ * (p15_2 + p16_2)) * (abs(q15_16_2)^α)
+    cx[86] = p17_2 * p17_2 - p18_2 * p18_2 - h * (1 + γ * (p17_2 + p18_2)) * (abs(q17_18_2)^α)
+    cx[87] = p18_2 * p18_2 - p19_2 * p19_2 - h * (1 + γ * (p18_2 + p19_2)) * (abs(q18_19_2)^α)
+    cx[88] = p20_2 * p20_2 - p21_2 * p21_2 - h * (1 + γ * (p20_2 + p21_2)) * (abs(q20_21_2)^α)
+    cx[89] = p21_2 * p21_2 - p22_2 * p22_2 - h * (1 + γ * (p21_2 + p22_2)) * (abs(q21_22_2)^α)
+    cx[90] = p22_2 * p22_2 - p23_2 * p23_2 - h * (1 + γ * (p22_2 + p23_2)) * (abs(q22_23_2)^α)
+
+    # time step 3
+
     cx[91] =
-      p1_3 / ((1) + (1) * p1_3) - p1_2 / ((1) + (1) * p1_2) - T(0.75) * q1_17_3 - T(0.75) * q1_2_3 +
-      in1_3 - T(0.25) * q1_17_2 - T(0.25) * q1_2_2
+      p1_3 / (1 + p1_3) - p1_2 / (1 + p1_2) - θ * q1_17_3 - θ * q1_2_3 + in1_3 - (1 - θ) * q1_17_2 -
+      (1 - θ) * q1_2_2
     cx[92] =
-      p2_3 / ((1) + (1) * p2_3) - p2_2 / ((1) + (1) * p2_2) - T(0.75) * q2_3_3 + T(0.75) * q1_2_3 -
-      T(0.25) * q2_3_2 + T(0.25) * q1_2_2 - 1
-    cx[93] =
-      p3_3 / ((1) + (1) * p3_3) - p3_2 / ((1) + (1) * p3_2) - f3_4_3 +
-      T(0.75) * q2_3_3 +
-      T(0.25) * q2_3_2
-    cx[94] =
-      p4_3 / ((1) + (1) * p4_3) - p4_2 / ((1) + (1) * p4_2) - T(0.75) * q4_5_3 + f3_4_3 -
-      T(0.25) * q4_5_2
+      p2_3 / (1 + p2_3) - p2_2 / (1 + p2_2) - θ * q2_3_3 + θ * q1_2_3 - (1 - θ) * q2_3_2 +
+      (1 - θ) * q1_2_2 - 1
+    cx[93] = p3_3 / (1 + p3_3) - p3_2 / (1 + p3_2) - f3_4_3 + θ * q2_3_3 + (1 - θ) * q2_3_2
+    cx[94] = p4_3 / (1 + p4_3) - p4_2 / (1 + p4_2) - θ * q4_5_3 + f3_4_3 - (1 - θ) * q4_5_2
     cx[95] =
-      p5_3 / ((1) + (1) * p5_3) - p5_2 / ((1) + (1) * p5_2) - T(0.75) * q5_6_3 - f5_7_3 +
-      T(0.75) * q4_5_3 - T(0.25) * q5_6_2 + T(0.25) * q4_5_2
-    cx[96] =
-      p6_3 / ((1) + (1) * p6_3) - p6_2 / ((1) + (1) * p6_2) + T(0.75) * q5_6_3 + T(0.25) * q5_6_2 -
-      1
-    cx[97] =
-      p7_3 / ((1) + (1) * p7_3) - p7_2 / ((1) + (1) * p7_2) - T(0.75) * q7_8_3 + f5_7_3 -
-      T(0.25) * q7_8_2
+      p5_3 / (1 + p5_3) - p5_2 / (1 + p5_2) - θ * q5_6_3 - f5_7_3 + θ * q4_5_3 - (1 - θ) * q5_6_2 +
+      (1 - θ) * q4_5_2
+    cx[96] = p6_3 / (1 + p6_3) - p6_2 / (1 + p6_2) + θ * q5_6_3 + (1 - θ) * q5_6_2 - 1
+    cx[97] = p7_3 / (1 + p7_3) - p7_2 / (1 + p7_2) - θ * q7_8_3 + f5_7_3 - (1 - θ) * q7_8_2
     cx[98] =
-      p8_3 / ((1) + (1) * p8_3) - p8_2 / ((1) + (1) * p8_2) - T(0.75) * q8_9_3 - T(0.75) * q8_10_3 -
-      T(0.75) * q8_11_3 + T(0.75) * q7_8_3 - T(0.25) * q8_9_2 - T(0.25) * q8_10_2 -
-      T(0.25) * q8_11_2 + T(0.25) * q7_8_2
-    cx[99] =
-      p9_3 / ((1) + (1) * p9_3) - p9_2 / ((1) + (1) * p9_2) + T(0.75) * q8_9_3 + T(0.25) * q8_9_2
-    cx[100] =
-      p10_3 / ((1) + (1) * p10_3) - p10_2 / ((1) + (1) * p10_2) +
-      T(0.75) * q8_10_3 +
-      T(0.25) * q8_10_2 - 1
+      p8_3 / (1 + p8_3) - p8_2 / (1 + p8_2) - θ * q8_9_3 - θ * q8_10_3 - θ * q8_11_3 + θ * q7_8_3 -
+      (1 - θ) * q8_9_2 - (1 - θ) * q8_10_2 - (1 - θ) * q8_11_2 + (1 - θ) * q7_8_2
+    cx[99] = p9_3 / (1 + p9_3) - p9_2 / (1 + p9_2) + θ * q8_9_3 + (1 - θ) * q8_9_2
+    cx[100] = p10_3 / (1 + p10_3) - p10_2 / (1 + p10_2) + θ * q8_10_3 + (1 - θ) * q8_10_2 - 1
     cx[101] =
-      p11_3 / ((1) + (1) * p11_3) - p11_2 / ((1) + (1) * p11_2) - T(0.75) * q11_12_3 +
-      T(0.75) * q8_11_3 - T(0.25) * q11_12_2 + T(0.25) * q8_11_2
+      p11_3 / (1 + p11_3) - p11_2 / (1 + p11_2) - θ * q11_12_3 + θ * q8_11_3 - (1 - θ) * q11_12_2 +
+      (1 - θ) * q8_11_2
     cx[102] =
-      p12_3 / ((1) + (1) * p12_3) - p12_2 / ((1) + (1) * p12_2) - T(0.75) * q12_13_3 +
-      T(0.75) * q11_12_3 - T(0.25) * q12_13_2 + T(0.25) * q11_12_2
+      p12_3 / (1 + p12_3) - p12_2 / (1 + p12_2) - θ * q12_13_3 + θ * q11_12_3 - (1 - θ) * q12_13_2 +
+      (1 - θ) * q11_12_2
     cx[103] =
-      p13_3 / ((1) + (1) * p13_3) - p13_2 / ((1) + (1) * p13_2) - T(0.75) * q13_14_3 -
-      T(0.75) * q13_15_3 + T(0.75) * q12_13_3 - T(0.25) * q13_14_2 - T(0.25) * q13_15_2 +
-      T(0.25) * q12_13_2 - 1
-    cx[104] =
-      p14_3 / ((1) + (1) * p14_3) - p14_2 / ((1) + (1) * p14_2) +
-      T(0.75) * q13_14_3 +
-      T(0.25) * q13_14_2
+      p13_3 / (1 + p13_3) - p13_2 / (1 + p13_2) - θ * q13_14_3 - θ * q13_15_3 + θ * q12_13_3 -
+      (1 - θ) * q13_14_2 - (1 - θ) * q13_15_2 + (1 - θ) * q12_13_2 - 1
+    cx[104] = p14_3 / (1 + p14_3) - p14_2 / (1 + p14_2) + θ * q13_14_3 + (1 - θ) * q13_14_2
     cx[105] =
-      p15_3 / ((1) + (1) * p15_3) - p15_2 / ((1) + (1) * p15_2) - T(0.75) * q15_16_3 +
-      T(0.75) * q13_15_3 - T(0.25) * q15_16_2 + T(0.25) * q13_15_2 - 1
+      p15_3 / (1 + p15_3) - p15_2 / (1 + p15_2) - θ * q15_16_3 + θ * q13_15_3 - (1 - θ) * q15_16_2 +
+      (1 - θ) * q13_15_2 - 1
     cx[106] =
-      p16_3 / ((1) + (1) * p16_3) - p16_2 / ((1) + (1) * p16_2) +
-      T(0.75) * q15_16_3 +
-      T(0.25) * q15_16_2 - out16_3
+      p16_3 / (1 + p16_3) - p16_2 / (1 + p16_2) + θ * q15_16_3 + (1 - θ) * q15_16_2 - out16_3
     cx[107] =
-      p17_3 / ((1) + (1) * p17_3) - p17_2 / ((1) + (1) * p17_2) - T(0.75) * q17_18_3 +
-      T(0.75) * q1_17_3 - T(0.25) * q17_18_2 + T(0.25) * q1_17_2 - 1
+      p17_3 / (1 + p17_3) - p17_2 / (1 + p17_2) - θ * q17_18_3 + θ * q1_17_3 - (1 - θ) * q17_18_2 +
+      (1 - θ) * q1_17_2 - 1
     cx[108] =
-      p18_3 / ((1) + (1) * p18_3) - p18_2 / ((1) + (1) * p18_2) - T(0.75) * q18_19_3 +
-      T(0.75) * q17_18_3 - T(0.25) * q18_19_2 + T(0.25) * q17_18_2 - 1
+      p18_3 / (1 + p18_3) - p18_2 / (1 + p18_2) - θ * q18_19_3 + θ * q17_18_3 - (1 - θ) * q18_19_2 +
+      (1 - θ) * q17_18_2 - 1
     cx[109] =
-      p19_3 / ((1) + (1) * p19_3) - p19_2 / ((1) + (1) * p19_2) - f19_20_3 +
-      T(0.75) * q18_19_3 +
-      T(0.25) * q18_19_2
+      p19_3 / (1 + p19_3) - p19_2 / (1 + p19_2) - f19_20_3 + θ * q18_19_3 + (1 - θ) * q18_19_2
     cx[110] =
-      p20_3 / ((1) + (1) * p20_3) - p20_2 / ((1) + (1) * p20_2) - T(0.75) * q20_21_3 + f19_20_3 -
-      T(0.25) * q20_21_2
+      p20_3 / (1 + p20_3) - p20_2 / (1 + p20_2) - θ * q20_21_3 + f19_20_3 - (1 - θ) * q20_21_2
     cx[111] =
-      p21_3 / ((1) + (1) * p21_3) - p21_2 / ((1) + (1) * p21_2) - T(0.75) * q21_22_3 +
-      T(0.75) * q20_21_3 - T(0.25) * q21_22_2 + T(0.25) * q20_21_2 - 1
+      p21_3 / (1 + p21_3) - p21_2 / (1 + p21_2) - θ * q21_22_3 + θ * q20_21_3 - (1 - θ) * q21_22_2 +
+      (1 - θ) * q20_21_2 - 1
     cx[112] =
-      p22_3 / ((1) + (1) * p22_3) - p22_2 / ((1) + (1) * p22_2) - T(0.75) * q22_23_3 +
-      T(0.75) * q21_22_3 - T(0.25) * q22_23_2 + T(0.25) * q21_22_2 - 1
+      p22_3 / (1 + p22_3) - p22_2 / (1 + p22_2) - θ * q22_23_3 + θ * q21_22_3 - (1 - θ) * q22_23_2 +
+      (1 - θ) * q21_22_2 - 1
     cx[113] =
-      p23_3 / ((1) + (1) * p23_3) - p23_2 / ((1) + (1) * p23_2) +
-      T(0.75) * q22_23_3 +
-      T(0.25) * q22_23_2 - out23_3
+      p23_3 / (1 + p23_3) - p23_2 / (1 + p23_2) + θ * q22_23_3 + (1 - θ) * q22_23_2 - out23_3
     cx[114] = p3_3 * r3_4_3 - p4_3
     cx[115] = p5_3 * r5_7_3 - p7_3
     cx[116] = p19_3 * r19_20_3 - p20_3
-    cx[117] =
-      p1_3 * p1_3 - p2_3 * p2_3 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p1_3 + p2_3)) * ((abs(q1_2_3))^T(1.8539))
-    cx[118] =
-      p1_3 * p1_3 - p17_3 * p17_3 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p1_3 + p17_3)) * ((abs(q1_17_3))^T(1.8539))
-    cx[119] =
-      p2_3 * p2_3 - p3_3 * p3_3 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p2_3 + p3_3)) * ((abs(q2_3_3))^T(1.8539))
-    cx[120] =
-      p4_3 * p4_3 - p5_3 * p5_3 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p4_3 + p5_3)) * ((abs(q4_5_3))^T(1.8539))
-    cx[121] =
-      p5_3 * p5_3 - p6_3 * p6_3 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p5_3 + p6_3)) * ((abs(q5_6_3))^T(1.8539))
-    cx[122] =
-      p7_3 * p7_3 - p8_3 * p8_3 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p7_3 + p8_3)) * ((abs(q7_8_3))^T(1.8539))
-    cx[123] =
-      p8_3 * p8_3 - p9_3 * p9_3 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p8_3 + p9_3)) * ((abs(q8_9_3))^T(1.8539))
-    cx[124] =
-      p8_3 * p8_3 - p10_3 * p10_3 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p8_3 + p10_3)) * ((abs(q8_10_3))^T(1.8539))
-    cx[125] =
-      p8_3 * p8_3 - p11_3 * p11_3 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p8_3 + p11_3)) * ((abs(q8_11_3))^T(1.8539))
-    cx[126] =
-      p11_3 * p11_3 - p12_3 * p12_3 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p11_3 + p12_3)) * ((abs(q11_12_3))^T(1.8539))
-    cx[127] =
-      p12_3 * p12_3 - p13_3 * p13_3 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p12_3 + p13_3)) * ((abs(q12_13_3))^T(1.8539))
-    cx[128] =
-      p13_3 * p13_3 - p14_3 * p14_3 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p13_3 + p14_3)) * ((abs(q13_14_3))^T(1.8539))
-    cx[129] =
-      p13_3 * p13_3 - p15_3 * p15_3 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p13_3 + p15_3)) * ((abs(q13_15_3))^T(1.8539))
-    cx[130] =
-      p15_3 * p15_3 - p16_3 * p16_3 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p15_3 + p16_3)) * ((abs(q15_16_3))^T(1.8539))
-    cx[131] =
-      p17_3 * p17_3 - p18_3 * p18_3 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p17_3 + p18_3)) * ((abs(q17_18_3))^T(1.8539))
-    cx[132] =
-      p18_3 * p18_3 - p19_3 * p19_3 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p18_3 + p19_3)) * ((abs(q18_19_3))^T(1.8539))
-    cx[133] =
-      p20_3 * p20_3 - p21_3 * p21_3 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p20_3 + p21_3)) * ((abs(q20_21_3))^T(1.8539))
-    cx[134] =
-      p21_3 * p21_3 - p22_3 * p22_3 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p21_3 + p22_3)) * ((abs(q21_22_3))^T(1.8539))
-    cx[135] =
-      p22_3 * p22_3 - p23_3 * p23_3 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p22_3 + p23_3)) * ((abs(q22_23_3))^T(1.8539))
+    cx[117] = p1_3 * p1_3 - p2_3 * p2_3 - h * (1 + γ * (p1_3 + p2_3)) * (abs(q1_2_3)^α)
+    cx[118] = p1_3 * p1_3 - p17_3 * p17_3 - h * (1 + γ * (p1_3 + p17_3)) * (abs(q1_17_3)^α)
+    cx[119] = p2_3 * p2_3 - p3_3 * p3_3 - h * (1 + γ * (p2_3 + p3_3)) * (abs(q2_3_3)^α)
+    cx[120] = p4_3 * p4_3 - p5_3 * p5_3 - h * (1 + γ * (p4_3 + p5_3)) * (abs(q4_5_3)^α)
+    cx[121] = p5_3 * p5_3 - p6_3 * p6_3 - h * (1 + γ * (p5_3 + p6_3)) * (abs(q5_6_3)^α)
+    cx[122] = p7_3 * p7_3 - p8_3 * p8_3 - h * (1 + γ * (p7_3 + p8_3)) * (abs(q7_8_3)^α)
+    cx[123] = p8_3 * p8_3 - p9_3 * p9_3 - h * (1 + γ * (p8_3 + p9_3)) * (abs(q8_9_3)^α)
+    cx[124] = p8_3 * p8_3 - p10_3 * p10_3 - h * (1 + γ * (p8_3 + p10_3)) * (abs(q8_10_3)^α)
+    cx[125] = p8_3 * p8_3 - p11_3 * p11_3 - h * (1 + γ * (p8_3 + p11_3)) * (abs(q8_11_3)^α)
+    cx[126] = p11_3 * p11_3 - p12_3 * p12_3 - h * (1 + γ * (p11_3 + p12_3)) * (abs(q11_12_3)^α)
+    cx[127] = p12_3 * p12_3 - p13_3 * p13_3 - h * (1 + γ * (p12_3 + p13_3)) * (abs(q12_13_3)^α)
+    cx[128] = p13_3 * p13_3 - p14_3 * p14_3 - h * (1 + γ * (p13_3 + p14_3)) * (abs(q13_14_3)^α)
+    cx[129] = p13_3 * p13_3 - p15_3 * p15_3 - h * (1 + γ * (p13_3 + p15_3)) * (abs(q13_15_3)^α)
+    cx[130] = p15_3 * p15_3 - p16_3 * p16_3 - h * (1 + γ * (p15_3 + p16_3)) * (abs(q15_16_3)^α)
+    cx[131] = p17_3 * p17_3 - p18_3 * p18_3 - h * (1 + γ * (p17_3 + p18_3)) * (abs(q17_18_3)^α)
+    cx[132] = p18_3 * p18_3 - p19_3 * p19_3 - h * (1 + γ * (p18_3 + p19_3)) * (abs(q18_19_3)^α)
+    cx[133] = p20_3 * p20_3 - p21_3 * p21_3 - h * (1 + γ * (p20_3 + p21_3)) * (abs(q20_21_3)^α)
+    cx[134] = p21_3 * p21_3 - p22_3 * p22_3 - h * (1 + γ * (p21_3 + p22_3)) * (abs(q21_22_3)^α)
+    cx[135] = p22_3 * p22_3 - p23_3 * p23_3 - h * (1 + γ * (p22_3 + p23_3)) * (abs(q22_23_3)^α)
+
+    # time step 4
+
     cx[136] =
-      p1_4 / ((1) + (1) * p1_4) - p1_3 / ((1) + (1) * p1_3) - T(0.75) * q1_17_4 - T(0.75) * q1_2_4 +
-      in1_4 - T(0.25) * q1_17_3 - T(0.25) * q1_2_3
+      p1_4 / (1 + p1_4) - p1_3 / (1 + p1_3) - θ * q1_17_4 - θ * q1_2_4 + in1_4 - (1 - θ) * q1_17_3 -
+      (1 - θ) * q1_2_3
     cx[137] =
-      p2_4 / ((1) + (1) * p2_4) - p2_3 / ((1) + (1) * p2_3) - T(0.75) * q2_3_4 + T(0.75) * q1_2_4 -
-      T(0.25) * q2_3_3 + T(0.25) * q1_2_3 - 1
-    cx[138] =
-      p3_4 / ((1) + (1) * p3_4) - p3_3 / ((1) + (1) * p3_3) - f3_4_4 +
-      T(0.75) * q2_3_4 +
-      T(0.25) * q2_3_3
-    cx[139] =
-      p4_4 / ((1) + (1) * p4_4) - p4_3 / ((1) + (1) * p4_3) - T(0.75) * q4_5_4 + f3_4_4 -
-      T(0.25) * q4_5_3
+      p2_4 / (1 + p2_4) - p2_3 / (1 + p2_3) - θ * q2_3_4 + θ * q1_2_4 - (1 - θ) * q2_3_3 +
+      (1 - θ) * q1_2_3 - 1
+    cx[138] = p3_4 / (1 + p3_4) - p3_3 / (1 + p3_3) - f3_4_4 + θ * q2_3_4 + (1 - θ) * q2_3_3
+    cx[139] = p4_4 / (1 + p4_4) - p4_3 / (1 + p4_3) - θ * q4_5_4 + f3_4_4 - (1 - θ) * q4_5_3
     cx[140] =
-      p5_4 / ((1) + (1) * p5_4) - p5_3 / ((1) + (1) * p5_3) - T(0.75) * q5_6_4 - f5_7_4 +
-      T(0.75) * q4_5_4 - T(0.25) * q5_6_3 + T(0.25) * q4_5_3
-    cx[141] =
-      p6_4 / ((1) + (1) * p6_4) - p6_3 / ((1) + (1) * p6_3) + T(0.75) * q5_6_4 + T(0.25) * q5_6_3 -
-      1
-    cx[142] =
-      p7_4 / ((1) + (1) * p7_4) - p7_3 / ((1) + (1) * p7_3) - T(0.75) * q7_8_4 + f5_7_4 -
-      T(0.25) * q7_8_3
+      p5_4 / (1 + p5_4) - p5_3 / (1 + p5_3) - θ * q5_6_4 - f5_7_4 + θ * q4_5_4 - (1 - θ) * q5_6_3 +
+      (1 - θ) * q4_5_3
+    cx[141] = p6_4 / (1 + p6_4) - p6_3 / (1 + p6_3) + θ * q5_6_4 + (1 - θ) * q5_6_3 - 1
+    cx[142] = p7_4 / (1 + p7_4) - p7_3 / (1 + p7_3) - θ * q7_8_4 + f5_7_4 - (1 - θ) * q7_8_3
     cx[143] =
-      p8_4 / ((1) + (1) * p8_4) - p8_3 / ((1) + (1) * p8_3) - T(0.75) * q8_9_4 - T(0.75) * q8_10_4 -
-      T(0.75) * q8_11_4 + T(0.75) * q7_8_4 - T(0.25) * q8_9_3 - T(0.25) * q8_10_3 -
-      T(0.25) * q8_11_3 + T(0.25) * q7_8_3
-    cx[144] =
-      p9_4 / ((1) + (1) * p9_4) - p9_3 / ((1) + (1) * p9_3) + T(0.75) * q8_9_4 + T(0.25) * q8_9_3
-    cx[145] =
-      p10_4 / ((1) + (1) * p10_4) - p10_3 / ((1) + (1) * p10_3) +
-      T(0.75) * q8_10_4 +
-      T(0.25) * q8_10_3 - 1
+      p8_4 / (1 + p8_4) - p8_3 / (1 + p8_3) - θ * q8_9_4 - θ * q8_10_4 - θ * q8_11_4 + θ * q7_8_4 -
+      (1 - θ) * q8_9_3 - (1 - θ) * q8_10_3 - (1 - θ) * q8_11_3 + (1 - θ) * q7_8_3
+    cx[144] = p9_4 / (1 + p9_4) - p9_3 / (1 + p9_3) + θ * q8_9_4 + (1 - θ) * q8_9_3
+    cx[145] = p10_4 / (1 + p10_4) - p10_3 / (1 + p10_3) + θ * q8_10_4 + (1 - θ) * q8_10_3 - 1
     cx[146] =
-      p11_4 / ((1) + (1) * p11_4) - p11_3 / ((1) + (1) * p11_3) - T(0.75) * q11_12_4 +
-      T(0.75) * q8_11_4 - T(0.25) * q11_12_3 + T(0.25) * q8_11_3
+      p11_4 / (1 + p11_4) - p11_3 / (1 + p11_3) - θ * q11_12_4 + θ * q8_11_4 - (1 - θ) * q11_12_3 +
+      (1 - θ) * q8_11_3
     cx[147] =
-      p12_4 / ((1) + (1) * p12_4) - p12_3 / ((1) + (1) * p12_3) - T(0.75) * q12_13_4 +
-      T(0.75) * q11_12_4 - T(0.25) * q12_13_3 + T(0.25) * q11_12_3
+      p12_4 / (1 + p12_4) - p12_3 / (1 + p12_3) - θ * q12_13_4 + θ * q11_12_4 - (1 - θ) * q12_13_3 +
+      (1 - θ) * q11_12_3
     cx[148] =
-      p13_4 / ((1) + (1) * p13_4) - p13_3 / ((1) + (1) * p13_3) - T(0.75) * q13_14_4 -
-      T(0.75) * q13_15_4 + T(0.75) * q12_13_4 - T(0.25) * q13_14_3 - T(0.25) * q13_15_3 +
-      T(0.25) * q12_13_3 - 1
-    cx[149] =
-      p14_4 / ((1) + (1) * p14_4) - p14_3 / ((1) + (1) * p14_3) +
-      T(0.75) * q13_14_4 +
-      T(0.25) * q13_14_3
+      p13_4 / (1 + p13_4) - p13_3 / (1 + p13_3) - θ * q13_14_4 - θ * q13_15_4 + θ * q12_13_4 -
+      (1 - θ) * q13_14_3 - (1 - θ) * q13_15_3 + (1 - θ) * q12_13_3 - 1
+    cx[149] = p14_4 / (1 + p14_4) - p14_3 / (1 + p14_3) + θ * q13_14_4 + (1 - θ) * q13_14_3
     cx[150] =
-      p15_4 / ((1) + (1) * p15_4) - p15_3 / ((1) + (1) * p15_3) - T(0.75) * q15_16_4 +
-      T(0.75) * q13_15_4 - T(0.25) * q15_16_3 + T(0.25) * q13_15_3 - 1
+      p15_4 / (1 + p15_4) - p15_3 / (1 + p15_3) - θ * q15_16_4 + θ * q13_15_4 - (1 - θ) * q15_16_3 +
+      (1 - θ) * q13_15_3 - 1
     cx[151] =
-      p16_4 / ((1) + (1) * p16_4) - p16_3 / ((1) + (1) * p16_3) +
-      T(0.75) * q15_16_4 +
-      T(0.25) * q15_16_3 - out16_4
+      p16_4 / (1 + p16_4) - p16_3 / (1 + p16_3) + θ * q15_16_4 + (1 - θ) * q15_16_3 - out16_4
     cx[152] =
-      p17_4 / ((1) + (1) * p17_4) - p17_3 / ((1) + (1) * p17_3) - T(0.75) * q17_18_4 +
-      T(0.75) * q1_17_4 - T(0.25) * q17_18_3 + T(0.25) * q1_17_3 - 1
+      p17_4 / (1 + p17_4) - p17_3 / (1 + p17_3) - θ * q17_18_4 + θ * q1_17_4 - (1 - θ) * q17_18_3 +
+      (1 - θ) * q1_17_3 - 1
     cx[153] =
-      p18_4 / ((1) + (1) * p18_4) - p18_3 / ((1) + (1) * p18_3) - T(0.75) * q18_19_4 +
-      T(0.75) * q17_18_4 - T(0.25) * q18_19_3 + T(0.25) * q17_18_3 - 1
+      p18_4 / (1 + p18_4) - p18_3 / (1 + p18_3) - θ * q18_19_4 + θ * q17_18_4 - (1 - θ) * q18_19_3 +
+      (1 - θ) * q17_18_3 - 1
     cx[154] =
-      p19_4 / ((1) + (1) * p19_4) - p19_3 / ((1) + (1) * p19_3) - f19_20_4 +
-      T(0.75) * q18_19_4 +
-      T(0.25) * q18_19_3
+      p19_4 / (1 + p19_4) - p19_3 / (1 + p19_3) - f19_20_4 + θ * q18_19_4 + (1 - θ) * q18_19_3
     cx[155] =
-      p20_4 / ((1) + (1) * p20_4) - p20_3 / ((1) + (1) * p20_3) - T(0.75) * q20_21_4 + f19_20_4 -
-      T(0.25) * q20_21_3
+      p20_4 / (1 + p20_4) - p20_3 / (1 + p20_3) - θ * q20_21_4 + f19_20_4 - (1 - θ) * q20_21_3
     cx[156] =
-      p21_4 / ((1) + (1) * p21_4) - p21_3 / ((1) + (1) * p21_3) - T(0.75) * q21_22_4 +
-      T(0.75) * q20_21_4 - T(0.25) * q21_22_3 + T(0.25) * q20_21_3 - 1
+      p21_4 / (1 + p21_4) - p21_3 / (1 + p21_3) - θ * q21_22_4 + θ * q20_21_4 - (1 - θ) * q21_22_3 +
+      (1 - θ) * q20_21_3 - 1
     cx[157] =
-      p22_4 / ((1) + (1) * p22_4) - p22_3 / ((1) + (1) * p22_3) - T(0.75) * q22_23_4 +
-      T(0.75) * q21_22_4 - T(0.25) * q22_23_3 + T(0.25) * q21_22_3 - 1
+      p22_4 / (1 + p22_4) - p22_3 / (1 + p22_3) - θ * q22_23_4 + θ * q21_22_4 - (1 - θ) * q22_23_3 +
+      (1 - θ) * q21_22_3 - 1
     cx[158] =
-      p23_4 / ((1) + (1) * p23_4) - p23_3 / ((1) + (1) * p23_3) +
-      T(0.75) * q22_23_4 +
-      T(0.25) * q22_23_3 - out23_4
+      p23_4 / (1 + p23_4) - p23_3 / (1 + p23_3) + θ * q22_23_4 + (1 - θ) * q22_23_3 - out23_4
     cx[159] = p3_4 * r3_4_4 - p4_4
     cx[160] = p5_4 * r5_7_4 - p7_4
     cx[161] = p19_4 * r19_20_4 - p20_4
-    cx[162] =
-      p1_4 * p1_4 - p2_4 * p2_4 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p1_4 + p2_4)) * ((abs(q1_2_4))^T(1.8539))
-    cx[163] =
-      p1_4 * p1_4 - p17_4 * p17_4 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p1_4 + p17_4)) * ((abs(q1_17_4))^T(1.8539))
-    cx[164] =
-      p2_4 * p2_4 - p3_4 * p3_4 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p2_4 + p3_4)) * ((abs(q2_3_4))^T(1.8539))
-    cx[165] =
-      p4_4 * p4_4 - p5_4 * p5_4 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p4_4 + p5_4)) * ((abs(q4_5_4))^T(1.8539))
-    cx[166] =
-      p5_4 * p5_4 - p6_4 * p6_4 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p5_4 + p6_4)) * ((abs(q5_6_4))^T(1.8539))
-    cx[167] =
-      p7_4 * p7_4 - p8_4 * p8_4 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p7_4 + p8_4)) * ((abs(q7_8_4))^T(1.8539))
-    cx[168] =
-      p8_4 * p8_4 - p9_4 * p9_4 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p8_4 + p9_4)) * ((abs(q8_9_4))^T(1.8539))
-    cx[169] =
-      p8_4 * p8_4 - p10_4 * p10_4 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p8_4 + p10_4)) * ((abs(q8_10_4))^T(1.8539))
-    cx[170] =
-      p8_4 * p8_4 - p11_4 * p11_4 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p8_4 + p11_4)) * ((abs(q8_11_4))^T(1.8539))
-    cx[171] =
-      p11_4 * p11_4 - p12_4 * p12_4 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p11_4 + p12_4)) * ((abs(q11_12_4))^T(1.8539))
-    cx[172] =
-      p12_4 * p12_4 - p13_4 * p13_4 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p12_4 + p13_4)) * ((abs(q12_13_4))^T(1.8539))
-    cx[173] =
-      p13_4 * p13_4 - p14_4 * p14_4 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p13_4 + p14_4)) * ((abs(q13_14_4))^T(1.8539))
-    cx[174] =
-      p13_4 * p13_4 - p15_4 * p15_4 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p13_4 + p15_4)) * ((abs(q13_15_4))^T(1.8539))
-    cx[175] =
-      p15_4 * p15_4 - p16_4 * p16_4 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p15_4 + p16_4)) * ((abs(q15_16_4))^T(1.8539))
-    cx[176] =
-      p17_4 * p17_4 - p18_4 * p18_4 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p17_4 + p18_4)) * ((abs(q17_18_4))^T(1.8539))
-    cx[177] =
-      p18_4 * p18_4 - p19_4 * p19_4 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p18_4 + p19_4)) * ((abs(q18_19_4))^T(1.8539))
-    cx[178] =
-      p20_4 * p20_4 - p21_4 * p21_4 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p20_4 + p21_4)) * ((abs(q20_21_4))^T(1.8539))
-    cx[179] =
-      p21_4 * p21_4 - p22_4 * p22_4 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p21_4 + p22_4)) * ((abs(q21_22_4))^T(1.8539))
-    cx[180] =
-      p22_4 * p22_4 - p23_4 * p23_4 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p22_4 + p23_4)) * ((abs(q22_23_4))^T(1.8539))
+    cx[162] = p1_4 * p1_4 - p2_4 * p2_4 - h * (1 + γ * (p1_4 + p2_4)) * (abs(q1_2_4)^α)
+    cx[163] = p1_4 * p1_4 - p17_4 * p17_4 - h * (1 + γ * (p1_4 + p17_4)) * (abs(q1_17_4)^α)
+    cx[164] = p2_4 * p2_4 - p3_4 * p3_4 - h * (1 + γ * (p2_4 + p3_4)) * (abs(q2_3_4)^α)
+    cx[165] = p4_4 * p4_4 - p5_4 * p5_4 - h * (1 + γ * (p4_4 + p5_4)) * (abs(q4_5_4)^α)
+    cx[166] = p5_4 * p5_4 - p6_4 * p6_4 - h * (1 + γ * (p5_4 + p6_4)) * (abs(q5_6_4)^α)
+    cx[167] = p7_4 * p7_4 - p8_4 * p8_4 - h * (1 + γ * (p7_4 + p8_4)) * (abs(q7_8_4)^α)
+    cx[168] = p8_4 * p8_4 - p9_4 * p9_4 - h * (1 + γ * (p8_4 + p9_4)) * (abs(q8_9_4)^α)
+    cx[169] = p8_4 * p8_4 - p10_4 * p10_4 - h * (1 + γ * (p8_4 + p10_4)) * (abs(q8_10_4)^α)
+    cx[170] = p8_4 * p8_4 - p11_4 * p11_4 - h * (1 + γ * (p8_4 + p11_4)) * (abs(q8_11_4)^α)
+    cx[171] = p11_4 * p11_4 - p12_4 * p12_4 - h * (1 + γ * (p11_4 + p12_4)) * (abs(q11_12_4)^α)
+    cx[172] = p12_4 * p12_4 - p13_4 * p13_4 - h * (1 + γ * (p12_4 + p13_4)) * (abs(q12_13_4)^α)
+    cx[173] = p13_4 * p13_4 - p14_4 * p14_4 - h * (1 + γ * (p13_4 + p14_4)) * (abs(q13_14_4)^α)
+    cx[174] = p13_4 * p13_4 - p15_4 * p15_4 - h * (1 + γ * (p13_4 + p15_4)) * (abs(q13_15_4)^α)
+    cx[175] = p15_4 * p15_4 - p16_4 * p16_4 - h * (1 + γ * (p15_4 + p16_4)) * (abs(q15_16_4)^α)
+    cx[176] = p17_4 * p17_4 - p18_4 * p18_4 - h * (1 + γ * (p17_4 + p18_4)) * (abs(q17_18_4)^α)
+    cx[177] = p18_4 * p18_4 - p19_4 * p19_4 - h * (1 + γ * (p18_4 + p19_4)) * (abs(q18_19_4)^α)
+    cx[178] = p20_4 * p20_4 - p21_4 * p21_4 - h * (1 + γ * (p20_4 + p21_4)) * (abs(q20_21_4)^α)
+    cx[179] = p21_4 * p21_4 - p22_4 * p22_4 - h * (1 + γ * (p21_4 + p22_4)) * (abs(q21_22_4)^α)
+    cx[180] = p22_4 * p22_4 - p23_4 * p23_4 - h * (1 + γ * (p22_4 + p23_4)) * (abs(q22_23_4)^α)
+
+    # time step 5
+
     cx[181] =
-      p1_5 / ((1) + (1) * p1_5) - p1_4 / ((1) + (1) * p1_4) - T(0.75) * q1_17_5 - T(0.75) * q1_2_5 +
-      in1_5 - T(0.25) * q1_17_4 - T(0.25) * q1_2_4
+      p1_5 / (1 + p1_5) - p1_4 / (1 + p1_4) - θ * q1_17_5 - θ * q1_2_5 + in1_5 - (1 - θ) * q1_17_4 -
+      (1 - θ) * q1_2_4
     cx[182] =
-      p2_5 / ((1) + (1) * p2_5) - p2_4 / ((1) + (1) * p2_4) - T(0.75) * q2_3_5 + T(0.75) * q1_2_5 -
-      T(0.25) * q2_3_4 + T(0.25) * q1_2_4 - 1
-    cx[183] =
-      p3_5 / ((1) + (1) * p3_5) - p3_4 / ((1) + (1) * p3_4) - f3_4_5 +
-      T(0.75) * q2_3_5 +
-      T(0.25) * q2_3_4
-    cx[184] =
-      p4_5 / ((1) + (1) * p4_5) - p4_4 / ((1) + (1) * p4_4) - T(0.75) * q4_5_5 + f3_4_5 -
-      T(0.25) * q4_5_4
+      p2_5 / (1 + p2_5) - p2_4 / (1 + p2_4) - θ * q2_3_5 + θ * q1_2_5 - (1 - θ) * q2_3_4 +
+      (1 - θ) * q1_2_4 - 1
+    cx[183] = p3_5 / (1 + p3_5) - p3_4 / (1 + p3_4) - f3_4_5 + θ * q2_3_5 + (1 - θ) * q2_3_4
+    cx[184] = p4_5 / (1 + p4_5) - p4_4 / (1 + p4_4) - θ * q4_5_5 + f3_4_5 - (1 - θ) * q4_5_4
     cx[185] =
-      p5_5 / ((1) + (1) * p5_5) - p5_4 / ((1) + (1) * p5_4) - T(0.75) * q5_6_5 - f5_7_5 +
-      T(0.75) * q4_5_5 - T(0.25) * q5_6_4 + T(0.25) * q4_5_4
-    cx[186] =
-      p6_5 / ((1) + (1) * p6_5) - p6_4 / ((1) + (1) * p6_4) + T(0.75) * q5_6_5 + T(0.25) * q5_6_4 -
-      1
-    cx[187] =
-      p7_5 / ((1) + (1) * p7_5) - p7_4 / ((1) + (1) * p7_4) - T(0.75) * q7_8_5 + f5_7_5 -
-      T(0.25) * q7_8_4
+      p5_5 / (1 + p5_5) - p5_4 / (1 + p5_4) - θ * q5_6_5 - f5_7_5 + θ * q4_5_5 - (1 - θ) * q5_6_4 +
+      (1 - θ) * q4_5_4
+    cx[186] = p6_5 / (1 + p6_5) - p6_4 / (1 + p6_4) + θ * q5_6_5 + (1 - θ) * q5_6_4 - 1
+    cx[187] = p7_5 / (1 + p7_5) - p7_4 / (1 + p7_4) - θ * q7_8_5 + f5_7_5 - (1 - θ) * q7_8_4
     cx[188] =
-      p8_5 / ((1) + (1) * p8_5) - p8_4 / ((1) + (1) * p8_4) - T(0.75) * q8_9_5 - T(0.75) * q8_10_5 -
-      T(0.75) * q8_11_5 + T(0.75) * q7_8_5 - T(0.25) * q8_9_4 - T(0.25) * q8_10_4 -
-      T(0.25) * q8_11_4 + T(0.25) * q7_8_4
-    cx[189] =
-      p9_5 / ((1) + (1) * p9_5) - p9_4 / ((1) + (1) * p9_4) + T(0.75) * q8_9_5 + T(0.25) * q8_9_4
-    cx[190] =
-      p10_5 / ((1) + (1) * p10_5) - p10_4 / ((1) + (1) * p10_4) +
-      T(0.75) * q8_10_5 +
-      T(0.25) * q8_10_4 - 1
+      p8_5 / (1 + p8_5) - p8_4 / (1 + p8_4) - θ * q8_9_5 - θ * q8_10_5 - θ * q8_11_5 + θ * q7_8_5 -
+      (1 - θ) * q8_9_4 - (1 - θ) * q8_10_4 - (1 - θ) * q8_11_4 + (1 - θ) * q7_8_4
+    cx[189] = p9_5 / (1 + p9_5) - p9_4 / (1 + p9_4) + θ * q8_9_5 + (1 - θ) * q8_9_4
+    cx[190] = p10_5 / (1 + p10_5) - p10_4 / (1 + p10_4) + θ * q8_10_5 + (1 - θ) * q8_10_4 - 1
     cx[191] =
-      p11_5 / ((1) + (1) * p11_5) - p11_4 / ((1) + (1) * p11_4) - T(0.75) * q11_12_5 +
-      T(0.75) * q8_11_5 - T(0.25) * q11_12_4 + T(0.25) * q8_11_4
+      p11_5 / (1 + p11_5) - p11_4 / (1 + p11_4) - θ * q11_12_5 + θ * q8_11_5 - (1 - θ) * q11_12_4 +
+      (1 - θ) * q8_11_4
     cx[192] =
-      p12_5 / ((1) + (1) * p12_5) - p12_4 / ((1) + (1) * p12_4) - T(0.75) * q12_13_5 +
-      T(0.75) * q11_12_5 - T(0.25) * q12_13_4 + T(0.25) * q11_12_4
+      p12_5 / (1 + p12_5) - p12_4 / (1 + p12_4) - θ * q12_13_5 + θ * q11_12_5 - (1 - θ) * q12_13_4 +
+      (1 - θ) * q11_12_4
     cx[193] =
-      p13_5 / ((1) + (1) * p13_5) - p13_4 / ((1) + (1) * p13_4) - T(0.75) * q13_14_5 -
-      T(0.75) * q13_15_5 + T(0.75) * q12_13_5 - T(0.25) * q13_14_4 - T(0.25) * q13_15_4 +
-      T(0.25) * q12_13_4 - 1
-    cx[194] =
-      p14_5 / ((1) + (1) * p14_5) - p14_4 / ((1) + (1) * p14_4) +
-      T(0.75) * q13_14_5 +
-      T(0.25) * q13_14_4
+      p13_5 / (1 + p13_5) - p13_4 / (1 + p13_4) - θ * q13_14_5 - θ * q13_15_5 + θ * q12_13_5 -
+      (1 - θ) * q13_14_4 - (1 - θ) * q13_15_4 + (1 - θ) * q12_13_4 - 1
+    cx[194] = p14_5 / (1 + p14_5) - p14_4 / (1 + p14_4) + θ * q13_14_5 + (1 - θ) * q13_14_4
     cx[195] =
-      p15_5 / ((1) + (1) * p15_5) - p15_4 / ((1) + (1) * p15_4) - T(0.75) * q15_16_5 +
-      T(0.75) * q13_15_5 - T(0.25) * q15_16_4 + T(0.25) * q13_15_4 - 1
+      p15_5 / (1 + p15_5) - p15_4 / (1 + p15_4) - θ * q15_16_5 + θ * q13_15_5 - (1 - θ) * q15_16_4 +
+      (1 - θ) * q13_15_4 - 1
     cx[196] =
-      p16_5 / ((1) + (1) * p16_5) - p16_4 / ((1) + (1) * p16_4) +
-      T(0.75) * q15_16_5 +
-      T(0.25) * q15_16_4 - out16_5
+      p16_5 / (1 + p16_5) - p16_4 / (1 + p16_4) + θ * q15_16_5 + (1 - θ) * q15_16_4 - out16_5
     cx[197] =
-      p17_5 / ((1) + (1) * p17_5) - p17_4 / ((1) + (1) * p17_4) - T(0.75) * q17_18_5 +
-      T(0.75) * q1_17_5 - T(0.25) * q17_18_4 + T(0.25) * q1_17_4 - 1
+      p17_5 / (1 + p17_5) - p17_4 / (1 + p17_4) - θ * q17_18_5 + θ * q1_17_5 - (1 - θ) * q17_18_4 +
+      (1 - θ) * q1_17_4 - 1
     cx[198] =
-      p18_5 / ((1) + (1) * p18_5) - p18_4 / ((1) + (1) * p18_4) - T(0.75) * q18_19_5 +
-      T(0.75) * q17_18_5 - T(0.25) * q18_19_4 + T(0.25) * q17_18_4 - 1
+      p18_5 / (1 + p18_5) - p18_4 / (1 + p18_4) - θ * q18_19_5 + θ * q17_18_5 - (1 - θ) * q18_19_4 +
+      (1 - θ) * q17_18_4 - 1
     cx[199] =
-      p19_5 / ((1) + (1) * p19_5) - p19_4 / ((1) + (1) * p19_4) - f19_20_5 +
-      T(0.75) * q18_19_5 +
-      T(0.25) * q18_19_4
+      p19_5 / (1 + p19_5) - p19_4 / (1 + p19_4) - f19_20_5 + θ * q18_19_5 + (1 - θ) * q18_19_4
     cx[200] =
-      p20_5 / ((1) + (1) * p20_5) - p20_4 / ((1) + (1) * p20_4) - T(0.75) * q20_21_5 + f19_20_5 -
-      T(0.25) * q20_21_4
+      p20_5 / (1 + p20_5) - p20_4 / (1 + p20_4) - θ * q20_21_5 + f19_20_5 - (1 - θ) * q20_21_4
     cx[201] =
-      p21_5 / ((1) + (1) * p21_5) - p21_4 / ((1) + (1) * p21_4) - T(0.75) * q21_22_5 +
-      T(0.75) * q20_21_5 - T(0.25) * q21_22_4 + T(0.25) * q20_21_4 - 1
+      p21_5 / (1 + p21_5) - p21_4 / (1 + p21_4) - θ * q21_22_5 + θ * q20_21_5 - (1 - θ) * q21_22_4 +
+      (1 - θ) * q20_21_4 - 1
     cx[202] =
-      p22_5 / ((1) + (1) * p22_5) - p22_4 / ((1) + (1) * p22_4) - T(0.75) * q22_23_5 +
-      T(0.75) * q21_22_5 - T(0.25) * q22_23_4 + T(0.25) * q21_22_4 - 1
+      p22_5 / (1 + p22_5) - p22_4 / (1 + p22_4) - θ * q22_23_5 + θ * q21_22_5 - (1 - θ) * q22_23_4 +
+      (1 - θ) * q21_22_4 - 1
     cx[203] =
-      p23_5 / ((1) + (1) * p23_5) - p23_4 / ((1) + (1) * p23_4) +
-      T(0.75) * q22_23_5 +
-      T(0.25) * q22_23_4 - out23_5
+      p23_5 / (1 + p23_5) - p23_4 / (1 + p23_4) + θ * q22_23_5 + (1 - θ) * q22_23_4 - out23_5
     cx[204] = p3_5 * r3_4_5 - p4_5
     cx[205] = p5_5 * r5_7_5 - p7_5
     cx[206] = p19_5 * r19_20_5 - p20_5
-    cx[207] =
-      p1_5 * p1_5 - p2_5 * p2_5 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p1_5 + p2_5)) * ((abs(q1_2_5))^T(1.8539))
-    cx[208] =
-      p1_5 * p1_5 - p17_5 * p17_5 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p1_5 + p17_5)) * ((abs(q1_17_5))^T(1.8539))
-    cx[209] =
-      p2_5 * p2_5 - p3_5 * p3_5 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p2_5 + p3_5)) * ((abs(q2_3_5))^T(1.8539))
-    cx[210] =
-      p4_5 * p4_5 - p5_5 * p5_5 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p4_5 + p5_5)) * ((abs(q4_5_5))^T(1.8539))
-    cx[211] =
-      p5_5 * p5_5 - p6_5 * p6_5 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p5_5 + p6_5)) * ((abs(q5_6_5))^T(1.8539))
-    cx[212] =
-      p7_5 * p7_5 - p8_5 * p8_5 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p7_5 + p8_5)) * ((abs(q7_8_5))^T(1.8539))
-    cx[213] =
-      p8_5 * p8_5 - p9_5 * p9_5 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p8_5 + p9_5)) * ((abs(q8_9_5))^T(1.8539))
-    cx[214] =
-      p8_5 * p8_5 - p10_5 * p10_5 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p8_5 + p10_5)) * ((abs(q8_10_5))^T(1.8539))
-    cx[215] =
-      p8_5 * p8_5 - p11_5 * p11_5 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p8_5 + p11_5)) * ((abs(q8_11_5))^T(1.8539))
-    cx[216] =
-      p11_5 * p11_5 - p12_5 * p12_5 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p11_5 + p12_5)) * ((abs(q11_12_5))^T(1.8539))
-    cx[217] =
-      p12_5 * p12_5 - p13_5 * p13_5 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p12_5 + p13_5)) * ((abs(q12_13_5))^T(1.8539))
-    cx[218] =
-      p13_5 * p13_5 - p14_5 * p14_5 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p13_5 + p14_5)) * ((abs(q13_14_5))^T(1.8539))
-    cx[219] =
-      p13_5 * p13_5 - p15_5 * p15_5 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p13_5 + p15_5)) * ((abs(q13_15_5))^T(1.8539))
-    cx[220] =
-      p15_5 * p15_5 - p16_5 * p16_5 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p15_5 + p16_5)) * ((abs(q15_16_5))^T(1.8539))
-    cx[221] =
-      p17_5 * p17_5 - p18_5 * p18_5 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p17_5 + p18_5)) * ((abs(q17_18_5))^T(1.8539))
-    cx[222] =
-      p18_5 * p18_5 - p19_5 * p19_5 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p18_5 + p19_5)) * ((abs(q18_19_5))^T(1.8539))
-    cx[223] =
-      p20_5 * p20_5 - p21_5 * p21_5 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p20_5 + p21_5)) * ((abs(q20_21_5))^T(1.8539))
-    cx[224] =
-      p21_5 * p21_5 - p22_5 * p22_5 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p21_5 + p22_5)) * ((abs(q21_22_5))^T(1.8539))
-    cx[225] =
-      p22_5 * p22_5 - p23_5 * p23_5 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p22_5 + p23_5)) * ((abs(q22_23_5))^T(1.8539))
+    cx[207] = p1_5 * p1_5 - p2_5 * p2_5 - h * (1 + γ * (p1_5 + p2_5)) * (abs(q1_2_5)^α)
+    cx[208] = p1_5 * p1_5 - p17_5 * p17_5 - h * (1 + γ * (p1_5 + p17_5)) * (abs(q1_17_5)^α)
+    cx[209] = p2_5 * p2_5 - p3_5 * p3_5 - h * (1 + γ * (p2_5 + p3_5)) * (abs(q2_3_5)^α)
+    cx[210] = p4_5 * p4_5 - p5_5 * p5_5 - h * (1 + γ * (p4_5 + p5_5)) * (abs(q4_5_5)^α)
+    cx[211] = p5_5 * p5_5 - p6_5 * p6_5 - h * (1 + γ * (p5_5 + p6_5)) * (abs(q5_6_5)^α)
+    cx[212] = p7_5 * p7_5 - p8_5 * p8_5 - h * (1 + γ * (p7_5 + p8_5)) * (abs(q7_8_5)^α)
+    cx[213] = p8_5 * p8_5 - p9_5 * p9_5 - h * (1 + γ * (p8_5 + p9_5)) * (abs(q8_9_5)^α)
+    cx[214] = p8_5 * p8_5 - p10_5 * p10_5 - h * (1 + γ * (p8_5 + p10_5)) * (abs(q8_10_5)^α)
+    cx[215] = p8_5 * p8_5 - p11_5 * p11_5 - h * (1 + γ * (p8_5 + p11_5)) * (abs(q8_11_5)^α)
+    cx[216] = p11_5 * p11_5 - p12_5 * p12_5 - h * (1 + γ * (p11_5 + p12_5)) * (abs(q11_12_5)^α)
+    cx[217] = p12_5 * p12_5 - p13_5 * p13_5 - h * (1 + γ * (p12_5 + p13_5)) * (abs(q12_13_5)^α)
+    cx[218] = p13_5 * p13_5 - p14_5 * p14_5 - h * (1 + γ * (p13_5 + p14_5)) * (abs(q13_14_5)^α)
+    cx[219] = p13_5 * p13_5 - p15_5 * p15_5 - h * (1 + γ * (p13_5 + p15_5)) * (abs(q13_15_5)^α)
+    cx[220] = p15_5 * p15_5 - p16_5 * p16_5 - h * (1 + γ * (p15_5 + p16_5)) * (abs(q15_16_5)^α)
+    cx[221] = p17_5 * p17_5 - p18_5 * p18_5 - h * (1 + γ * (p17_5 + p18_5)) * (abs(q17_18_5)^α)
+    cx[222] = p18_5 * p18_5 - p19_5 * p19_5 - h * (1 + γ * (p18_5 + p19_5)) * (abs(q18_19_5)^α)
+    cx[223] = p20_5 * p20_5 - p21_5 * p21_5 - h * (1 + γ * (p20_5 + p21_5)) * (abs(q20_21_5)^α)
+    cx[224] = p21_5 * p21_5 - p22_5 * p22_5 - h * (1 + γ * (p21_5 + p22_5)) * (abs(q21_22_5)^α)
+    cx[225] = p22_5 * p22_5 - p23_5 * p23_5 - h * (1 + γ * (p22_5 + p23_5)) * (abs(q22_23_5)^α)
+
+    # time step 6
+
     cx[226] =
-      p1_6 / ((1) + (1) * p1_6) - p1_5 / ((1) + (1) * p1_5) - T(0.75) * q1_17_6 - T(0.75) * q1_2_6 +
-      in1_6 - T(0.25) * q1_17_5 - T(0.25) * q1_2_5
+      p1_6 / (1 + p1_6) - p1_5 / (1 + p1_5) - θ * q1_17_6 - θ * q1_2_6 + in1_6 - (1 - θ) * q1_17_5 -
+      (1 - θ) * q1_2_5
     cx[227] =
-      p2_6 / ((1) + (1) * p2_6) - p2_5 / ((1) + (1) * p2_5) - T(0.75) * q2_3_6 + T(0.75) * q1_2_6 -
-      T(0.25) * q2_3_5 + T(0.25) * q1_2_5 - 1
-    cx[228] =
-      p3_6 / ((1) + (1) * p3_6) - p3_5 / ((1) + (1) * p3_5) - f3_4_6 +
-      T(0.75) * q2_3_6 +
-      T(0.25) * q2_3_5
-    cx[229] =
-      p4_6 / ((1) + (1) * p4_6) - p4_5 / ((1) + (1) * p4_5) - T(0.75) * q4_5_6 + f3_4_6 -
-      T(0.25) * q4_5_5
+      p2_6 / (1 + p2_6) - p2_5 / (1 + p2_5) - θ * q2_3_6 + θ * q1_2_6 - (1 - θ) * q2_3_5 +
+      (1 - θ) * q1_2_5 - 1
+    cx[228] = p3_6 / (1 + p3_6) - p3_5 / (1 + p3_5) - f3_4_6 + θ * q2_3_6 + (1 - θ) * q2_3_5
+    cx[229] = p4_6 / (1 + p4_6) - p4_5 / (1 + p4_5) - θ * q4_5_6 + f3_4_6 - (1 - θ) * q4_5_5
     cx[230] =
-      p5_6 / ((1) + (1) * p5_6) - p5_5 / ((1) + (1) * p5_5) - T(0.75) * q5_6_6 - f5_7_6 +
-      T(0.75) * q4_5_6 - T(0.25) * q5_6_5 + T(0.25) * q4_5_5
-    cx[231] =
-      p6_6 / ((1) + (1) * p6_6) - p6_5 / ((1) + (1) * p6_5) + T(0.75) * q5_6_6 + T(0.25) * q5_6_5 -
-      1
-    cx[232] =
-      p7_6 / ((1) + (1) * p7_6) - p7_5 / ((1) + (1) * p7_5) - T(0.75) * q7_8_6 + f5_7_6 -
-      T(0.25) * q7_8_5
+      p5_6 / (1 + p5_6) - p5_5 / (1 + p5_5) - θ * q5_6_6 - f5_7_6 + θ * q4_5_6 - (1 - θ) * q5_6_5 +
+      (1 - θ) * q4_5_5
+    cx[231] = p6_6 / (1 + p6_6) - p6_5 / (1 + p6_5) + θ * q5_6_6 + (1 - θ) * q5_6_5 - 1
+    cx[232] = p7_6 / (1 + p7_6) - p7_5 / (1 + p7_5) - θ * q7_8_6 + f5_7_6 - (1 - θ) * q7_8_5
     cx[233] =
-      p8_6 / ((1) + (1) * p8_6) - p8_5 / ((1) + (1) * p8_5) - T(0.75) * q8_9_6 - T(0.75) * q8_10_6 -
-      T(0.75) * q8_11_6 + T(0.75) * q7_8_6 - T(0.25) * q8_9_5 - T(0.25) * q8_10_5 -
-      T(0.25) * q8_11_5 + T(0.25) * q7_8_5
-    cx[234] =
-      p9_6 / ((1) + (1) * p9_6) - p9_5 / ((1) + (1) * p9_5) + T(0.75) * q8_9_6 + T(0.25) * q8_9_5
-    cx[235] =
-      p10_6 / ((1) + (1) * p10_6) - p10_5 / ((1) + (1) * p10_5) +
-      T(0.75) * q8_10_6 +
-      T(0.25) * q8_10_5 - 1
+      p8_6 / (1 + p8_6) - p8_5 / (1 + p8_5) - θ * q8_9_6 - θ * q8_10_6 - θ * q8_11_6 + θ * q7_8_6 -
+      (1 - θ) * q8_9_5 - (1 - θ) * q8_10_5 - (1 - θ) * q8_11_5 + (1 - θ) * q7_8_5
+    cx[234] = p9_6 / (1 + p9_6) - p9_5 / (1 + p9_5) + θ * q8_9_6 + (1 - θ) * q8_9_5
+    cx[235] = p10_6 / (1 + p10_6) - p10_5 / (1 + p10_5) + θ * q8_10_6 + (1 - θ) * q8_10_5 - 1
     cx[236] =
-      p11_6 / ((1) + (1) * p11_6) - p11_5 / ((1) + (1) * p11_5) - T(0.75) * q11_12_6 +
-      T(0.75) * q8_11_6 - T(0.25) * q11_12_5 + T(0.25) * q8_11_5
+      p11_6 / (1 + p11_6) - p11_5 / (1 + p11_5) - θ * q11_12_6 + θ * q8_11_6 - (1 - θ) * q11_12_5 +
+      (1 - θ) * q8_11_5
     cx[237] =
-      p12_6 / ((1) + (1) * p12_6) - p12_5 / ((1) + (1) * p12_5) - T(0.75) * q12_13_6 +
-      T(0.75) * q11_12_6 - T(0.25) * q12_13_5 + T(0.25) * q11_12_5
+      p12_6 / (1 + p12_6) - p12_5 / (1 + p12_5) - θ * q12_13_6 + θ * q11_12_6 - (1 - θ) * q12_13_5 +
+      (1 - θ) * q11_12_5
     cx[238] =
-      p13_6 / ((1) + (1) * p13_6) - p13_5 / ((1) + (1) * p13_5) - T(0.75) * q13_14_6 -
-      T(0.75) * q13_15_6 + T(0.75) * q12_13_6 - T(0.25) * q13_14_5 - T(0.25) * q13_15_5 +
-      T(0.25) * q12_13_5 - 1
-    cx[239] =
-      p14_6 / ((1) + (1) * p14_6) - p14_5 / ((1) + (1) * p14_5) +
-      T(0.75) * q13_14_6 +
-      T(0.25) * q13_14_5
+      p13_6 / (1 + p13_6) - p13_5 / (1 + p13_5) - θ * q13_14_6 - θ * q13_15_6 + θ * q12_13_6 -
+      (1 - θ) * q13_14_5 - (1 - θ) * q13_15_5 + (1 - θ) * q12_13_5 - 1
+    cx[239] = p14_6 / (1 + p14_6) - p14_5 / (1 + p14_5) + θ * q13_14_6 + (1 - θ) * q13_14_5
     cx[240] =
-      p15_6 / ((1) + (1) * p15_6) - p15_5 / ((1) + (1) * p15_5) - T(0.75) * q15_16_6 +
-      T(0.75) * q13_15_6 - T(0.25) * q15_16_5 + T(0.25) * q13_15_5 - 1
+      p15_6 / (1 + p15_6) - p15_5 / (1 + p15_5) - θ * q15_16_6 + θ * q13_15_6 - (1 - θ) * q15_16_5 +
+      (1 - θ) * q13_15_5 - 1
     cx[241] =
-      p16_6 / ((1) + (1) * p16_6) - p16_5 / ((1) + (1) * p16_5) +
-      T(0.75) * q15_16_6 +
-      T(0.25) * q15_16_5 - out16_6
+      p16_6 / (1 + p16_6) - p16_5 / (1 + p16_5) + θ * q15_16_6 + (1 - θ) * q15_16_5 - out16_6
     cx[242] =
-      p17_6 / ((1) + (1) * p17_6) - p17_5 / ((1) + (1) * p17_5) - T(0.75) * q17_18_6 +
-      T(0.75) * q1_17_6 - T(0.25) * q17_18_5 + T(0.25) * q1_17_5 - 1
+      p17_6 / (1 + p17_6) - p17_5 / (1 + p17_5) - θ * q17_18_6 + θ * q1_17_6 - (1 - θ) * q17_18_5 +
+      (1 - θ) * q1_17_5 - 1
     cx[243] =
-      p18_6 / ((1) + (1) * p18_6) - p18_5 / ((1) + (1) * p18_5) - T(0.75) * q18_19_6 +
-      T(0.75) * q17_18_6 - T(0.25) * q18_19_5 + T(0.25) * q17_18_5 - 1
+      p18_6 / (1 + p18_6) - p18_5 / (1 + p18_5) - θ * q18_19_6 + θ * q17_18_6 - (1 - θ) * q18_19_5 +
+      (1 - θ) * q17_18_5 - 1
     cx[244] =
-      p19_6 / ((1) + (1) * p19_6) - p19_5 / ((1) + (1) * p19_5) - f19_20_6 +
-      T(0.75) * q18_19_6 +
-      T(0.25) * q18_19_5
+      p19_6 / (1 + p19_6) - p19_5 / (1 + p19_5) - f19_20_6 + θ * q18_19_6 + (1 - θ) * q18_19_5
     cx[245] =
-      p20_6 / ((1) + (1) * p20_6) - p20_5 / ((1) + (1) * p20_5) - T(0.75) * q20_21_6 + f19_20_6 -
-      T(0.25) * q20_21_5
+      p20_6 / (1 + p20_6) - p20_5 / (1 + p20_5) - θ * q20_21_6 + f19_20_6 - (1 - θ) * q20_21_5
     cx[246] =
-      p21_6 / ((1) + (1) * p21_6) - p21_5 / ((1) + (1) * p21_5) - T(0.75) * q21_22_6 +
-      T(0.75) * q20_21_6 - T(0.25) * q21_22_5 + T(0.25) * q20_21_5 - 1
+      p21_6 / (1 + p21_6) - p21_5 / (1 + p21_5) - θ * q21_22_6 + θ * q20_21_6 - (1 - θ) * q21_22_5 +
+      (1 - θ) * q20_21_5 - 1
     cx[247] =
-      p22_6 / ((1) + (1) * p22_6) - p22_5 / ((1) + (1) * p22_5) - T(0.75) * q22_23_6 +
-      T(0.75) * q21_22_6 - T(0.25) * q22_23_5 + T(0.25) * q21_22_5 - 1
+      p22_6 / (1 + p22_6) - p22_5 / (1 + p22_5) - θ * q22_23_6 + θ * q21_22_6 - (1 - θ) * q22_23_5 +
+      (1 - θ) * q21_22_5 - 1
     cx[248] =
-      p23_6 / ((1) + (1) * p23_6) - p23_5 / ((1) + (1) * p23_5) +
-      T(0.75) * q22_23_6 +
-      T(0.25) * q22_23_5 - out23_6
+      p23_6 / (1 + p23_6) - p23_5 / (1 + p23_5) + θ * q22_23_6 + (1 - θ) * q22_23_5 - out23_6
     cx[249] = p3_6 * r3_4_6 - p4_6
     cx[250] = p5_6 * r5_7_6 - p7_6
     cx[251] = p19_6 * r19_20_6 - p20_6
-    cx[252] =
-      p1_6 * p1_6 - p2_6 * p2_6 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p1_6 + p2_6)) * ((abs(q1_2_6))^T(1.8539))
-    cx[253] =
-      p1_6 * p1_6 - p17_6 * p17_6 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p1_6 + p17_6)) * ((abs(q1_17_6))^T(1.8539))
-    cx[254] =
-      p2_6 * p2_6 - p3_6 * p3_6 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p2_6 + p3_6)) * ((abs(q2_3_6))^T(1.8539))
-    cx[255] =
-      p4_6 * p4_6 - p5_6 * p5_6 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p4_6 + p5_6)) * ((abs(q4_5_6))^T(1.8539))
-    cx[256] =
-      p5_6 * p5_6 - p6_6 * p6_6 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p5_6 + p6_6)) * ((abs(q5_6_6))^T(1.8539))
-    cx[257] =
-      p7_6 * p7_6 - p8_6 * p8_6 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p7_6 + p8_6)) * ((abs(q7_8_6))^T(1.8539))
-    cx[258] =
-      p8_6 * p8_6 - p9_6 * p9_6 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p8_6 + p9_6)) * ((abs(q8_9_6))^T(1.8539))
-    cx[259] =
-      p8_6 * p8_6 - p10_6 * p10_6 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p8_6 + p10_6)) * ((abs(q8_10_6))^T(1.8539))
-    cx[260] =
-      p8_6 * p8_6 - p11_6 * p11_6 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p8_6 + p11_6)) * ((abs(q8_11_6))^T(1.8539))
-    cx[261] =
-      p11_6 * p11_6 - p12_6 * p12_6 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p11_6 + p12_6)) * ((abs(q11_12_6))^T(1.8539))
-    cx[262] =
-      p12_6 * p12_6 - p13_6 * p13_6 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p12_6 + p13_6)) * ((abs(q12_13_6))^T(1.8539))
-    cx[263] =
-      p13_6 * p13_6 - p14_6 * p14_6 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p13_6 + p14_6)) * ((abs(q13_14_6))^T(1.8539))
-    cx[264] =
-      p13_6 * p13_6 - p15_6 * p15_6 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p13_6 + p15_6)) * ((abs(q13_15_6))^T(1.8539))
-    cx[265] =
-      p15_6 * p15_6 - p16_6 * p16_6 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p15_6 + p16_6)) * ((abs(q15_16_6))^T(1.8539))
-    cx[266] =
-      p17_6 * p17_6 - p18_6 * p18_6 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p17_6 + p18_6)) * ((abs(q17_18_6))^T(1.8539))
-    cx[267] =
-      p18_6 * p18_6 - p19_6 * p19_6 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p18_6 + p19_6)) * ((abs(q18_19_6))^T(1.8539))
-    cx[268] =
-      p20_6 * p20_6 - p21_6 * p21_6 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p20_6 + p21_6)) * ((abs(q20_21_6))^T(1.8539))
-    cx[269] =
-      p21_6 * p21_6 - p22_6 * p22_6 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p21_6 + p22_6)) * ((abs(q21_22_6))^T(1.8539))
-    cx[270] =
-      p22_6 * p22_6 - p23_6 * p23_6 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p22_6 + p23_6)) * ((abs(q22_23_6))^T(1.8539))
+    cx[252] = p1_6 * p1_6 - p2_6 * p2_6 - h * (1 + γ * (p1_6 + p2_6)) * (abs(q1_2_6)^α)
+    cx[253] = p1_6 * p1_6 - p17_6 * p17_6 - h * (1 + γ * (p1_6 + p17_6)) * (abs(q1_17_6)^α)
+    cx[254] = p2_6 * p2_6 - p3_6 * p3_6 - h * (1 + γ * (p2_6 + p3_6)) * (abs(q2_3_6)^α)
+    cx[255] = p4_6 * p4_6 - p5_6 * p5_6 - h * (1 + γ * (p4_6 + p5_6)) * (abs(q4_5_6)^α)
+    cx[256] = p5_6 * p5_6 - p6_6 * p6_6 - h * (1 + γ * (p5_6 + p6_6)) * (abs(q5_6_6)^α)
+    cx[257] = p7_6 * p7_6 - p8_6 * p8_6 - h * (1 + γ * (p7_6 + p8_6)) * (abs(q7_8_6)^α)
+    cx[258] = p8_6 * p8_6 - p9_6 * p9_6 - h * (1 + γ * (p8_6 + p9_6)) * (abs(q8_9_6)^α)
+    cx[259] = p8_6 * p8_6 - p10_6 * p10_6 - h * (1 + γ * (p8_6 + p10_6)) * (abs(q8_10_6)^α)
+    cx[260] = p8_6 * p8_6 - p11_6 * p11_6 - h * (1 + γ * (p8_6 + p11_6)) * (abs(q8_11_6)^α)
+    cx[261] = p11_6 * p11_6 - p12_6 * p12_6 - h * (1 + γ * (p11_6 + p12_6)) * (abs(q11_12_6)^α)
+    cx[262] = p12_6 * p12_6 - p13_6 * p13_6 - h * (1 + γ * (p12_6 + p13_6)) * (abs(q12_13_6)^α)
+    cx[263] = p13_6 * p13_6 - p14_6 * p14_6 - h * (1 + γ * (p13_6 + p14_6)) * (abs(q13_14_6)^α)
+    cx[264] = p13_6 * p13_6 - p15_6 * p15_6 - h * (1 + γ * (p13_6 + p15_6)) * (abs(q13_15_6)^α)
+    cx[265] = p15_6 * p15_6 - p16_6 * p16_6 - h * (1 + γ * (p15_6 + p16_6)) * (abs(q15_16_6)^α)
+    cx[266] = p17_6 * p17_6 - p18_6 * p18_6 - h * (1 + γ * (p17_6 + p18_6)) * (abs(q17_18_6)^α)
+    cx[267] = p18_6 * p18_6 - p19_6 * p19_6 - h * (1 + γ * (p18_6 + p19_6)) * (abs(q18_19_6)^α)
+    cx[268] = p20_6 * p20_6 - p21_6 * p21_6 - h * (1 + γ * (p20_6 + p21_6)) * (abs(q20_21_6)^α)
+    cx[269] = p21_6 * p21_6 - p22_6 * p22_6 - h * (1 + γ * (p21_6 + p22_6)) * (abs(q21_22_6)^α)
+    cx[270] = p22_6 * p22_6 - p23_6 * p23_6 - h * (1 + γ * (p22_6 + p23_6)) * (abs(q22_23_6)^α)
+
+    # time step 7
+
     cx[271] =
-      p1_7 / ((1) + (1) * p1_7) - p1_6 / ((1) + (1) * p1_6) - T(0.75) * q1_17_7 - T(0.75) * q1_2_7 +
-      in1_7 - T(0.25) * q1_17_6 - T(0.25) * q1_2_6
+      p1_7 / (1 + p1_7) - p1_6 / (1 + p1_6) - θ * q1_17_7 - θ * q1_2_7 + in1_7 - (1 - θ) * q1_17_6 -
+      (1 - θ) * q1_2_6
     cx[272] =
-      p2_7 / ((1) + (1) * p2_7) - p2_6 / ((1) + (1) * p2_6) - T(0.75) * q2_3_7 + T(0.75) * q1_2_7 -
-      T(0.25) * q2_3_6 + T(0.25) * q1_2_6 - 1
-    cx[273] =
-      p3_7 / ((1) + (1) * p3_7) - p3_6 / ((1) + (1) * p3_6) - f3_4_7 +
-      T(0.75) * q2_3_7 +
-      T(0.25) * q2_3_6
-    cx[274] =
-      p4_7 / ((1) + (1) * p4_7) - p4_6 / ((1) + (1) * p4_6) - T(0.75) * q4_5_7 + f3_4_7 -
-      T(0.25) * q4_5_6
+      p2_7 / (1 + p2_7) - p2_6 / (1 + p2_6) - θ * q2_3_7 + θ * q1_2_7 - (1 - θ) * q2_3_6 +
+      (1 - θ) * q1_2_6 - 1
+    cx[273] = p3_7 / (1 + p3_7) - p3_6 / (1 + p3_6) - f3_4_7 + θ * q2_3_7 + (1 - θ) * q2_3_6
+    cx[274] = p4_7 / (1 + p4_7) - p4_6 / (1 + p4_6) - θ * q4_5_7 + f3_4_7 - (1 - θ) * q4_5_6
     cx[275] =
-      p5_7 / ((1) + (1) * p5_7) - p5_6 / ((1) + (1) * p5_6) - T(0.75) * q5_6_7 - f5_7_7 +
-      T(0.75) * q4_5_7 - T(0.25) * q5_6_6 + T(0.25) * q4_5_6
-    cx[276] =
-      p6_7 / ((1) + (1) * p6_7) - p6_6 / ((1) + (1) * p6_6) + T(0.75) * q5_6_7 + T(0.25) * q5_6_6 -
-      1
-    cx[277] =
-      p7_7 / ((1) + (1) * p7_7) - p7_6 / ((1) + (1) * p7_6) - T(0.75) * q7_8_7 + f5_7_7 -
-      T(0.25) * q7_8_6
+      p5_7 / (1 + p5_7) - p5_6 / (1 + p5_6) - θ * q5_6_7 - f5_7_7 + θ * q4_5_7 - (1 - θ) * q5_6_6 +
+      (1 - θ) * q4_5_6
+    cx[276] = p6_7 / (1 + p6_7) - p6_6 / (1 + p6_6) + θ * q5_6_7 + (1 - θ) * q5_6_6 - 1
+    cx[277] = p7_7 / (1 + p7_7) - p7_6 / (1 + p7_6) - θ * q7_8_7 + f5_7_7 - (1 - θ) * q7_8_6
     cx[278] =
-      p8_7 / ((1) + (1) * p8_7) - p8_6 / ((1) + (1) * p8_6) - T(0.75) * q8_9_7 - T(0.75) * q8_10_7 -
-      T(0.75) * q8_11_7 + T(0.75) * q7_8_7 - T(0.25) * q8_9_6 - T(0.25) * q8_10_6 -
-      T(0.25) * q8_11_6 + T(0.25) * q7_8_6
-    cx[279] =
-      p9_7 / ((1) + (1) * p9_7) - p9_6 / ((1) + (1) * p9_6) + T(0.75) * q8_9_7 + T(0.25) * q8_9_6
-    cx[280] =
-      p10_7 / ((1) + (1) * p10_7) - p10_6 / ((1) + (1) * p10_6) +
-      T(0.75) * q8_10_7 +
-      T(0.25) * q8_10_6 - 1
+      p8_7 / (1 + p8_7) - p8_6 / (1 + p8_6) - θ * q8_9_7 - θ * q8_10_7 - θ * q8_11_7 + θ * q7_8_7 -
+      (1 - θ) * q8_9_6 - (1 - θ) * q8_10_6 - (1 - θ) * q8_11_6 + (1 - θ) * q7_8_6
+    cx[279] = p9_7 / (1 + p9_7) - p9_6 / (1 + p9_6) + θ * q8_9_7 + (1 - θ) * q8_9_6
+    cx[280] = p10_7 / (1 + p10_7) - p10_6 / (1 + p10_6) + θ * q8_10_7 + (1 - θ) * q8_10_6 - 1
     cx[281] =
-      p11_7 / ((1) + (1) * p11_7) - p11_6 / ((1) + (1) * p11_6) - T(0.75) * q11_12_7 +
-      T(0.75) * q8_11_7 - T(0.25) * q11_12_6 + T(0.25) * q8_11_6
+      p11_7 / (1 + p11_7) - p11_6 / (1 + p11_6) - θ * q11_12_7 + θ * q8_11_7 - (1 - θ) * q11_12_6 +
+      (1 - θ) * q8_11_6
     cx[282] =
-      p12_7 / ((1) + (1) * p12_7) - p12_6 / ((1) + (1) * p12_6) - T(0.75) * q12_13_7 +
-      T(0.75) * q11_12_7 - T(0.25) * q12_13_6 + T(0.25) * q11_12_6
+      p12_7 / (1 + p12_7) - p12_6 / (1 + p12_6) - θ * q12_13_7 + θ * q11_12_7 - (1 - θ) * q12_13_6 +
+      (1 - θ) * q11_12_6
     cx[283] =
-      p13_7 / ((1) + (1) * p13_7) - p13_6 / ((1) + (1) * p13_6) - T(0.75) * q13_14_7 -
-      T(0.75) * q13_15_7 + T(0.75) * q12_13_7 - T(0.25) * q13_14_6 - T(0.25) * q13_15_6 +
-      T(0.25) * q12_13_6 - 1
-    cx[284] =
-      p14_7 / ((1) + (1) * p14_7) - p14_6 / ((1) + (1) * p14_6) +
-      T(0.75) * q13_14_7 +
-      T(0.25) * q13_14_6
+      p13_7 / (1 + p13_7) - p13_6 / (1 + p13_6) - θ * q13_14_7 - θ * q13_15_7 + θ * q12_13_7 -
+      (1 - θ) * q13_14_6 - (1 - θ) * q13_15_6 + (1 - θ) * q12_13_6 - 1
+    cx[284] = p14_7 / (1 + p14_7) - p14_6 / (1 + p14_6) + θ * q13_14_7 + (1 - θ) * q13_14_6
     cx[285] =
-      p15_7 / ((1) + (1) * p15_7) - p15_6 / ((1) + (1) * p15_6) - T(0.75) * q15_16_7 +
-      T(0.75) * q13_15_7 - T(0.25) * q15_16_6 + T(0.25) * q13_15_6 - 1
+      p15_7 / (1 + p15_7) - p15_6 / (1 + p15_6) - θ * q15_16_7 + θ * q13_15_7 - (1 - θ) * q15_16_6 +
+      (1 - θ) * q13_15_6 - 1
     cx[286] =
-      p16_7 / ((1) + (1) * p16_7) - p16_6 / ((1) + (1) * p16_6) +
-      T(0.75) * q15_16_7 +
-      T(0.25) * q15_16_6 - out16_7
+      p16_7 / (1 + p16_7) - p16_6 / (1 + p16_6) + θ * q15_16_7 + (1 - θ) * q15_16_6 - out16_7
     cx[287] =
-      p17_7 / ((1) + (1) * p17_7) - p17_6 / ((1) + (1) * p17_6) - T(0.75) * q17_18_7 +
-      T(0.75) * q1_17_7 - T(0.25) * q17_18_6 + T(0.25) * q1_17_6 - 1
+      p17_7 / (1 + p17_7) - p17_6 / (1 + p17_6) - θ * q17_18_7 + θ * q1_17_7 - (1 - θ) * q17_18_6 +
+      (1 - θ) * q1_17_6 - 1
     cx[288] =
-      p18_7 / ((1) + (1) * p18_7) - p18_6 / ((1) + (1) * p18_6) - T(0.75) * q18_19_7 +
-      T(0.75) * q17_18_7 - T(0.25) * q18_19_6 + T(0.25) * q17_18_6 - 1
+      p18_7 / (1 + p18_7) - p18_6 / (1 + p18_6) - θ * q18_19_7 + θ * q17_18_7 - (1 - θ) * q18_19_6 +
+      (1 - θ) * q17_18_6 - 1
     cx[289] =
-      p19_7 / ((1) + (1) * p19_7) - p19_6 / ((1) + (1) * p19_6) - f19_20_7 +
-      T(0.75) * q18_19_7 +
-      T(0.25) * q18_19_6
+      p19_7 / (1 + p19_7) - p19_6 / (1 + p19_6) - f19_20_7 + θ * q18_19_7 + (1 - θ) * q18_19_6
     cx[290] =
-      p20_7 / ((1) + (1) * p20_7) - p20_6 / ((1) + (1) * p20_6) - T(0.75) * q20_21_7 + f19_20_7 -
-      T(0.25) * q20_21_6
+      p20_7 / (1 + p20_7) - p20_6 / (1 + p20_6) - θ * q20_21_7 + f19_20_7 - (1 - θ) * q20_21_6
     cx[291] =
-      p21_7 / ((1) + (1) * p21_7) - p21_6 / ((1) + (1) * p21_6) - T(0.75) * q21_22_7 +
-      T(0.75) * q20_21_7 - T(0.25) * q21_22_6 + T(0.25) * q20_21_6 - 1
+      p21_7 / (1 + p21_7) - p21_6 / (1 + p21_6) - θ * q21_22_7 + θ * q20_21_7 - (1 - θ) * q21_22_6 +
+      (1 - θ) * q20_21_6 - 1
     cx[292] =
-      p22_7 / ((1) + (1) * p22_7) - p22_6 / ((1) + (1) * p22_6) - T(0.75) * q22_23_7 +
-      T(0.75) * q21_22_7 - T(0.25) * q22_23_6 + T(0.25) * q21_22_6 - 1
+      p22_7 / (1 + p22_7) - p22_6 / (1 + p22_6) - θ * q22_23_7 + θ * q21_22_7 - (1 - θ) * q22_23_6 +
+      (1 - θ) * q21_22_6 - 1
     cx[293] =
-      p23_7 / ((1) + (1) * p23_7) - p23_6 / ((1) + (1) * p23_6) +
-      T(0.75) * q22_23_7 +
-      T(0.25) * q22_23_6 - out23_7
+      p23_7 / (1 + p23_7) - p23_6 / (1 + p23_6) + θ * q22_23_7 + (1 - θ) * q22_23_6 - out23_7
     cx[294] = p3_7 * r3_4_7 - p4_7
     cx[295] = p5_7 * r5_7_7 - p7_7
     cx[296] = p19_7 * r19_20_7 - p20_7
-    cx[297] =
-      p1_7 * p1_7 - p2_7 * p2_7 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p1_7 + p2_7)) * ((abs(q1_2_7))^T(1.8539))
-    cx[298] =
-      p1_7 * p1_7 - p17_7 * p17_7 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p1_7 + p17_7)) * ((abs(q1_17_7))^T(1.8539))
-    cx[299] =
-      p2_7 * p2_7 - p3_7 * p3_7 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p2_7 + p3_7)) * ((abs(q2_3_7))^T(1.8539))
-    cx[300] =
-      p4_7 * p4_7 - p5_7 * p5_7 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p4_7 + p5_7)) * ((abs(q4_5_7))^T(1.8539))
-    cx[301] =
-      p5_7 * p5_7 - p6_7 * p6_7 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p5_7 + p6_7)) * ((abs(q5_6_7))^T(1.8539))
-    cx[302] =
-      p7_7 * p7_7 - p8_7 * p8_7 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p7_7 + p8_7)) * ((abs(q7_8_7))^T(1.8539))
-    cx[303] =
-      p8_7 * p8_7 - p9_7 * p9_7 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p8_7 + p9_7)) * ((abs(q8_9_7))^T(1.8539))
-    cx[304] =
-      p8_7 * p8_7 - p10_7 * p10_7 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p8_7 + p10_7)) * ((abs(q8_10_7))^T(1.8539))
-    cx[305] =
-      p8_7 * p8_7 - p11_7 * p11_7 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p8_7 + p11_7)) * ((abs(q8_11_7))^T(1.8539))
-    cx[306] =
-      p11_7 * p11_7 - p12_7 * p12_7 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p11_7 + p12_7)) * ((abs(q11_12_7))^T(1.8539))
-    cx[307] =
-      p12_7 * p12_7 - p13_7 * p13_7 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p12_7 + p13_7)) * ((abs(q12_13_7))^T(1.8539))
-    cx[308] =
-      p13_7 * p13_7 - p14_7 * p14_7 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p13_7 + p14_7)) * ((abs(q13_14_7))^T(1.8539))
-    cx[309] =
-      p13_7 * p13_7 - p15_7 * p15_7 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p13_7 + p15_7)) * ((abs(q13_15_7))^T(1.8539))
-    cx[310] =
-      p15_7 * p15_7 - p16_7 * p16_7 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p15_7 + p16_7)) * ((abs(q15_16_7))^T(1.8539))
-    cx[311] =
-      p17_7 * p17_7 - p18_7 * p18_7 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p17_7 + p18_7)) * ((abs(q17_18_7))^T(1.8539))
-    cx[312] =
-      p18_7 * p18_7 - p19_7 * p19_7 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p18_7 + p19_7)) * ((abs(q18_19_7))^T(1.8539))
-    cx[313] =
-      p20_7 * p20_7 - p21_7 * p21_7 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p20_7 + p21_7)) * ((abs(q20_21_7))^T(1.8539))
-    cx[314] =
-      p21_7 * p21_7 - p22_7 * p22_7 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p21_7 + p22_7)) * ((abs(q21_22_7))^T(1.8539))
-    cx[315] =
-      p22_7 * p22_7 - p23_7 * p23_7 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p22_7 + p23_7)) * ((abs(q22_23_7))^T(1.8539))
+    cx[297] = p1_7 * p1_7 - p2_7 * p2_7 - h * (1 + γ * (p1_7 + p2_7)) * (abs(q1_2_7)^α)
+    cx[298] = p1_7 * p1_7 - p17_7 * p17_7 - h * (1 + γ * (p1_7 + p17_7)) * (abs(q1_17_7)^α)
+    cx[299] = p2_7 * p2_7 - p3_7 * p3_7 - h * (1 + γ * (p2_7 + p3_7)) * (abs(q2_3_7)^α)
+    cx[300] = p4_7 * p4_7 - p5_7 * p5_7 - h * (1 + γ * (p4_7 + p5_7)) * (abs(q4_5_7)^α)
+    cx[301] = p5_7 * p5_7 - p6_7 * p6_7 - h * (1 + γ * (p5_7 + p6_7)) * (abs(q5_6_7)^α)
+    cx[302] = p7_7 * p7_7 - p8_7 * p8_7 - h * (1 + γ * (p7_7 + p8_7)) * (abs(q7_8_7)^α)
+    cx[303] = p8_7 * p8_7 - p9_7 * p9_7 - h * (1 + γ * (p8_7 + p9_7)) * (abs(q8_9_7)^α)
+    cx[304] = p8_7 * p8_7 - p10_7 * p10_7 - h * (1 + γ * (p8_7 + p10_7)) * (abs(q8_10_7)^α)
+    cx[305] = p8_7 * p8_7 - p11_7 * p11_7 - h * (1 + γ * (p8_7 + p11_7)) * (abs(q8_11_7)^α)
+    cx[306] = p11_7 * p11_7 - p12_7 * p12_7 - h * (1 + γ * (p11_7 + p12_7)) * (abs(q11_12_7)^α)
+    cx[307] = p12_7 * p12_7 - p13_7 * p13_7 - h * (1 + γ * (p12_7 + p13_7)) * (abs(q12_13_7)^α)
+    cx[308] = p13_7 * p13_7 - p14_7 * p14_7 - h * (1 + γ * (p13_7 + p14_7)) * (abs(q13_14_7)^α)
+    cx[309] = p13_7 * p13_7 - p15_7 * p15_7 - h * (1 + γ * (p13_7 + p15_7)) * (abs(q13_15_7)^α)
+    cx[310] = p15_7 * p15_7 - p16_7 * p16_7 - h * (1 + γ * (p15_7 + p16_7)) * (abs(q15_16_7)^α)
+    cx[311] = p17_7 * p17_7 - p18_7 * p18_7 - h * (1 + γ * (p17_7 + p18_7)) * (abs(q17_18_7)^α)
+    cx[312] = p18_7 * p18_7 - p19_7 * p19_7 - h * (1 + γ * (p18_7 + p19_7)) * (abs(q18_19_7)^α)
+    cx[313] = p20_7 * p20_7 - p21_7 * p21_7 - h * (1 + γ * (p20_7 + p21_7)) * (abs(q20_21_7)^α)
+    cx[314] = p21_7 * p21_7 - p22_7 * p22_7 - h * (1 + γ * (p21_7 + p22_7)) * (abs(q21_22_7)^α)
+    cx[315] = p22_7 * p22_7 - p23_7 * p23_7 - h * (1 + γ * (p22_7 + p23_7)) * (abs(q22_23_7)^α)
+
+    # time step 8
+
     cx[316] =
-      p1_8 / ((1) + (1) * p1_8) - p1_7 / ((1) + (1) * p1_7) - T(0.75) * q1_17_8 - T(0.75) * q1_2_8 +
-      in1_8 - T(0.25) * q1_17_7 - T(0.25) * q1_2_7
+      p1_8 / (1 + p1_8) - p1_7 / (1 + p1_7) - θ * q1_17_8 - θ * q1_2_8 + in1_8 - (1 - θ) * q1_17_7 -
+      (1 - θ) * q1_2_7
     cx[317] =
-      p2_8 / ((1) + (1) * p2_8) - p2_7 / ((1) + (1) * p2_7) - T(0.75) * q2_3_8 + T(0.75) * q1_2_8 -
-      T(0.25) * q2_3_7 + T(0.25) * q1_2_7 - 1
-    cx[318] =
-      p3_8 / ((1) + (1) * p3_8) - p3_7 / ((1) + (1) * p3_7) - f3_4_8 +
-      T(0.75) * q2_3_8 +
-      T(0.25) * q2_3_7
-    cx[319] =
-      p4_8 / ((1) + (1) * p4_8) - p4_7 / ((1) + (1) * p4_7) - T(0.75) * q4_5_8 + f3_4_8 -
-      T(0.25) * q4_5_7
+      p2_8 / (1 + p2_8) - p2_7 / (1 + p2_7) - θ * q2_3_8 + θ * q1_2_8 - (1 - θ) * q2_3_7 +
+      (1 - θ) * q1_2_7 - 1
+    cx[318] = p3_8 / (1 + p3_8) - p3_7 / (1 + p3_7) - f3_4_8 + θ * q2_3_8 + (1 - θ) * q2_3_7
+    cx[319] = p4_8 / (1 + p4_8) - p4_7 / (1 + p4_7) - θ * q4_5_8 + f3_4_8 - (1 - θ) * q4_5_7
     cx[320] =
-      p5_8 / ((1) + (1) * p5_8) - p5_7 / ((1) + (1) * p5_7) - T(0.75) * q5_6_8 - f5_7_8 +
-      T(0.75) * q4_5_8 - T(0.25) * q5_6_7 + T(0.25) * q4_5_7
-    cx[321] =
-      p6_8 / ((1) + (1) * p6_8) - p6_7 / ((1) + (1) * p6_7) + T(0.75) * q5_6_8 + T(0.25) * q5_6_7 -
-      1
-    cx[322] =
-      p7_8 / ((1) + (1) * p7_8) - p7_7 / ((1) + (1) * p7_7) - T(0.75) * q7_8_8 + f5_7_8 -
-      T(0.25) * q7_8_7
+      p5_8 / (1 + p5_8) - p5_7 / (1 + p5_7) - θ * q5_6_8 - f5_7_8 + θ * q4_5_8 - (1 - θ) * q5_6_7 +
+      (1 - θ) * q4_5_7
+    cx[321] = p6_8 / (1 + p6_8) - p6_7 / (1 + p6_7) + θ * q5_6_8 + (1 - θ) * q5_6_7 - 1
+    cx[322] = p7_8 / (1 + p7_8) - p7_7 / (1 + p7_7) - θ * q7_8_8 + f5_7_8 - (1 - θ) * q7_8_7
     cx[323] =
-      p8_8 / ((1) + (1) * p8_8) - p8_7 / ((1) + (1) * p8_7) - T(0.75) * q8_9_8 - T(0.75) * q8_10_8 -
-      T(0.75) * q8_11_8 + T(0.75) * q7_8_8 - T(0.25) * q8_9_7 - T(0.25) * q8_10_7 -
-      T(0.25) * q8_11_7 + T(0.25) * q7_8_7
-    cx[324] =
-      p9_8 / ((1) + (1) * p9_8) - p9_7 / ((1) + (1) * p9_7) + T(0.75) * q8_9_8 + T(0.25) * q8_9_7
-    cx[325] =
-      p10_8 / ((1) + (1) * p10_8) - p10_7 / ((1) + (1) * p10_7) +
-      T(0.75) * q8_10_8 +
-      T(0.25) * q8_10_7 - 1
+      p8_8 / (1 + p8_8) - p8_7 / (1 + p8_7) - θ * q8_9_8 - θ * q8_10_8 - θ * q8_11_8 + θ * q7_8_8 -
+      (1 - θ) * q8_9_7 - (1 - θ) * q8_10_7 - (1 - θ) * q8_11_7 + (1 - θ) * q7_8_7
+    cx[324] = p9_8 / (1 + p9_8) - p9_7 / (1 + p9_7) + θ * q8_9_8 + (1 - θ) * q8_9_7
+    cx[325] = p10_8 / (1 + p10_8) - p10_7 / (1 + p10_7) + θ * q8_10_8 + (1 - θ) * q8_10_7 - 1
     cx[326] =
-      p11_8 / ((1) + (1) * p11_8) - p11_7 / ((1) + (1) * p11_7) - T(0.75) * q11_12_8 +
-      T(0.75) * q8_11_8 - T(0.25) * q11_12_7 + T(0.25) * q8_11_7
+      p11_8 / (1 + p11_8) - p11_7 / (1 + p11_7) - θ * q11_12_8 + θ * q8_11_8 - (1 - θ) * q11_12_7 +
+      (1 - θ) * q8_11_7
     cx[327] =
-      p12_8 / ((1) + (1) * p12_8) - p12_7 / ((1) + (1) * p12_7) - T(0.75) * q12_13_8 +
-      T(0.75) * q11_12_8 - T(0.25) * q12_13_7 + T(0.25) * q11_12_7
+      p12_8 / (1 + p12_8) - p12_7 / (1 + p12_7) - θ * q12_13_8 + θ * q11_12_8 - (1 - θ) * q12_13_7 +
+      (1 - θ) * q11_12_7
     cx[328] =
-      p13_8 / ((1) + (1) * p13_8) - p13_7 / ((1) + (1) * p13_7) - T(0.75) * q13_14_8 -
-      T(0.75) * q13_15_8 + T(0.75) * q12_13_8 - T(0.25) * q13_14_7 - T(0.25) * q13_15_7 +
-      T(0.25) * q12_13_7 - 1
-    cx[329] =
-      p14_8 / ((1) + (1) * p14_8) - p14_7 / ((1) + (1) * p14_7) +
-      T(0.75) * q13_14_8 +
-      T(0.25) * q13_14_7
+      p13_8 / (1 + p13_8) - p13_7 / (1 + p13_7) - θ * q13_14_8 - θ * q13_15_8 + θ * q12_13_8 -
+      (1 - θ) * q13_14_7 - (1 - θ) * q13_15_7 + (1 - θ) * q12_13_7 - 1
+    cx[329] = p14_8 / (1 + p14_8) - p14_7 / (1 + p14_7) + θ * q13_14_8 + (1 - θ) * q13_14_7
     cx[330] =
-      p15_8 / ((1) + (1) * p15_8) - p15_7 / ((1) + (1) * p15_7) - T(0.75) * q15_16_8 +
-      T(0.75) * q13_15_8 - T(0.25) * q15_16_7 + T(0.25) * q13_15_7 - 1
+      p15_8 / (1 + p15_8) - p15_7 / (1 + p15_7) - θ * q15_16_8 + θ * q13_15_8 - (1 - θ) * q15_16_7 +
+      (1 - θ) * q13_15_7 - 1
     cx[331] =
-      p16_8 / ((1) + (1) * p16_8) - p16_7 / ((1) + (1) * p16_7) +
-      T(0.75) * q15_16_8 +
-      T(0.25) * q15_16_7 - out16_8
+      p16_8 / (1 + p16_8) - p16_7 / (1 + p16_7) + θ * q15_16_8 + (1 - θ) * q15_16_7 - out16_8
     cx[332] =
-      p17_8 / ((1) + (1) * p17_8) - p17_7 / ((1) + (1) * p17_7) - T(0.75) * q17_18_8 +
-      T(0.75) * q1_17_8 - T(0.25) * q17_18_7 + T(0.25) * q1_17_7 - 1
+      p17_8 / (1 + p17_8) - p17_7 / (1 + p17_7) - θ * q17_18_8 + θ * q1_17_8 - (1 - θ) * q17_18_7 +
+      (1 - θ) * q1_17_7 - 1
     cx[333] =
-      p18_8 / ((1) + (1) * p18_8) - p18_7 / ((1) + (1) * p18_7) - T(0.75) * q18_19_8 +
-      T(0.75) * q17_18_8 - T(0.25) * q18_19_7 + T(0.25) * q17_18_7 - 1
+      p18_8 / (1 + p18_8) - p18_7 / (1 + p18_7) - θ * q18_19_8 + θ * q17_18_8 - (1 - θ) * q18_19_7 +
+      (1 - θ) * q17_18_7 - 1
     cx[334] =
-      p19_8 / ((1) + (1) * p19_8) - p19_7 / ((1) + (1) * p19_7) - f19_20_8 +
-      T(0.75) * q18_19_8 +
-      T(0.25) * q18_19_7
+      p19_8 / (1 + p19_8) - p19_7 / (1 + p19_7) - f19_20_8 + θ * q18_19_8 + (1 - θ) * q18_19_7
     cx[335] =
-      p20_8 / ((1) + (1) * p20_8) - p20_7 / ((1) + (1) * p20_7) - T(0.75) * q20_21_8 + f19_20_8 -
-      T(0.25) * q20_21_7
+      p20_8 / (1 + p20_8) - p20_7 / (1 + p20_7) - θ * q20_21_8 + f19_20_8 - (1 - θ) * q20_21_7
     cx[336] =
-      p21_8 / ((1) + (1) * p21_8) - p21_7 / ((1) + (1) * p21_7) - T(0.75) * q21_22_8 +
-      T(0.75) * q20_21_8 - T(0.25) * q21_22_7 + T(0.25) * q20_21_7 - 1
+      p21_8 / (1 + p21_8) - p21_7 / (1 + p21_7) - θ * q21_22_8 + θ * q20_21_8 - (1 - θ) * q21_22_7 +
+      (1 - θ) * q20_21_7 - 1
     cx[337] =
-      p22_8 / ((1) + (1) * p22_8) - p22_7 / ((1) + (1) * p22_7) - T(0.75) * q22_23_8 +
-      T(0.75) * q21_22_8 - T(0.25) * q22_23_7 + T(0.25) * q21_22_7 - 1
+      p22_8 / (1 + p22_8) - p22_7 / (1 + p22_7) - θ * q22_23_8 + θ * q21_22_8 - (1 - θ) * q22_23_7 +
+      (1 - θ) * q21_22_7 - 1
     cx[338] =
-      p23_8 / ((1) + (1) * p23_8) - p23_7 / ((1) + (1) * p23_7) +
-      T(0.75) * q22_23_8 +
-      T(0.25) * q22_23_7 - out23_8
+      p23_8 / (1 + p23_8) - p23_7 / (1 + p23_7) + θ * q22_23_8 + (1 - θ) * q22_23_7 - out23_8
     cx[339] = p3_8 * r3_4_8 - p4_8
     cx[340] = p5_8 * r5_7_8 - p7_8
     cx[341] = p19_8 * r19_20_8 - p20_8
-    cx[342] =
-      p1_8 * p1_8 - p2_8 * p2_8 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p1_8 + p2_8)) * ((abs(q1_2_8))^T(1.8539))
-    cx[343] =
-      p1_8 * p1_8 - p17_8 * p17_8 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p1_8 + p17_8)) * ((abs(q1_17_8))^T(1.8539))
-    cx[344] =
-      p2_8 * p2_8 - p3_8 * p3_8 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p2_8 + p3_8)) * ((abs(q2_3_8))^T(1.8539))
-    cx[345] =
-      p4_8 * p4_8 - p5_8 * p5_8 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p4_8 + p5_8)) * ((abs(q4_5_8))^T(1.8539))
-    cx[346] =
-      p5_8 * p5_8 - p6_8 * p6_8 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p5_8 + p6_8)) * ((abs(q5_6_8))^T(1.8539))
-    cx[347] =
-      p7_8 * p7_8 - p8_8 * p8_8 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p7_8 + p8_8)) * ((abs(q7_8_8))^T(1.8539))
-    cx[348] =
-      p8_8 * p8_8 - p9_8 * p9_8 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p8_8 + p9_8)) * ((abs(q8_9_8))^T(1.8539))
-    cx[349] =
-      p8_8 * p8_8 - p10_8 * p10_8 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p8_8 + p10_8)) * ((abs(q8_10_8))^T(1.8539))
-    cx[350] =
-      p8_8 * p8_8 - p11_8 * p11_8 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p8_8 + p11_8)) * ((abs(q8_11_8))^T(1.8539))
-    cx[351] =
-      p11_8 * p11_8 - p12_8 * p12_8 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p11_8 + p12_8)) * ((abs(q11_12_8))^T(1.8539))
-    cx[352] =
-      p12_8 * p12_8 - p13_8 * p13_8 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p12_8 + p13_8)) * ((abs(q12_13_8))^T(1.8539))
-    cx[353] =
-      p13_8 * p13_8 - p14_8 * p14_8 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p13_8 + p14_8)) * ((abs(q13_14_8))^T(1.8539))
-    cx[354] =
-      p13_8 * p13_8 - p15_8 * p15_8 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p13_8 + p15_8)) * ((abs(q13_15_8))^T(1.8539))
-    cx[355] =
-      p15_8 * p15_8 - p16_8 * p16_8 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p15_8 + p16_8)) * ((abs(q15_16_8))^T(1.8539))
-    cx[356] =
-      p17_8 * p17_8 - p18_8 * p18_8 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p17_8 + p18_8)) * ((abs(q17_18_8))^T(1.8539))
-    cx[357] =
-      p18_8 * p18_8 - p19_8 * p19_8 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p18_8 + p19_8)) * ((abs(q18_19_8))^T(1.8539))
-    cx[358] =
-      p20_8 * p20_8 - p21_8 * p21_8 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p20_8 + p21_8)) * ((abs(q20_21_8))^T(1.8539))
-    cx[359] =
-      p21_8 * p21_8 - p22_8 * p22_8 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p21_8 + p22_8)) * ((abs(q21_22_8))^T(1.8539))
-    cx[360] =
-      p22_8 * p22_8 - p23_8 * p23_8 -
-      T(0.01) * ((1) + (T(0.5) * 1) * (p22_8 + p23_8)) * ((abs(q22_23_8))^T(1.8539))
+    cx[342] = p1_8 * p1_8 - p2_8 * p2_8 - h * (1 + γ * (p1_8 + p2_8)) * (abs(q1_2_8)^α)
+    cx[343] = p1_8 * p1_8 - p17_8 * p17_8 - h * (1 + γ * (p1_8 + p17_8)) * (abs(q1_17_8)^α)
+    cx[344] = p2_8 * p2_8 - p3_8 * p3_8 - h * (1 + γ * (p2_8 + p3_8)) * (abs(q2_3_8)^α)
+    cx[345] = p4_8 * p4_8 - p5_8 * p5_8 - h * (1 + γ * (p4_8 + p5_8)) * (abs(q4_5_8)^α)
+    cx[346] = p5_8 * p5_8 - p6_8 * p6_8 - h * (1 + γ * (p5_8 + p6_8)) * (abs(q5_6_8)^α)
+    cx[347] = p7_8 * p7_8 - p8_8 * p8_8 - h * (1 + γ * (p7_8 + p8_8)) * (abs(q7_8_8)^α)
+    cx[348] = p8_8 * p8_8 - p9_8 * p9_8 - h * (1 + γ * (p8_8 + p9_8)) * (abs(q8_9_8)^α)
+    cx[349] = p8_8 * p8_8 - p10_8 * p10_8 - h * (1 + γ * (p8_8 + p10_8)) * (abs(q8_10_8)^α)
+    cx[350] = p8_8 * p8_8 - p11_8 * p11_8 - h * (1 + γ * (p8_8 + p11_8)) * (abs(q8_11_8)^α)
+    cx[351] = p11_8 * p11_8 - p12_8 * p12_8 - h * (1 + γ * (p11_8 + p12_8)) * (abs(q11_12_8)^α)
+    cx[352] = p12_8 * p12_8 - p13_8 * p13_8 - h * (1 + γ * (p12_8 + p13_8)) * (abs(q12_13_8)^α)
+    cx[353] = p13_8 * p13_8 - p14_8 * p14_8 - h * (1 + γ * (p13_8 + p14_8)) * (abs(q13_14_8)^α)
+    cx[354] = p13_8 * p13_8 - p15_8 * p15_8 - h * (1 + γ * (p13_8 + p15_8)) * (abs(q13_15_8)^α)
+    cx[355] = p15_8 * p15_8 - p16_8 * p16_8 - h * (1 + γ * (p15_8 + p16_8)) * (abs(q15_16_8)^α)
+    cx[356] = p17_8 * p17_8 - p18_8 * p18_8 - h * (1 + γ * (p17_8 + p18_8)) * (abs(q17_18_8)^α)
+    cx[357] = p18_8 * p18_8 - p19_8 * p19_8 - h * (1 + γ * (p18_8 + p19_8)) * (abs(q18_19_8)^α)
+    cx[358] = p20_8 * p20_8 - p21_8 * p21_8 - h * (1 + γ * (p20_8 + p21_8)) * (abs(q20_21_8)^α)
+    cx[359] = p21_8 * p21_8 - p22_8 * p22_8 - h * (1 + γ * (p21_8 + p22_8)) * (abs(q21_22_8)^α)
+    cx[360] = p22_8 * p22_8 - p23_8 * p23_8 - h * (1 + γ * (p22_8 + p23_8)) * (abs(q22_23_8)^α)
+
     return cx
   end
   lvar = T[

From 115b4fd2eb5e84ac53c698d5307e35ab7aa128ae Mon Sep 17 00:00:00 2001
From: Guillaume Dalle <22795598+gdalle@users.noreply.github.com>
Date: Fri, 14 Jun 2024 13:48:15 +0200
Subject: [PATCH 3/3] Finish parsing

---
 src/ADNLPProblems/britgas.jl | 2121 ++--------------------------------
 1 file changed, 96 insertions(+), 2025 deletions(-)

diff --git a/src/ADNLPProblems/britgas.jl b/src/ADNLPProblems/britgas.jl
index 82452d1d..270c18c1 100644
--- a/src/ADNLPProblems/britgas.jl
+++ b/src/ADNLPProblems/britgas.jl
@@ -47,28 +47,17 @@ function britgas(; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) wh
     (21, 22),
     (22, 23),
   ]
-  q_outneighbors = [i => Int[] for i = 1:23]
-  q_inneighbors = [i => Int[] for i = 1:23]
-  for (i, j) in q_ind
-    push!(q_outneighbors[i], j)
-    push!(q_inneighbors[j], i)
-  end
-  q_neighbors = [vcat(q_inneighbors[i], q_outneighbors[i]) for i in 1:23]
 
   # f and r variables are indexed with some pairs from 1:23 × 1:23
   fr_ind = [(3, 4), (5, 7), (19, 20)]
-  fr_outneighbors = [i => Int[] for i = 1:23]
-  fr_inneighbors = [i => Int[] for i = 1:23]
-  for (i, j) in fr_ind
-    push!(fr_outneighbors[i], j)
-    push!(fr_inneighbors[j], i)
-  end
-  fr_neighbors = [vcat(fr_inneighbors[i], outneighbors[i]) for i in 1:23]
 
   # in and out variables are indexed with some indices from 1:23
   in_ind = [1]
   out_ind = [16, 23]
 
+  # in some constraints we remove one
+  ones_ind = [2, 6, 10, 13, 15, 17, 18, 21, 22]
+
   function f(x)
     f_1 = view(x, 379:381)
     r_1 = view(x, 382:384)
@@ -93,458 +82,7 @@ function britgas(; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) wh
     o = sum(mapreduce(_britgas_obj, +, f_[t], r_[t]) for t = 1:8)
     return o
   end
-  x0 = T[
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-    1.0,
-    1.0,
-    1.0,
-    1.0,
-    1.0,
-    1.0,
-    1.0,
-    1.0,
-    1.0,
-    1.0,
-    1.0,
-    1.0,
-    1.0,
-    1.0,
-    1.0,
-    1.0,
-    1.0,
-    1.0,
-    1.0,
-    1.0,
-    1.0,
-    1.0,
-    1.0,
-    1.0,
-    1.0,
-    1.0,
-    1.0,
-    1.0,
-    1.0,
-    1.0,
-    1.0,
-    1.0,
-    1.0,
-    1.0,
-    1.0,
-    1.0,
-    1.0,
-    1.0,
-    1.0,
-    1.0,
-    1.0,
-    1.0,
-    1.0,
-    1.0,
-    1.0,
-    1.0,
-    1.0,
-    1.0,
-    1.0,
-    1.0,
-    1.0,
-    1.0,
-    1.0,
-    1.0,
-    1.0,
-    1.0,
-    1.0,
-    1.0,
-    1.0,
-    1.0,
-  ]
+  x0 = ones(T, 450)
   function c!(cx, x)
     p_0 = view(x, 1:23)
     p_1 = view(x, 24:46)
@@ -556,1572 +94,105 @@ function britgas(; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) wh
     p_7 = view(x, 162:184)
     p_8 = view(x, 185:207)
 
-    q_0 = Dict(q_ind .=> view(x, 208:226))
-    q_1 = Dict(q_ind .=> view(x, 227:245))
-    q_2 = Dict(q_ind .=> view(x, 246:264))
-    q_3 = Dict(q_ind .=> view(x, 265:283))
-    q_4 = Dict(q_ind .=> view(x, 284:302))
-    q_5 = Dict(q_ind .=> view(x, 303:321))
-    q_6 = Dict(q_ind .=> view(x, 322:340))
-    q_7 = Dict(q_ind .=> view(x, 341:359))
-    q_8 = Dict(q_ind .=> view(x, 360:378))
+    q_0 = view(x, 208:226)
+    q_1 = view(x, 227:245)
+    q_2 = view(x, 246:264)
+    q_3 = view(x, 265:283)
+    q_4 = view(x, 284:302)
+    q_5 = view(x, 303:321)
+    q_6 = view(x, 322:340)
+    q_7 = view(x, 341:359)
+    q_8 = view(x, 360:378)
 
-    f_1 = Dict(fr_ind .=> view(x, 379:381))
-    r_1 = Dict(fr_ind .=> view(x, 382:384))
-    f_2 = Dict(fr_ind .=> view(x, 385:387))
-    r_2 = Dict(fr_ind .=> view(x, 388:390))
-    f_3 = Dict(fr_ind .=> view(x, 391:393))
-    r_3 = Dict(fr_ind .=> view(x, 394:396))
-    f_4 = Dict(fr_ind .=> view(x, 397:399))
-    r_4 = Dict(fr_ind .=> view(x, 400:402))
-    f_5 = Dict(fr_ind .=> view(x, 403:405))
-    r_5 = Dict(fr_ind .=> view(x, 406:408))
-    f_6 = Dict(fr_ind .=> view(x, 409:411))
-    r_6 = Dict(fr_ind .=> view(x, 412:414))
-    f_7 = Dict(fr_ind .=> view(x, 415:417))
-    r_7 = Dict(fr_ind .=> view(x, 418:420))
-    f_8 = Dict(fr_ind .=> view(x, 421:423))
-    r_8 = Dict(fr_ind .=> view(x, 424:426))
+    f_1 = view(x, 379:381)
+    r_1 = view(x, 382:384)
+    f_2 = view(x, 385:387)
+    r_2 = view(x, 388:390)
+    f_3 = view(x, 391:393)
+    r_3 = view(x, 394:396)
+    f_4 = view(x, 397:399)
+    r_4 = view(x, 400:402)
+    f_5 = view(x, 403:405)
+    r_5 = view(x, 406:408)
+    f_6 = view(x, 409:411)
+    r_6 = view(x, 412:414)
+    f_7 = view(x, 415:417)
+    r_7 = view(x, 418:420)
+    f_8 = view(x, 421:423)
+    r_8 = view(x, 424:426)
 
-    in_1 = Dict.(in_ind .=> view(x, 427:427))
-    out_1 = Dict(out_ind .=> view(x, 428:429))
-    in_2 = Dict.(in_ind .=> view(x, 430:430))
-    out_2 = Dict(out_ind .=> view(x, 431:432))
-    in_3 = Dict.(in_ind .=> view(x, 433:433))
-    out_3 = Dict(out_ind .=> view(x, 434:435))
-    in_4 = Dict.(in_ind .=> view(x, 436:436))
-    out_4 = Dict(out_ind .=> view(x, 437:438))
-    in_5 = Dict.(in_ind .=> view(x, 439:439))
-    out_5 = Dict(out_ind .=> view(x, 440:441))
-    in_6 = Dict.(in_ind .=> view(x, 442:442))
-    out_6 = Dict(out_ind .=> view(x, 443:444))
-    in_7 = Dict.(in_ind .=> view(x, 445:445))
-    out_7 = Dict(out_ind .=> view(x, 446:447))
-    in_8 = Dict.(in_ind .=> view(x, 448:448))
-    out_8 = Dict(out_ind .=> view(x, 449:450))
+    in_1 = view(x, 427:427)
+    out_1 = view(x, 428:429)
+    in_2 = view(x, 430:430)
+    out_2 = view(x, 431:432)
+    in_3 = view(x, 433:433)
+    out_3 = view(x, 434:435)
+    in_4 = view(x, 436:436)
+    out_4 = view(x, 437:438)
+    in_5 = view(x, 439:439)
+    out_5 = view(x, 440:441)
+    in_6 = view(x, 442:442)
+    out_6 = view(x, 443:444)
+    in_7 = view(x, 445:445)
+    out_7 = view(x, 446:447)
+    in_8 = view(x, 448:448)
+    out_8 = view(x, 449:450)
 
     # multi-step variables
-    p_ = [p_1, p_2, p_3, p_4, p_5, p_6, p_7, p_8]
-    q_ = [q_1, q_2, q_3, q_4, q_5, q_6, q_7, q_8]
-    f_ = [f_1, f_2, f_3, f_4, f_5, f_6, f_7, f_8]
-    r_ = [r_1, r_2, r_3, r_4, r_5, r_6, r_7, r_8]
-    in_ = [in_1, in_2, in_3, in_4, in_5, in_6, in_7, in_8]
-    out_ = [out_1, out_2, out_3, out_4, out_5, out_6, out_7, out_8]
-
-    # time step 1
-
-    cx[1] =
-      p_1[1] / (1 + p_1[1]) - p_0[1] / (1 + p_0[1]) - θ * q1_17_1 - θ * q1_2_1 + in_1[1] -
-      (1 - θ) * q1_17_0 - (1 - θ) * q1_2_0
-
-    cx[1] =
-      p1_1 / (1 + p1_1) - p1_0 / (1 + p1_0) - θ * q1_17_1 - θ * q1_2_1 + in1_1 - (1 - θ) * q1_17_0 -
-      (1 - θ) * q1_2_0
-    cx[2] =
-      p2_1 / (1 + p2_1) - p2_0 / (1 + p2_0) - θ * q2_3_1 + θ * q1_2_1 - (1 - θ) * q2_3_0 +
-      (1 - θ) * q1_2_0 - 1
-    cx[3] = p3_1 / (1 + p3_1) - p3_0 / (1 + p3_0) - f3_4_1 + θ * q2_3_1 + (1 - θ) * q2_3_0
-    cx[4] = p4_1 / (1 + p4_1) - p4_0 / (1 + p4_0) - θ * q4_5_1 + f3_4_1 - (1 - θ) * q4_5_0
-    cx[5] =
-      p5_1 / (1 + p5_1) - p5_0 / (1 + p5_0) - θ * q5_6_1 - f5_7_1 + θ * q4_5_1 - (1 - θ) * q5_6_0 +
-      (1 - θ) * q4_5_0
-    cx[6] = p6_1 / (1 + p6_1) - p6_0 / (1 + p6_0) + θ * q5_6_1 + (1 - θ) * q5_6_0 - 1
-    cx[7] = p7_1 / (1 + p7_1) - p7_0 / (1 + p7_0) - θ * q7_8_1 + f5_7_1 - (1 - θ) * q7_8_0
-    cx[8] =
-      p8_1 / (1 + p8_1) - p8_0 / (1 + p8_0) - θ * q8_9_1 - θ * q8_10_1 - θ * q8_11_1 + θ * q7_8_1 -
-      (1 - θ) * q8_9_0 - (1 - θ) * q8_10_0 - (1 - θ) * q8_11_0 + (1 - θ) * q7_8_0
-    cx[9] = p9_1 / (1 + p9_1) - p9_0 / (1 + p9_0) + θ * q8_9_1 + (1 - θ) * q8_9_0
-    cx[10] = p10_1 / (1 + p10_1) - p10_0 / (1 + p10_0) + θ * q8_10_1 + (1 - θ) * q8_10_0 - 1
-    cx[11] =
-      p11_1 / (1 + p11_1) - p11_0 / (1 + p11_0) - θ * q11_12_1 + θ * q8_11_1 - (1 - θ) * q11_12_0 +
-      (1 - θ) * q8_11_0
-    cx[12] =
-      p12_1 / (1 + p12_1) - p12_0 / (1 + p12_0) - θ * q12_13_1 + θ * q11_12_1 - (1 - θ) * q12_13_0 +
-      (1 - θ) * q11_12_0
-    cx[13] =
-      p13_1 / (1 + p13_1) - p13_0 / (1 + p13_0) - θ * q13_14_1 - θ * q13_15_1 + θ * q12_13_1 -
-      (1 - θ) * q13_14_0 - (1 - θ) * q13_15_0 + (1 - θ) * q12_13_0 - 1
-    cx[14] = p14_1 / (1 + p14_1) - p14_0 / (1 + p14_0) + θ * q13_14_1 + (1 - θ) * q13_14_0
-    cx[15] =
-      p15_1 / (1 + p15_1) - p15_0 / (1 + p15_0) - θ * q15_16_1 + θ * q13_15_1 - (1 - θ) * q15_16_0 +
-      (1 - θ) * q13_15_0 - 1
-    cx[16] = p16_1 / (1 + p16_1) - p16_0 / (1 + p16_0) + θ * q15_16_1 + (1 - θ) * q15_16_0 - out16_1
-    cx[17] =
-      p17_1 / (1 + p17_1) - p17_0 / (1 + p17_0) - θ * q17_18_1 + θ * q1_17_1 - (1 - θ) * q17_18_0 +
-      (1 - θ) * q1_17_0 - 1
-    cx[18] =
-      p18_1 / (1 + p18_1) - p18_0 / (1 + p18_0) - θ * q18_19_1 + θ * q17_18_1 - (1 - θ) * q18_19_0 +
-      (1 - θ) * q17_18_0 - 1
-    cx[19] =
-      p19_1 / (1 + p19_1) - p19_0 / (1 + p19_0) - f19_20_1 + θ * q18_19_1 + (1 - θ) * q18_19_0
-    cx[20] =
-      p20_1 / (1 + p20_1) - p20_0 / (1 + p20_0) - θ * q20_21_1 + f19_20_1 - (1 - θ) * q20_21_0
-    cx[21] =
-      p21_1 / (1 + p21_1) - p21_0 / (1 + p21_0) - θ * q21_22_1 + θ * q20_21_1 - (1 - θ) * q21_22_0 +
-      (1 - θ) * q20_21_0 - 1
-    cx[22] =
-      p22_1 / (1 + p22_1) - p22_0 / (1 + p22_0) - θ * q22_23_1 + θ * q21_22_1 - (1 - θ) * q22_23_0 +
-      (1 - θ) * q21_22_0 - 1
-    cx[23] = p23_1 / (1 + p23_1) - p23_0 / (1 + p23_0) + θ * q22_23_1 + (1 - θ) * q22_23_0 - out23_1
-    cx[24] = p3_1 * r3_4_1 - p4_1
-    cx[25] = p5_1 * r5_7_1 - p7_1
-    cx[26] = p19_1 * r19_20_1 - p20_1
-    cx[27] = p1_1 * p1_1 - p2_1 * p2_1 - h * (1 + γ * (p1_1 + p2_1)) * (abs(q1_2_1)^α)
-    cx[28] = p1_1 * p1_1 - p17_1 * p17_1 - h * (1 + γ * (p1_1 + p17_1)) * (abs(q1_17_1)^α)
-    cx[29] = p2_1 * p2_1 - p3_1 * p3_1 - h * (1 + γ * (p2_1 + p3_1)) * (abs(q2_3_1)^α)
-    cx[30] = p4_1 * p4_1 - p5_1 * p5_1 - h * (1 + γ * (p4_1 + p5_1)) * (abs(q4_5_1)^α)
-    cx[31] = p5_1 * p5_1 - p6_1 * p6_1 - h * (1 + γ * (p5_1 + p6_1)) * (abs(q5_6_1)^α)
-    cx[32] = p7_1 * p7_1 - p8_1 * p8_1 - h * (1 + γ * (p7_1 + p8_1)) * (abs(q7_8_1)^α)
-    cx[33] = p8_1 * p8_1 - p9_1 * p9_1 - h * (1 + γ * (p8_1 + p9_1)) * (abs(q8_9_1)^α)
-    cx[34] = p8_1 * p8_1 - p10_1 * p10_1 - h * (1 + γ * (p8_1 + p10_1)) * (abs(q8_10_1)^α)
-    cx[35] = p8_1 * p8_1 - p11_1 * p11_1 - h * (1 + γ * (p8_1 + p11_1)) * (abs(q8_11_1)^α)
-    cx[36] = p11_1 * p11_1 - p12_1 * p12_1 - h * (1 + γ * (p11_1 + p12_1)) * (abs(q11_12_1)^α)
-    cx[37] = p12_1 * p12_1 - p13_1 * p13_1 - h * (1 + γ * (p12_1 + p13_1)) * (abs(q12_13_1)^α)
-    cx[38] = p13_1 * p13_1 - p14_1 * p14_1 - h * (1 + γ * (p13_1 + p14_1)) * (abs(q13_14_1)^α)
-    cx[39] = p13_1 * p13_1 - p15_1 * p15_1 - h * (1 + γ * (p13_1 + p15_1)) * (abs(q13_15_1)^α)
-    cx[40] = p15_1 * p15_1 - p16_1 * p16_1 - h * (1 + γ * (p15_1 + p16_1)) * (abs(q15_16_1)^α)
-    cx[41] = p17_1 * p17_1 - p18_1 * p18_1 - h * (1 + γ * (p17_1 + p18_1)) * (abs(q17_18_1)^α)
-    cx[42] = p18_1 * p18_1 - p19_1 * p19_1 - h * (1 + γ * (p18_1 + p19_1)) * (abs(q18_19_1)^α)
-    cx[43] = p20_1 * p20_1 - p21_1 * p21_1 - h * (1 + γ * (p20_1 + p21_1)) * (abs(q20_21_1)^α)
-    cx[44] = p21_1 * p21_1 - p22_1 * p22_1 - h * (1 + γ * (p21_1 + p22_1)) * (abs(q21_22_1)^α)
-    cx[45] = p22_1 * p22_1 - p23_1 * p23_1 - h * (1 + γ * (p22_1 + p23_1)) * (abs(q22_23_1)^α)
-
-    # time step 2
-
-    cx[46] =
-      p1_2 / (1 + p1_2) - p1_1 / (1 + p1_1) - θ * q1_17_2 - θ * q1_2_2 + in1_2 - (1 - θ) * q1_17_1 -
-      (1 - θ) * q1_2_1
-    cx[47] =
-      p2_2 / (1 + p2_2) - p2_1 / (1 + p2_1) - θ * q2_3_2 + θ * q1_2_2 - (1 - θ) * q2_3_1 +
-      (1 - θ) * q1_2_1 - 1
-    cx[48] = p3_2 / (1 + p3_2) - p3_1 / (1 + p3_1) - f3_4_2 + θ * q2_3_2 + (1 - θ) * q2_3_1
-    cx[49] = p4_2 / (1 + p4_2) - p4_1 / (1 + p4_1) - θ * q4_5_2 + f3_4_2 - (1 - θ) * q4_5_1
-    cx[50] =
-      p5_2 / (1 + p5_2) - p5_1 / (1 + p5_1) - θ * q5_6_2 - f5_7_2 + θ * q4_5_2 - (1 - θ) * q5_6_1 +
-      (1 - θ) * q4_5_1
-    cx[51] = p6_2 / (1 + p6_2) - p6_1 / (1 + p6_1) + θ * q5_6_2 + (1 - θ) * q5_6_1 - 1
-    cx[52] = p7_2 / (1 + p7_2) - p7_1 / (1 + p7_1) - θ * q7_8_2 + f5_7_2 - (1 - θ) * q7_8_1
-    cx[53] =
-      p8_2 / (1 + p8_2) - p8_1 / (1 + p8_1) - θ * q8_9_2 - θ * q8_10_2 - θ * q8_11_2 + θ * q7_8_2 -
-      (1 - θ) * q8_9_1 - (1 - θ) * q8_10_1 - (1 - θ) * q8_11_1 + (1 - θ) * q7_8_1
-    cx[54] = p9_2 / (1 + p9_2) - p9_1 / (1 + p9_1) + θ * q8_9_2 + (1 - θ) * q8_9_1
-    cx[55] = p10_2 / (1 + p10_2) - p10_1 / (1 + p10_1) + θ * q8_10_2 + (1 - θ) * q8_10_1 - 1
-    cx[56] =
-      p11_2 / (1 + p11_2) - p11_1 / (1 + p11_1) - θ * q11_12_2 + θ * q8_11_2 - (1 - θ) * q11_12_1 +
-      (1 - θ) * q8_11_1
-    cx[57] =
-      p12_2 / (1 + p12_2) - p12_1 / (1 + p12_1) - θ * q12_13_2 + θ * q11_12_2 - (1 - θ) * q12_13_1 +
-      (1 - θ) * q11_12_1
-    cx[58] =
-      p13_2 / (1 + p13_2) - p13_1 / (1 + p13_1) - θ * q13_14_2 - θ * q13_15_2 + θ * q12_13_2 -
-      (1 - θ) * q13_14_1 - (1 - θ) * q13_15_1 + (1 - θ) * q12_13_1 - 1
-    cx[59] = p14_2 / (1 + p14_2) - p14_1 / (1 + p14_1) + θ * q13_14_2 + (1 - θ) * q13_14_1
-    cx[60] =
-      p15_2 / (1 + p15_2) - p15_1 / (1 + p15_1) - θ * q15_16_2 + θ * q13_15_2 - (1 - θ) * q15_16_1 +
-      (1 - θ) * q13_15_1 - 1
-    cx[61] = p16_2 / (1 + p16_2) - p16_1 / (1 + p16_1) + θ * q15_16_2 + (1 - θ) * q15_16_1 - out16_2
-    cx[62] =
-      p17_2 / (1 + p17_2) - p17_1 / (1 + p17_1) - θ * q17_18_2 + θ * q1_17_2 - (1 - θ) * q17_18_1 +
-      (1 - θ) * q1_17_1 - 1
-    cx[63] =
-      p18_2 / (1 + p18_2) - p18_1 / (1 + p18_1) - θ * q18_19_2 + θ * q17_18_2 - (1 - θ) * q18_19_1 +
-      (1 - θ) * q17_18_1 - 1
-    cx[64] =
-      p19_2 / (1 + p19_2) - p19_1 / (1 + p19_1) - f19_20_2 + θ * q18_19_2 + (1 - θ) * q18_19_1
-    cx[65] =
-      p20_2 / (1 + p20_2) - p20_1 / (1 + p20_1) - θ * q20_21_2 + f19_20_2 - (1 - θ) * q20_21_1
-    cx[66] =
-      p21_2 / (1 + p21_2) - p21_1 / (1 + p21_1) - θ * q21_22_2 + θ * q20_21_2 - (1 - θ) * q21_22_1 +
-      (1 - θ) * q20_21_1 - 1
-    cx[67] =
-      p22_2 / (1 + p22_2) - p22_1 / (1 + p22_1) - θ * q22_23_2 + θ * q21_22_2 - (1 - θ) * q22_23_1 +
-      (1 - θ) * q21_22_1 - 1
-    cx[68] = p23_2 / (1 + p23_2) - p23_1 / (1 + p23_1) + θ * q22_23_2 + (1 - θ) * q22_23_1 - out23_2
-    cx[69] = p3_2 * r3_4_2 - p4_2
-    cx[70] = p5_2 * r5_7_2 - p7_2
-    cx[71] = p19_2 * r19_20_2 - p20_2
-    cx[72] = p1_2 * p1_2 - p2_2 * p2_2 - h * (1 + γ * (p1_2 + p2_2)) * (abs(q1_2_2)^α)
-    cx[73] = p1_2 * p1_2 - p17_2 * p17_2 - h * (1 + γ * (p1_2 + p17_2)) * (abs(q1_17_2)^α)
-    cx[74] = p2_2 * p2_2 - p3_2 * p3_2 - h * (1 + γ * (p2_2 + p3_2)) * (abs(q2_3_2)^α)
-    cx[75] = p4_2 * p4_2 - p5_2 * p5_2 - h * (1 + γ * (p4_2 + p5_2)) * (abs(q4_5_2)^α)
-    cx[76] = p5_2 * p5_2 - p6_2 * p6_2 - h * (1 + γ * (p5_2 + p6_2)) * (abs(q5_6_2)^α)
-    cx[77] = p7_2 * p7_2 - p8_2 * p8_2 - h * (1 + γ * (p7_2 + p8_2)) * (abs(q7_8_2)^α)
-    cx[78] = p8_2 * p8_2 - p9_2 * p9_2 - h * (1 + γ * (p8_2 + p9_2)) * (abs(q8_9_2)^α)
-    cx[79] = p8_2 * p8_2 - p10_2 * p10_2 - h * (1 + γ * (p8_2 + p10_2)) * (abs(q8_10_2)^α)
-    cx[80] = p8_2 * p8_2 - p11_2 * p11_2 - h * (1 + γ * (p8_2 + p11_2)) * (abs(q8_11_2)^α)
-    cx[81] = p11_2 * p11_2 - p12_2 * p12_2 - h * (1 + γ * (p11_2 + p12_2)) * (abs(q11_12_2)^α)
-    cx[82] = p12_2 * p12_2 - p13_2 * p13_2 - h * (1 + γ * (p12_2 + p13_2)) * (abs(q12_13_2)^α)
-    cx[83] = p13_2 * p13_2 - p14_2 * p14_2 - h * (1 + γ * (p13_2 + p14_2)) * (abs(q13_14_2)^α)
-    cx[84] = p13_2 * p13_2 - p15_2 * p15_2 - h * (1 + γ * (p13_2 + p15_2)) * (abs(q13_15_2)^α)
-    cx[85] = p15_2 * p15_2 - p16_2 * p16_2 - h * (1 + γ * (p15_2 + p16_2)) * (abs(q15_16_2)^α)
-    cx[86] = p17_2 * p17_2 - p18_2 * p18_2 - h * (1 + γ * (p17_2 + p18_2)) * (abs(q17_18_2)^α)
-    cx[87] = p18_2 * p18_2 - p19_2 * p19_2 - h * (1 + γ * (p18_2 + p19_2)) * (abs(q18_19_2)^α)
-    cx[88] = p20_2 * p20_2 - p21_2 * p21_2 - h * (1 + γ * (p20_2 + p21_2)) * (abs(q20_21_2)^α)
-    cx[89] = p21_2 * p21_2 - p22_2 * p22_2 - h * (1 + γ * (p21_2 + p22_2)) * (abs(q21_22_2)^α)
-    cx[90] = p22_2 * p22_2 - p23_2 * p23_2 - h * (1 + γ * (p22_2 + p23_2)) * (abs(q22_23_2)^α)
-
-    # time step 3
-
-    cx[91] =
-      p1_3 / (1 + p1_3) - p1_2 / (1 + p1_2) - θ * q1_17_3 - θ * q1_2_3 + in1_3 - (1 - θ) * q1_17_2 -
-      (1 - θ) * q1_2_2
-    cx[92] =
-      p2_3 / (1 + p2_3) - p2_2 / (1 + p2_2) - θ * q2_3_3 + θ * q1_2_3 - (1 - θ) * q2_3_2 +
-      (1 - θ) * q1_2_2 - 1
-    cx[93] = p3_3 / (1 + p3_3) - p3_2 / (1 + p3_2) - f3_4_3 + θ * q2_3_3 + (1 - θ) * q2_3_2
-    cx[94] = p4_3 / (1 + p4_3) - p4_2 / (1 + p4_2) - θ * q4_5_3 + f3_4_3 - (1 - θ) * q4_5_2
-    cx[95] =
-      p5_3 / (1 + p5_3) - p5_2 / (1 + p5_2) - θ * q5_6_3 - f5_7_3 + θ * q4_5_3 - (1 - θ) * q5_6_2 +
-      (1 - θ) * q4_5_2
-    cx[96] = p6_3 / (1 + p6_3) - p6_2 / (1 + p6_2) + θ * q5_6_3 + (1 - θ) * q5_6_2 - 1
-    cx[97] = p7_3 / (1 + p7_3) - p7_2 / (1 + p7_2) - θ * q7_8_3 + f5_7_3 - (1 - θ) * q7_8_2
-    cx[98] =
-      p8_3 / (1 + p8_3) - p8_2 / (1 + p8_2) - θ * q8_9_3 - θ * q8_10_3 - θ * q8_11_3 + θ * q7_8_3 -
-      (1 - θ) * q8_9_2 - (1 - θ) * q8_10_2 - (1 - θ) * q8_11_2 + (1 - θ) * q7_8_2
-    cx[99] = p9_3 / (1 + p9_3) - p9_2 / (1 + p9_2) + θ * q8_9_3 + (1 - θ) * q8_9_2
-    cx[100] = p10_3 / (1 + p10_3) - p10_2 / (1 + p10_2) + θ * q8_10_3 + (1 - θ) * q8_10_2 - 1
-    cx[101] =
-      p11_3 / (1 + p11_3) - p11_2 / (1 + p11_2) - θ * q11_12_3 + θ * q8_11_3 - (1 - θ) * q11_12_2 +
-      (1 - θ) * q8_11_2
-    cx[102] =
-      p12_3 / (1 + p12_3) - p12_2 / (1 + p12_2) - θ * q12_13_3 + θ * q11_12_3 - (1 - θ) * q12_13_2 +
-      (1 - θ) * q11_12_2
-    cx[103] =
-      p13_3 / (1 + p13_3) - p13_2 / (1 + p13_2) - θ * q13_14_3 - θ * q13_15_3 + θ * q12_13_3 -
-      (1 - θ) * q13_14_2 - (1 - θ) * q13_15_2 + (1 - θ) * q12_13_2 - 1
-    cx[104] = p14_3 / (1 + p14_3) - p14_2 / (1 + p14_2) + θ * q13_14_3 + (1 - θ) * q13_14_2
-    cx[105] =
-      p15_3 / (1 + p15_3) - p15_2 / (1 + p15_2) - θ * q15_16_3 + θ * q13_15_3 - (1 - θ) * q15_16_2 +
-      (1 - θ) * q13_15_2 - 1
-    cx[106] =
-      p16_3 / (1 + p16_3) - p16_2 / (1 + p16_2) + θ * q15_16_3 + (1 - θ) * q15_16_2 - out16_3
-    cx[107] =
-      p17_3 / (1 + p17_3) - p17_2 / (1 + p17_2) - θ * q17_18_3 + θ * q1_17_3 - (1 - θ) * q17_18_2 +
-      (1 - θ) * q1_17_2 - 1
-    cx[108] =
-      p18_3 / (1 + p18_3) - p18_2 / (1 + p18_2) - θ * q18_19_3 + θ * q17_18_3 - (1 - θ) * q18_19_2 +
-      (1 - θ) * q17_18_2 - 1
-    cx[109] =
-      p19_3 / (1 + p19_3) - p19_2 / (1 + p19_2) - f19_20_3 + θ * q18_19_3 + (1 - θ) * q18_19_2
-    cx[110] =
-      p20_3 / (1 + p20_3) - p20_2 / (1 + p20_2) - θ * q20_21_3 + f19_20_3 - (1 - θ) * q20_21_2
-    cx[111] =
-      p21_3 / (1 + p21_3) - p21_2 / (1 + p21_2) - θ * q21_22_3 + θ * q20_21_3 - (1 - θ) * q21_22_2 +
-      (1 - θ) * q20_21_2 - 1
-    cx[112] =
-      p22_3 / (1 + p22_3) - p22_2 / (1 + p22_2) - θ * q22_23_3 + θ * q21_22_3 - (1 - θ) * q22_23_2 +
-      (1 - θ) * q21_22_2 - 1
-    cx[113] =
-      p23_3 / (1 + p23_3) - p23_2 / (1 + p23_2) + θ * q22_23_3 + (1 - θ) * q22_23_2 - out23_3
-    cx[114] = p3_3 * r3_4_3 - p4_3
-    cx[115] = p5_3 * r5_7_3 - p7_3
-    cx[116] = p19_3 * r19_20_3 - p20_3
-    cx[117] = p1_3 * p1_3 - p2_3 * p2_3 - h * (1 + γ * (p1_3 + p2_3)) * (abs(q1_2_3)^α)
-    cx[118] = p1_3 * p1_3 - p17_3 * p17_3 - h * (1 + γ * (p1_3 + p17_3)) * (abs(q1_17_3)^α)
-    cx[119] = p2_3 * p2_3 - p3_3 * p3_3 - h * (1 + γ * (p2_3 + p3_3)) * (abs(q2_3_3)^α)
-    cx[120] = p4_3 * p4_3 - p5_3 * p5_3 - h * (1 + γ * (p4_3 + p5_3)) * (abs(q4_5_3)^α)
-    cx[121] = p5_3 * p5_3 - p6_3 * p6_3 - h * (1 + γ * (p5_3 + p6_3)) * (abs(q5_6_3)^α)
-    cx[122] = p7_3 * p7_3 - p8_3 * p8_3 - h * (1 + γ * (p7_3 + p8_3)) * (abs(q7_8_3)^α)
-    cx[123] = p8_3 * p8_3 - p9_3 * p9_3 - h * (1 + γ * (p8_3 + p9_3)) * (abs(q8_9_3)^α)
-    cx[124] = p8_3 * p8_3 - p10_3 * p10_3 - h * (1 + γ * (p8_3 + p10_3)) * (abs(q8_10_3)^α)
-    cx[125] = p8_3 * p8_3 - p11_3 * p11_3 - h * (1 + γ * (p8_3 + p11_3)) * (abs(q8_11_3)^α)
-    cx[126] = p11_3 * p11_3 - p12_3 * p12_3 - h * (1 + γ * (p11_3 + p12_3)) * (abs(q11_12_3)^α)
-    cx[127] = p12_3 * p12_3 - p13_3 * p13_3 - h * (1 + γ * (p12_3 + p13_3)) * (abs(q12_13_3)^α)
-    cx[128] = p13_3 * p13_3 - p14_3 * p14_3 - h * (1 + γ * (p13_3 + p14_3)) * (abs(q13_14_3)^α)
-    cx[129] = p13_3 * p13_3 - p15_3 * p15_3 - h * (1 + γ * (p13_3 + p15_3)) * (abs(q13_15_3)^α)
-    cx[130] = p15_3 * p15_3 - p16_3 * p16_3 - h * (1 + γ * (p15_3 + p16_3)) * (abs(q15_16_3)^α)
-    cx[131] = p17_3 * p17_3 - p18_3 * p18_3 - h * (1 + γ * (p17_3 + p18_3)) * (abs(q17_18_3)^α)
-    cx[132] = p18_3 * p18_3 - p19_3 * p19_3 - h * (1 + γ * (p18_3 + p19_3)) * (abs(q18_19_3)^α)
-    cx[133] = p20_3 * p20_3 - p21_3 * p21_3 - h * (1 + γ * (p20_3 + p21_3)) * (abs(q20_21_3)^α)
-    cx[134] = p21_3 * p21_3 - p22_3 * p22_3 - h * (1 + γ * (p21_3 + p22_3)) * (abs(q21_22_3)^α)
-    cx[135] = p22_3 * p22_3 - p23_3 * p23_3 - h * (1 + γ * (p22_3 + p23_3)) * (abs(q22_23_3)^α)
-
-    # time step 4
-
-    cx[136] =
-      p1_4 / (1 + p1_4) - p1_3 / (1 + p1_3) - θ * q1_17_4 - θ * q1_2_4 + in1_4 - (1 - θ) * q1_17_3 -
-      (1 - θ) * q1_2_3
-    cx[137] =
-      p2_4 / (1 + p2_4) - p2_3 / (1 + p2_3) - θ * q2_3_4 + θ * q1_2_4 - (1 - θ) * q2_3_3 +
-      (1 - θ) * q1_2_3 - 1
-    cx[138] = p3_4 / (1 + p3_4) - p3_3 / (1 + p3_3) - f3_4_4 + θ * q2_3_4 + (1 - θ) * q2_3_3
-    cx[139] = p4_4 / (1 + p4_4) - p4_3 / (1 + p4_3) - θ * q4_5_4 + f3_4_4 - (1 - θ) * q4_5_3
-    cx[140] =
-      p5_4 / (1 + p5_4) - p5_3 / (1 + p5_3) - θ * q5_6_4 - f5_7_4 + θ * q4_5_4 - (1 - θ) * q5_6_3 +
-      (1 - θ) * q4_5_3
-    cx[141] = p6_4 / (1 + p6_4) - p6_3 / (1 + p6_3) + θ * q5_6_4 + (1 - θ) * q5_6_3 - 1
-    cx[142] = p7_4 / (1 + p7_4) - p7_3 / (1 + p7_3) - θ * q7_8_4 + f5_7_4 - (1 - θ) * q7_8_3
-    cx[143] =
-      p8_4 / (1 + p8_4) - p8_3 / (1 + p8_3) - θ * q8_9_4 - θ * q8_10_4 - θ * q8_11_4 + θ * q7_8_4 -
-      (1 - θ) * q8_9_3 - (1 - θ) * q8_10_3 - (1 - θ) * q8_11_3 + (1 - θ) * q7_8_3
-    cx[144] = p9_4 / (1 + p9_4) - p9_3 / (1 + p9_3) + θ * q8_9_4 + (1 - θ) * q8_9_3
-    cx[145] = p10_4 / (1 + p10_4) - p10_3 / (1 + p10_3) + θ * q8_10_4 + (1 - θ) * q8_10_3 - 1
-    cx[146] =
-      p11_4 / (1 + p11_4) - p11_3 / (1 + p11_3) - θ * q11_12_4 + θ * q8_11_4 - (1 - θ) * q11_12_3 +
-      (1 - θ) * q8_11_3
-    cx[147] =
-      p12_4 / (1 + p12_4) - p12_3 / (1 + p12_3) - θ * q12_13_4 + θ * q11_12_4 - (1 - θ) * q12_13_3 +
-      (1 - θ) * q11_12_3
-    cx[148] =
-      p13_4 / (1 + p13_4) - p13_3 / (1 + p13_3) - θ * q13_14_4 - θ * q13_15_4 + θ * q12_13_4 -
-      (1 - θ) * q13_14_3 - (1 - θ) * q13_15_3 + (1 - θ) * q12_13_3 - 1
-    cx[149] = p14_4 / (1 + p14_4) - p14_3 / (1 + p14_3) + θ * q13_14_4 + (1 - θ) * q13_14_3
-    cx[150] =
-      p15_4 / (1 + p15_4) - p15_3 / (1 + p15_3) - θ * q15_16_4 + θ * q13_15_4 - (1 - θ) * q15_16_3 +
-      (1 - θ) * q13_15_3 - 1
-    cx[151] =
-      p16_4 / (1 + p16_4) - p16_3 / (1 + p16_3) + θ * q15_16_4 + (1 - θ) * q15_16_3 - out16_4
-    cx[152] =
-      p17_4 / (1 + p17_4) - p17_3 / (1 + p17_3) - θ * q17_18_4 + θ * q1_17_4 - (1 - θ) * q17_18_3 +
-      (1 - θ) * q1_17_3 - 1
-    cx[153] =
-      p18_4 / (1 + p18_4) - p18_3 / (1 + p18_3) - θ * q18_19_4 + θ * q17_18_4 - (1 - θ) * q18_19_3 +
-      (1 - θ) * q17_18_3 - 1
-    cx[154] =
-      p19_4 / (1 + p19_4) - p19_3 / (1 + p19_3) - f19_20_4 + θ * q18_19_4 + (1 - θ) * q18_19_3
-    cx[155] =
-      p20_4 / (1 + p20_4) - p20_3 / (1 + p20_3) - θ * q20_21_4 + f19_20_4 - (1 - θ) * q20_21_3
-    cx[156] =
-      p21_4 / (1 + p21_4) - p21_3 / (1 + p21_3) - θ * q21_22_4 + θ * q20_21_4 - (1 - θ) * q21_22_3 +
-      (1 - θ) * q20_21_3 - 1
-    cx[157] =
-      p22_4 / (1 + p22_4) - p22_3 / (1 + p22_3) - θ * q22_23_4 + θ * q21_22_4 - (1 - θ) * q22_23_3 +
-      (1 - θ) * q21_22_3 - 1
-    cx[158] =
-      p23_4 / (1 + p23_4) - p23_3 / (1 + p23_3) + θ * q22_23_4 + (1 - θ) * q22_23_3 - out23_4
-    cx[159] = p3_4 * r3_4_4 - p4_4
-    cx[160] = p5_4 * r5_7_4 - p7_4
-    cx[161] = p19_4 * r19_20_4 - p20_4
-    cx[162] = p1_4 * p1_4 - p2_4 * p2_4 - h * (1 + γ * (p1_4 + p2_4)) * (abs(q1_2_4)^α)
-    cx[163] = p1_4 * p1_4 - p17_4 * p17_4 - h * (1 + γ * (p1_4 + p17_4)) * (abs(q1_17_4)^α)
-    cx[164] = p2_4 * p2_4 - p3_4 * p3_4 - h * (1 + γ * (p2_4 + p3_4)) * (abs(q2_3_4)^α)
-    cx[165] = p4_4 * p4_4 - p5_4 * p5_4 - h * (1 + γ * (p4_4 + p5_4)) * (abs(q4_5_4)^α)
-    cx[166] = p5_4 * p5_4 - p6_4 * p6_4 - h * (1 + γ * (p5_4 + p6_4)) * (abs(q5_6_4)^α)
-    cx[167] = p7_4 * p7_4 - p8_4 * p8_4 - h * (1 + γ * (p7_4 + p8_4)) * (abs(q7_8_4)^α)
-    cx[168] = p8_4 * p8_4 - p9_4 * p9_4 - h * (1 + γ * (p8_4 + p9_4)) * (abs(q8_9_4)^α)
-    cx[169] = p8_4 * p8_4 - p10_4 * p10_4 - h * (1 + γ * (p8_4 + p10_4)) * (abs(q8_10_4)^α)
-    cx[170] = p8_4 * p8_4 - p11_4 * p11_4 - h * (1 + γ * (p8_4 + p11_4)) * (abs(q8_11_4)^α)
-    cx[171] = p11_4 * p11_4 - p12_4 * p12_4 - h * (1 + γ * (p11_4 + p12_4)) * (abs(q11_12_4)^α)
-    cx[172] = p12_4 * p12_4 - p13_4 * p13_4 - h * (1 + γ * (p12_4 + p13_4)) * (abs(q12_13_4)^α)
-    cx[173] = p13_4 * p13_4 - p14_4 * p14_4 - h * (1 + γ * (p13_4 + p14_4)) * (abs(q13_14_4)^α)
-    cx[174] = p13_4 * p13_4 - p15_4 * p15_4 - h * (1 + γ * (p13_4 + p15_4)) * (abs(q13_15_4)^α)
-    cx[175] = p15_4 * p15_4 - p16_4 * p16_4 - h * (1 + γ * (p15_4 + p16_4)) * (abs(q15_16_4)^α)
-    cx[176] = p17_4 * p17_4 - p18_4 * p18_4 - h * (1 + γ * (p17_4 + p18_4)) * (abs(q17_18_4)^α)
-    cx[177] = p18_4 * p18_4 - p19_4 * p19_4 - h * (1 + γ * (p18_4 + p19_4)) * (abs(q18_19_4)^α)
-    cx[178] = p20_4 * p20_4 - p21_4 * p21_4 - h * (1 + γ * (p20_4 + p21_4)) * (abs(q20_21_4)^α)
-    cx[179] = p21_4 * p21_4 - p22_4 * p22_4 - h * (1 + γ * (p21_4 + p22_4)) * (abs(q21_22_4)^α)
-    cx[180] = p22_4 * p22_4 - p23_4 * p23_4 - h * (1 + γ * (p22_4 + p23_4)) * (abs(q22_23_4)^α)
-
-    # time step 5
-
-    cx[181] =
-      p1_5 / (1 + p1_5) - p1_4 / (1 + p1_4) - θ * q1_17_5 - θ * q1_2_5 + in1_5 - (1 - θ) * q1_17_4 -
-      (1 - θ) * q1_2_4
-    cx[182] =
-      p2_5 / (1 + p2_5) - p2_4 / (1 + p2_4) - θ * q2_3_5 + θ * q1_2_5 - (1 - θ) * q2_3_4 +
-      (1 - θ) * q1_2_4 - 1
-    cx[183] = p3_5 / (1 + p3_5) - p3_4 / (1 + p3_4) - f3_4_5 + θ * q2_3_5 + (1 - θ) * q2_3_4
-    cx[184] = p4_5 / (1 + p4_5) - p4_4 / (1 + p4_4) - θ * q4_5_5 + f3_4_5 - (1 - θ) * q4_5_4
-    cx[185] =
-      p5_5 / (1 + p5_5) - p5_4 / (1 + p5_4) - θ * q5_6_5 - f5_7_5 + θ * q4_5_5 - (1 - θ) * q5_6_4 +
-      (1 - θ) * q4_5_4
-    cx[186] = p6_5 / (1 + p6_5) - p6_4 / (1 + p6_4) + θ * q5_6_5 + (1 - θ) * q5_6_4 - 1
-    cx[187] = p7_5 / (1 + p7_5) - p7_4 / (1 + p7_4) - θ * q7_8_5 + f5_7_5 - (1 - θ) * q7_8_4
-    cx[188] =
-      p8_5 / (1 + p8_5) - p8_4 / (1 + p8_4) - θ * q8_9_5 - θ * q8_10_5 - θ * q8_11_5 + θ * q7_8_5 -
-      (1 - θ) * q8_9_4 - (1 - θ) * q8_10_4 - (1 - θ) * q8_11_4 + (1 - θ) * q7_8_4
-    cx[189] = p9_5 / (1 + p9_5) - p9_4 / (1 + p9_4) + θ * q8_9_5 + (1 - θ) * q8_9_4
-    cx[190] = p10_5 / (1 + p10_5) - p10_4 / (1 + p10_4) + θ * q8_10_5 + (1 - θ) * q8_10_4 - 1
-    cx[191] =
-      p11_5 / (1 + p11_5) - p11_4 / (1 + p11_4) - θ * q11_12_5 + θ * q8_11_5 - (1 - θ) * q11_12_4 +
-      (1 - θ) * q8_11_4
-    cx[192] =
-      p12_5 / (1 + p12_5) - p12_4 / (1 + p12_4) - θ * q12_13_5 + θ * q11_12_5 - (1 - θ) * q12_13_4 +
-      (1 - θ) * q11_12_4
-    cx[193] =
-      p13_5 / (1 + p13_5) - p13_4 / (1 + p13_4) - θ * q13_14_5 - θ * q13_15_5 + θ * q12_13_5 -
-      (1 - θ) * q13_14_4 - (1 - θ) * q13_15_4 + (1 - θ) * q12_13_4 - 1
-    cx[194] = p14_5 / (1 + p14_5) - p14_4 / (1 + p14_4) + θ * q13_14_5 + (1 - θ) * q13_14_4
-    cx[195] =
-      p15_5 / (1 + p15_5) - p15_4 / (1 + p15_4) - θ * q15_16_5 + θ * q13_15_5 - (1 - θ) * q15_16_4 +
-      (1 - θ) * q13_15_4 - 1
-    cx[196] =
-      p16_5 / (1 + p16_5) - p16_4 / (1 + p16_4) + θ * q15_16_5 + (1 - θ) * q15_16_4 - out16_5
-    cx[197] =
-      p17_5 / (1 + p17_5) - p17_4 / (1 + p17_4) - θ * q17_18_5 + θ * q1_17_5 - (1 - θ) * q17_18_4 +
-      (1 - θ) * q1_17_4 - 1
-    cx[198] =
-      p18_5 / (1 + p18_5) - p18_4 / (1 + p18_4) - θ * q18_19_5 + θ * q17_18_5 - (1 - θ) * q18_19_4 +
-      (1 - θ) * q17_18_4 - 1
-    cx[199] =
-      p19_5 / (1 + p19_5) - p19_4 / (1 + p19_4) - f19_20_5 + θ * q18_19_5 + (1 - θ) * q18_19_4
-    cx[200] =
-      p20_5 / (1 + p20_5) - p20_4 / (1 + p20_4) - θ * q20_21_5 + f19_20_5 - (1 - θ) * q20_21_4
-    cx[201] =
-      p21_5 / (1 + p21_5) - p21_4 / (1 + p21_4) - θ * q21_22_5 + θ * q20_21_5 - (1 - θ) * q21_22_4 +
-      (1 - θ) * q20_21_4 - 1
-    cx[202] =
-      p22_5 / (1 + p22_5) - p22_4 / (1 + p22_4) - θ * q22_23_5 + θ * q21_22_5 - (1 - θ) * q22_23_4 +
-      (1 - θ) * q21_22_4 - 1
-    cx[203] =
-      p23_5 / (1 + p23_5) - p23_4 / (1 + p23_4) + θ * q22_23_5 + (1 - θ) * q22_23_4 - out23_5
-    cx[204] = p3_5 * r3_4_5 - p4_5
-    cx[205] = p5_5 * r5_7_5 - p7_5
-    cx[206] = p19_5 * r19_20_5 - p20_5
-    cx[207] = p1_5 * p1_5 - p2_5 * p2_5 - h * (1 + γ * (p1_5 + p2_5)) * (abs(q1_2_5)^α)
-    cx[208] = p1_5 * p1_5 - p17_5 * p17_5 - h * (1 + γ * (p1_5 + p17_5)) * (abs(q1_17_5)^α)
-    cx[209] = p2_5 * p2_5 - p3_5 * p3_5 - h * (1 + γ * (p2_5 + p3_5)) * (abs(q2_3_5)^α)
-    cx[210] = p4_5 * p4_5 - p5_5 * p5_5 - h * (1 + γ * (p4_5 + p5_5)) * (abs(q4_5_5)^α)
-    cx[211] = p5_5 * p5_5 - p6_5 * p6_5 - h * (1 + γ * (p5_5 + p6_5)) * (abs(q5_6_5)^α)
-    cx[212] = p7_5 * p7_5 - p8_5 * p8_5 - h * (1 + γ * (p7_5 + p8_5)) * (abs(q7_8_5)^α)
-    cx[213] = p8_5 * p8_5 - p9_5 * p9_5 - h * (1 + γ * (p8_5 + p9_5)) * (abs(q8_9_5)^α)
-    cx[214] = p8_5 * p8_5 - p10_5 * p10_5 - h * (1 + γ * (p8_5 + p10_5)) * (abs(q8_10_5)^α)
-    cx[215] = p8_5 * p8_5 - p11_5 * p11_5 - h * (1 + γ * (p8_5 + p11_5)) * (abs(q8_11_5)^α)
-    cx[216] = p11_5 * p11_5 - p12_5 * p12_5 - h * (1 + γ * (p11_5 + p12_5)) * (abs(q11_12_5)^α)
-    cx[217] = p12_5 * p12_5 - p13_5 * p13_5 - h * (1 + γ * (p12_5 + p13_5)) * (abs(q12_13_5)^α)
-    cx[218] = p13_5 * p13_5 - p14_5 * p14_5 - h * (1 + γ * (p13_5 + p14_5)) * (abs(q13_14_5)^α)
-    cx[219] = p13_5 * p13_5 - p15_5 * p15_5 - h * (1 + γ * (p13_5 + p15_5)) * (abs(q13_15_5)^α)
-    cx[220] = p15_5 * p15_5 - p16_5 * p16_5 - h * (1 + γ * (p15_5 + p16_5)) * (abs(q15_16_5)^α)
-    cx[221] = p17_5 * p17_5 - p18_5 * p18_5 - h * (1 + γ * (p17_5 + p18_5)) * (abs(q17_18_5)^α)
-    cx[222] = p18_5 * p18_5 - p19_5 * p19_5 - h * (1 + γ * (p18_5 + p19_5)) * (abs(q18_19_5)^α)
-    cx[223] = p20_5 * p20_5 - p21_5 * p21_5 - h * (1 + γ * (p20_5 + p21_5)) * (abs(q20_21_5)^α)
-    cx[224] = p21_5 * p21_5 - p22_5 * p22_5 - h * (1 + γ * (p21_5 + p22_5)) * (abs(q21_22_5)^α)
-    cx[225] = p22_5 * p22_5 - p23_5 * p23_5 - h * (1 + γ * (p22_5 + p23_5)) * (abs(q22_23_5)^α)
-
-    # time step 6
-
-    cx[226] =
-      p1_6 / (1 + p1_6) - p1_5 / (1 + p1_5) - θ * q1_17_6 - θ * q1_2_6 + in1_6 - (1 - θ) * q1_17_5 -
-      (1 - θ) * q1_2_5
-    cx[227] =
-      p2_6 / (1 + p2_6) - p2_5 / (1 + p2_5) - θ * q2_3_6 + θ * q1_2_6 - (1 - θ) * q2_3_5 +
-      (1 - θ) * q1_2_5 - 1
-    cx[228] = p3_6 / (1 + p3_6) - p3_5 / (1 + p3_5) - f3_4_6 + θ * q2_3_6 + (1 - θ) * q2_3_5
-    cx[229] = p4_6 / (1 + p4_6) - p4_5 / (1 + p4_5) - θ * q4_5_6 + f3_4_6 - (1 - θ) * q4_5_5
-    cx[230] =
-      p5_6 / (1 + p5_6) - p5_5 / (1 + p5_5) - θ * q5_6_6 - f5_7_6 + θ * q4_5_6 - (1 - θ) * q5_6_5 +
-      (1 - θ) * q4_5_5
-    cx[231] = p6_6 / (1 + p6_6) - p6_5 / (1 + p6_5) + θ * q5_6_6 + (1 - θ) * q5_6_5 - 1
-    cx[232] = p7_6 / (1 + p7_6) - p7_5 / (1 + p7_5) - θ * q7_8_6 + f5_7_6 - (1 - θ) * q7_8_5
-    cx[233] =
-      p8_6 / (1 + p8_6) - p8_5 / (1 + p8_5) - θ * q8_9_6 - θ * q8_10_6 - θ * q8_11_6 + θ * q7_8_6 -
-      (1 - θ) * q8_9_5 - (1 - θ) * q8_10_5 - (1 - θ) * q8_11_5 + (1 - θ) * q7_8_5
-    cx[234] = p9_6 / (1 + p9_6) - p9_5 / (1 + p9_5) + θ * q8_9_6 + (1 - θ) * q8_9_5
-    cx[235] = p10_6 / (1 + p10_6) - p10_5 / (1 + p10_5) + θ * q8_10_6 + (1 - θ) * q8_10_5 - 1
-    cx[236] =
-      p11_6 / (1 + p11_6) - p11_5 / (1 + p11_5) - θ * q11_12_6 + θ * q8_11_6 - (1 - θ) * q11_12_5 +
-      (1 - θ) * q8_11_5
-    cx[237] =
-      p12_6 / (1 + p12_6) - p12_5 / (1 + p12_5) - θ * q12_13_6 + θ * q11_12_6 - (1 - θ) * q12_13_5 +
-      (1 - θ) * q11_12_5
-    cx[238] =
-      p13_6 / (1 + p13_6) - p13_5 / (1 + p13_5) - θ * q13_14_6 - θ * q13_15_6 + θ * q12_13_6 -
-      (1 - θ) * q13_14_5 - (1 - θ) * q13_15_5 + (1 - θ) * q12_13_5 - 1
-    cx[239] = p14_6 / (1 + p14_6) - p14_5 / (1 + p14_5) + θ * q13_14_6 + (1 - θ) * q13_14_5
-    cx[240] =
-      p15_6 / (1 + p15_6) - p15_5 / (1 + p15_5) - θ * q15_16_6 + θ * q13_15_6 - (1 - θ) * q15_16_5 +
-      (1 - θ) * q13_15_5 - 1
-    cx[241] =
-      p16_6 / (1 + p16_6) - p16_5 / (1 + p16_5) + θ * q15_16_6 + (1 - θ) * q15_16_5 - out16_6
-    cx[242] =
-      p17_6 / (1 + p17_6) - p17_5 / (1 + p17_5) - θ * q17_18_6 + θ * q1_17_6 - (1 - θ) * q17_18_5 +
-      (1 - θ) * q1_17_5 - 1
-    cx[243] =
-      p18_6 / (1 + p18_6) - p18_5 / (1 + p18_5) - θ * q18_19_6 + θ * q17_18_6 - (1 - θ) * q18_19_5 +
-      (1 - θ) * q17_18_5 - 1
-    cx[244] =
-      p19_6 / (1 + p19_6) - p19_5 / (1 + p19_5) - f19_20_6 + θ * q18_19_6 + (1 - θ) * q18_19_5
-    cx[245] =
-      p20_6 / (1 + p20_6) - p20_5 / (1 + p20_5) - θ * q20_21_6 + f19_20_6 - (1 - θ) * q20_21_5
-    cx[246] =
-      p21_6 / (1 + p21_6) - p21_5 / (1 + p21_5) - θ * q21_22_6 + θ * q20_21_6 - (1 - θ) * q21_22_5 +
-      (1 - θ) * q20_21_5 - 1
-    cx[247] =
-      p22_6 / (1 + p22_6) - p22_5 / (1 + p22_5) - θ * q22_23_6 + θ * q21_22_6 - (1 - θ) * q22_23_5 +
-      (1 - θ) * q21_22_5 - 1
-    cx[248] =
-      p23_6 / (1 + p23_6) - p23_5 / (1 + p23_5) + θ * q22_23_6 + (1 - θ) * q22_23_5 - out23_6
-    cx[249] = p3_6 * r3_4_6 - p4_6
-    cx[250] = p5_6 * r5_7_6 - p7_6
-    cx[251] = p19_6 * r19_20_6 - p20_6
-    cx[252] = p1_6 * p1_6 - p2_6 * p2_6 - h * (1 + γ * (p1_6 + p2_6)) * (abs(q1_2_6)^α)
-    cx[253] = p1_6 * p1_6 - p17_6 * p17_6 - h * (1 + γ * (p1_6 + p17_6)) * (abs(q1_17_6)^α)
-    cx[254] = p2_6 * p2_6 - p3_6 * p3_6 - h * (1 + γ * (p2_6 + p3_6)) * (abs(q2_3_6)^α)
-    cx[255] = p4_6 * p4_6 - p5_6 * p5_6 - h * (1 + γ * (p4_6 + p5_6)) * (abs(q4_5_6)^α)
-    cx[256] = p5_6 * p5_6 - p6_6 * p6_6 - h * (1 + γ * (p5_6 + p6_6)) * (abs(q5_6_6)^α)
-    cx[257] = p7_6 * p7_6 - p8_6 * p8_6 - h * (1 + γ * (p7_6 + p8_6)) * (abs(q7_8_6)^α)
-    cx[258] = p8_6 * p8_6 - p9_6 * p9_6 - h * (1 + γ * (p8_6 + p9_6)) * (abs(q8_9_6)^α)
-    cx[259] = p8_6 * p8_6 - p10_6 * p10_6 - h * (1 + γ * (p8_6 + p10_6)) * (abs(q8_10_6)^α)
-    cx[260] = p8_6 * p8_6 - p11_6 * p11_6 - h * (1 + γ * (p8_6 + p11_6)) * (abs(q8_11_6)^α)
-    cx[261] = p11_6 * p11_6 - p12_6 * p12_6 - h * (1 + γ * (p11_6 + p12_6)) * (abs(q11_12_6)^α)
-    cx[262] = p12_6 * p12_6 - p13_6 * p13_6 - h * (1 + γ * (p12_6 + p13_6)) * (abs(q12_13_6)^α)
-    cx[263] = p13_6 * p13_6 - p14_6 * p14_6 - h * (1 + γ * (p13_6 + p14_6)) * (abs(q13_14_6)^α)
-    cx[264] = p13_6 * p13_6 - p15_6 * p15_6 - h * (1 + γ * (p13_6 + p15_6)) * (abs(q13_15_6)^α)
-    cx[265] = p15_6 * p15_6 - p16_6 * p16_6 - h * (1 + γ * (p15_6 + p16_6)) * (abs(q15_16_6)^α)
-    cx[266] = p17_6 * p17_6 - p18_6 * p18_6 - h * (1 + γ * (p17_6 + p18_6)) * (abs(q17_18_6)^α)
-    cx[267] = p18_6 * p18_6 - p19_6 * p19_6 - h * (1 + γ * (p18_6 + p19_6)) * (abs(q18_19_6)^α)
-    cx[268] = p20_6 * p20_6 - p21_6 * p21_6 - h * (1 + γ * (p20_6 + p21_6)) * (abs(q20_21_6)^α)
-    cx[269] = p21_6 * p21_6 - p22_6 * p22_6 - h * (1 + γ * (p21_6 + p22_6)) * (abs(q21_22_6)^α)
-    cx[270] = p22_6 * p22_6 - p23_6 * p23_6 - h * (1 + γ * (p22_6 + p23_6)) * (abs(q22_23_6)^α)
-
-    # time step 7
-
-    cx[271] =
-      p1_7 / (1 + p1_7) - p1_6 / (1 + p1_6) - θ * q1_17_7 - θ * q1_2_7 + in1_7 - (1 - θ) * q1_17_6 -
-      (1 - θ) * q1_2_6
-    cx[272] =
-      p2_7 / (1 + p2_7) - p2_6 / (1 + p2_6) - θ * q2_3_7 + θ * q1_2_7 - (1 - θ) * q2_3_6 +
-      (1 - θ) * q1_2_6 - 1
-    cx[273] = p3_7 / (1 + p3_7) - p3_6 / (1 + p3_6) - f3_4_7 + θ * q2_3_7 + (1 - θ) * q2_3_6
-    cx[274] = p4_7 / (1 + p4_7) - p4_6 / (1 + p4_6) - θ * q4_5_7 + f3_4_7 - (1 - θ) * q4_5_6
-    cx[275] =
-      p5_7 / (1 + p5_7) - p5_6 / (1 + p5_6) - θ * q5_6_7 - f5_7_7 + θ * q4_5_7 - (1 - θ) * q5_6_6 +
-      (1 - θ) * q4_5_6
-    cx[276] = p6_7 / (1 + p6_7) - p6_6 / (1 + p6_6) + θ * q5_6_7 + (1 - θ) * q5_6_6 - 1
-    cx[277] = p7_7 / (1 + p7_7) - p7_6 / (1 + p7_6) - θ * q7_8_7 + f5_7_7 - (1 - θ) * q7_8_6
-    cx[278] =
-      p8_7 / (1 + p8_7) - p8_6 / (1 + p8_6) - θ * q8_9_7 - θ * q8_10_7 - θ * q8_11_7 + θ * q7_8_7 -
-      (1 - θ) * q8_9_6 - (1 - θ) * q8_10_6 - (1 - θ) * q8_11_6 + (1 - θ) * q7_8_6
-    cx[279] = p9_7 / (1 + p9_7) - p9_6 / (1 + p9_6) + θ * q8_9_7 + (1 - θ) * q8_9_6
-    cx[280] = p10_7 / (1 + p10_7) - p10_6 / (1 + p10_6) + θ * q8_10_7 + (1 - θ) * q8_10_6 - 1
-    cx[281] =
-      p11_7 / (1 + p11_7) - p11_6 / (1 + p11_6) - θ * q11_12_7 + θ * q8_11_7 - (1 - θ) * q11_12_6 +
-      (1 - θ) * q8_11_6
-    cx[282] =
-      p12_7 / (1 + p12_7) - p12_6 / (1 + p12_6) - θ * q12_13_7 + θ * q11_12_7 - (1 - θ) * q12_13_6 +
-      (1 - θ) * q11_12_6
-    cx[283] =
-      p13_7 / (1 + p13_7) - p13_6 / (1 + p13_6) - θ * q13_14_7 - θ * q13_15_7 + θ * q12_13_7 -
-      (1 - θ) * q13_14_6 - (1 - θ) * q13_15_6 + (1 - θ) * q12_13_6 - 1
-    cx[284] = p14_7 / (1 + p14_7) - p14_6 / (1 + p14_6) + θ * q13_14_7 + (1 - θ) * q13_14_6
-    cx[285] =
-      p15_7 / (1 + p15_7) - p15_6 / (1 + p15_6) - θ * q15_16_7 + θ * q13_15_7 - (1 - θ) * q15_16_6 +
-      (1 - θ) * q13_15_6 - 1
-    cx[286] =
-      p16_7 / (1 + p16_7) - p16_6 / (1 + p16_6) + θ * q15_16_7 + (1 - θ) * q15_16_6 - out16_7
-    cx[287] =
-      p17_7 / (1 + p17_7) - p17_6 / (1 + p17_6) - θ * q17_18_7 + θ * q1_17_7 - (1 - θ) * q17_18_6 +
-      (1 - θ) * q1_17_6 - 1
-    cx[288] =
-      p18_7 / (1 + p18_7) - p18_6 / (1 + p18_6) - θ * q18_19_7 + θ * q17_18_7 - (1 - θ) * q18_19_6 +
-      (1 - θ) * q17_18_6 - 1
-    cx[289] =
-      p19_7 / (1 + p19_7) - p19_6 / (1 + p19_6) - f19_20_7 + θ * q18_19_7 + (1 - θ) * q18_19_6
-    cx[290] =
-      p20_7 / (1 + p20_7) - p20_6 / (1 + p20_6) - θ * q20_21_7 + f19_20_7 - (1 - θ) * q20_21_6
-    cx[291] =
-      p21_7 / (1 + p21_7) - p21_6 / (1 + p21_6) - θ * q21_22_7 + θ * q20_21_7 - (1 - θ) * q21_22_6 +
-      (1 - θ) * q20_21_6 - 1
-    cx[292] =
-      p22_7 / (1 + p22_7) - p22_6 / (1 + p22_6) - θ * q22_23_7 + θ * q21_22_7 - (1 - θ) * q22_23_6 +
-      (1 - θ) * q21_22_6 - 1
-    cx[293] =
-      p23_7 / (1 + p23_7) - p23_6 / (1 + p23_6) + θ * q22_23_7 + (1 - θ) * q22_23_6 - out23_7
-    cx[294] = p3_7 * r3_4_7 - p4_7
-    cx[295] = p5_7 * r5_7_7 - p7_7
-    cx[296] = p19_7 * r19_20_7 - p20_7
-    cx[297] = p1_7 * p1_7 - p2_7 * p2_7 - h * (1 + γ * (p1_7 + p2_7)) * (abs(q1_2_7)^α)
-    cx[298] = p1_7 * p1_7 - p17_7 * p17_7 - h * (1 + γ * (p1_7 + p17_7)) * (abs(q1_17_7)^α)
-    cx[299] = p2_7 * p2_7 - p3_7 * p3_7 - h * (1 + γ * (p2_7 + p3_7)) * (abs(q2_3_7)^α)
-    cx[300] = p4_7 * p4_7 - p5_7 * p5_7 - h * (1 + γ * (p4_7 + p5_7)) * (abs(q4_5_7)^α)
-    cx[301] = p5_7 * p5_7 - p6_7 * p6_7 - h * (1 + γ * (p5_7 + p6_7)) * (abs(q5_6_7)^α)
-    cx[302] = p7_7 * p7_7 - p8_7 * p8_7 - h * (1 + γ * (p7_7 + p8_7)) * (abs(q7_8_7)^α)
-    cx[303] = p8_7 * p8_7 - p9_7 * p9_7 - h * (1 + γ * (p8_7 + p9_7)) * (abs(q8_9_7)^α)
-    cx[304] = p8_7 * p8_7 - p10_7 * p10_7 - h * (1 + γ * (p8_7 + p10_7)) * (abs(q8_10_7)^α)
-    cx[305] = p8_7 * p8_7 - p11_7 * p11_7 - h * (1 + γ * (p8_7 + p11_7)) * (abs(q8_11_7)^α)
-    cx[306] = p11_7 * p11_7 - p12_7 * p12_7 - h * (1 + γ * (p11_7 + p12_7)) * (abs(q11_12_7)^α)
-    cx[307] = p12_7 * p12_7 - p13_7 * p13_7 - h * (1 + γ * (p12_7 + p13_7)) * (abs(q12_13_7)^α)
-    cx[308] = p13_7 * p13_7 - p14_7 * p14_7 - h * (1 + γ * (p13_7 + p14_7)) * (abs(q13_14_7)^α)
-    cx[309] = p13_7 * p13_7 - p15_7 * p15_7 - h * (1 + γ * (p13_7 + p15_7)) * (abs(q13_15_7)^α)
-    cx[310] = p15_7 * p15_7 - p16_7 * p16_7 - h * (1 + γ * (p15_7 + p16_7)) * (abs(q15_16_7)^α)
-    cx[311] = p17_7 * p17_7 - p18_7 * p18_7 - h * (1 + γ * (p17_7 + p18_7)) * (abs(q17_18_7)^α)
-    cx[312] = p18_7 * p18_7 - p19_7 * p19_7 - h * (1 + γ * (p18_7 + p19_7)) * (abs(q18_19_7)^α)
-    cx[313] = p20_7 * p20_7 - p21_7 * p21_7 - h * (1 + γ * (p20_7 + p21_7)) * (abs(q20_21_7)^α)
-    cx[314] = p21_7 * p21_7 - p22_7 * p22_7 - h * (1 + γ * (p21_7 + p22_7)) * (abs(q21_22_7)^α)
-    cx[315] = p22_7 * p22_7 - p23_7 * p23_7 - h * (1 + γ * (p22_7 + p23_7)) * (abs(q22_23_7)^α)
-
-    # time step 8
-
-    cx[316] =
-      p1_8 / (1 + p1_8) - p1_7 / (1 + p1_7) - θ * q1_17_8 - θ * q1_2_8 + in1_8 - (1 - θ) * q1_17_7 -
-      (1 - θ) * q1_2_7
-    cx[317] =
-      p2_8 / (1 + p2_8) - p2_7 / (1 + p2_7) - θ * q2_3_8 + θ * q1_2_8 - (1 - θ) * q2_3_7 +
-      (1 - θ) * q1_2_7 - 1
-    cx[318] = p3_8 / (1 + p3_8) - p3_7 / (1 + p3_7) - f3_4_8 + θ * q2_3_8 + (1 - θ) * q2_3_7
-    cx[319] = p4_8 / (1 + p4_8) - p4_7 / (1 + p4_7) - θ * q4_5_8 + f3_4_8 - (1 - θ) * q4_5_7
-    cx[320] =
-      p5_8 / (1 + p5_8) - p5_7 / (1 + p5_7) - θ * q5_6_8 - f5_7_8 + θ * q4_5_8 - (1 - θ) * q5_6_7 +
-      (1 - θ) * q4_5_7
-    cx[321] = p6_8 / (1 + p6_8) - p6_7 / (1 + p6_7) + θ * q5_6_8 + (1 - θ) * q5_6_7 - 1
-    cx[322] = p7_8 / (1 + p7_8) - p7_7 / (1 + p7_7) - θ * q7_8_8 + f5_7_8 - (1 - θ) * q7_8_7
-    cx[323] =
-      p8_8 / (1 + p8_8) - p8_7 / (1 + p8_7) - θ * q8_9_8 - θ * q8_10_8 - θ * q8_11_8 + θ * q7_8_8 -
-      (1 - θ) * q8_9_7 - (1 - θ) * q8_10_7 - (1 - θ) * q8_11_7 + (1 - θ) * q7_8_7
-    cx[324] = p9_8 / (1 + p9_8) - p9_7 / (1 + p9_7) + θ * q8_9_8 + (1 - θ) * q8_9_7
-    cx[325] = p10_8 / (1 + p10_8) - p10_7 / (1 + p10_7) + θ * q8_10_8 + (1 - θ) * q8_10_7 - 1
-    cx[326] =
-      p11_8 / (1 + p11_8) - p11_7 / (1 + p11_7) - θ * q11_12_8 + θ * q8_11_8 - (1 - θ) * q11_12_7 +
-      (1 - θ) * q8_11_7
-    cx[327] =
-      p12_8 / (1 + p12_8) - p12_7 / (1 + p12_7) - θ * q12_13_8 + θ * q11_12_8 - (1 - θ) * q12_13_7 +
-      (1 - θ) * q11_12_7
-    cx[328] =
-      p13_8 / (1 + p13_8) - p13_7 / (1 + p13_7) - θ * q13_14_8 - θ * q13_15_8 + θ * q12_13_8 -
-      (1 - θ) * q13_14_7 - (1 - θ) * q13_15_7 + (1 - θ) * q12_13_7 - 1
-    cx[329] = p14_8 / (1 + p14_8) - p14_7 / (1 + p14_7) + θ * q13_14_8 + (1 - θ) * q13_14_7
-    cx[330] =
-      p15_8 / (1 + p15_8) - p15_7 / (1 + p15_7) - θ * q15_16_8 + θ * q13_15_8 - (1 - θ) * q15_16_7 +
-      (1 - θ) * q13_15_7 - 1
-    cx[331] =
-      p16_8 / (1 + p16_8) - p16_7 / (1 + p16_7) + θ * q15_16_8 + (1 - θ) * q15_16_7 - out16_8
-    cx[332] =
-      p17_8 / (1 + p17_8) - p17_7 / (1 + p17_7) - θ * q17_18_8 + θ * q1_17_8 - (1 - θ) * q17_18_7 +
-      (1 - θ) * q1_17_7 - 1
-    cx[333] =
-      p18_8 / (1 + p18_8) - p18_7 / (1 + p18_7) - θ * q18_19_8 + θ * q17_18_8 - (1 - θ) * q18_19_7 +
-      (1 - θ) * q17_18_7 - 1
-    cx[334] =
-      p19_8 / (1 + p19_8) - p19_7 / (1 + p19_7) - f19_20_8 + θ * q18_19_8 + (1 - θ) * q18_19_7
-    cx[335] =
-      p20_8 / (1 + p20_8) - p20_7 / (1 + p20_7) - θ * q20_21_8 + f19_20_8 - (1 - θ) * q20_21_7
-    cx[336] =
-      p21_8 / (1 + p21_8) - p21_7 / (1 + p21_7) - θ * q21_22_8 + θ * q20_21_8 - (1 - θ) * q21_22_7 +
-      (1 - θ) * q20_21_7 - 1
-    cx[337] =
-      p22_8 / (1 + p22_8) - p22_7 / (1 + p22_7) - θ * q22_23_8 + θ * q21_22_8 - (1 - θ) * q22_23_7 +
-      (1 - θ) * q21_22_7 - 1
-    cx[338] =
-      p23_8 / (1 + p23_8) - p23_7 / (1 + p23_7) + θ * q22_23_8 + (1 - θ) * q22_23_7 - out23_8
-    cx[339] = p3_8 * r3_4_8 - p4_8
-    cx[340] = p5_8 * r5_7_8 - p7_8
-    cx[341] = p19_8 * r19_20_8 - p20_8
-    cx[342] = p1_8 * p1_8 - p2_8 * p2_8 - h * (1 + γ * (p1_8 + p2_8)) * (abs(q1_2_8)^α)
-    cx[343] = p1_8 * p1_8 - p17_8 * p17_8 - h * (1 + γ * (p1_8 + p17_8)) * (abs(q1_17_8)^α)
-    cx[344] = p2_8 * p2_8 - p3_8 * p3_8 - h * (1 + γ * (p2_8 + p3_8)) * (abs(q2_3_8)^α)
-    cx[345] = p4_8 * p4_8 - p5_8 * p5_8 - h * (1 + γ * (p4_8 + p5_8)) * (abs(q4_5_8)^α)
-    cx[346] = p5_8 * p5_8 - p6_8 * p6_8 - h * (1 + γ * (p5_8 + p6_8)) * (abs(q5_6_8)^α)
-    cx[347] = p7_8 * p7_8 - p8_8 * p8_8 - h * (1 + γ * (p7_8 + p8_8)) * (abs(q7_8_8)^α)
-    cx[348] = p8_8 * p8_8 - p9_8 * p9_8 - h * (1 + γ * (p8_8 + p9_8)) * (abs(q8_9_8)^α)
-    cx[349] = p8_8 * p8_8 - p10_8 * p10_8 - h * (1 + γ * (p8_8 + p10_8)) * (abs(q8_10_8)^α)
-    cx[350] = p8_8 * p8_8 - p11_8 * p11_8 - h * (1 + γ * (p8_8 + p11_8)) * (abs(q8_11_8)^α)
-    cx[351] = p11_8 * p11_8 - p12_8 * p12_8 - h * (1 + γ * (p11_8 + p12_8)) * (abs(q11_12_8)^α)
-    cx[352] = p12_8 * p12_8 - p13_8 * p13_8 - h * (1 + γ * (p12_8 + p13_8)) * (abs(q12_13_8)^α)
-    cx[353] = p13_8 * p13_8 - p14_8 * p14_8 - h * (1 + γ * (p13_8 + p14_8)) * (abs(q13_14_8)^α)
-    cx[354] = p13_8 * p13_8 - p15_8 * p15_8 - h * (1 + γ * (p13_8 + p15_8)) * (abs(q13_15_8)^α)
-    cx[355] = p15_8 * p15_8 - p16_8 * p16_8 - h * (1 + γ * (p15_8 + p16_8)) * (abs(q15_16_8)^α)
-    cx[356] = p17_8 * p17_8 - p18_8 * p18_8 - h * (1 + γ * (p17_8 + p18_8)) * (abs(q17_18_8)^α)
-    cx[357] = p18_8 * p18_8 - p19_8 * p19_8 - h * (1 + γ * (p18_8 + p19_8)) * (abs(q18_19_8)^α)
-    cx[358] = p20_8 * p20_8 - p21_8 * p21_8 - h * (1 + γ * (p20_8 + p21_8)) * (abs(q20_21_8)^α)
-    cx[359] = p21_8 * p21_8 - p22_8 * p22_8 - h * (1 + γ * (p21_8 + p22_8)) * (abs(q21_22_8)^α)
-    cx[360] = p22_8 * p22_8 - p23_8 * p23_8 - h * (1 + γ * (p22_8 + p23_8)) * (abs(q22_23_8)^α)
+    p = (p_1, p_2, p_3, p_4, p_5, p_6, p_7, p_8)
+    q = (q_1, q_2, q_3, q_4, q_5, q_6, q_7, q_8)
+    r = (r_1, r_2, r_3, r_4, r_5, r_6, r_7, r_8)
+    in_ = (in_1, in_2, in_3, in_4, in_5, in_6, in_7, in_8)
+    out_ = (out_1, out_2, out_3, out_4, out_5, out_6, out_7, out_8)
+
+    for t = 1:8
+      pt, qt, rt, int, outt = p[t], q[t], r[t], in_[t], out_[t]
+      p_prev = t == 1 ? p_0 : p[t - 1]
+      q_prev = t == 1 ? q_0 : q[t - 1]
+
+      mt = 1 + (t - 1) * 45
+
+      # 23 constraints
+      for i = 1:23
+        cx[mt + i] = pt[i] / (1 + pt[i]) - p_prev[i] / (1 + p_prev[i]) - 1
+      end
+      for (k, (i, j)) in enumerate(q_ind)
+        c[mt + i] -= (θ * qt[k] + (1 - θ) * q_prev[k])
+        c[mt + j] += (θ * qt[k] + (1 - θ) * q_prev[k])
+      end
+      for (k, i) in enumerate(in_ind)
+        c[mt + i] += int[j]
+      end
+      for (k, i) in enumerate(out_ind)
+        c[mt + i] -= outt[k]
+      end
+      for (k, i) in enumerate(ones_ind)
+        c[mt + i] -= 1
+      end
+
+      # 3 constraints
+      for (k, (i, j)) in enumerate(fr_ind)
+        cx[mt + 24 + k] = pt[i] * rt[k] - pt[j]
+      end
+
+      # 19 constraints
+      for (k, (i, j)) in enumerate(q_ind)
+        cx[mt + 28 + k] = pt[i]^2 - pt[j]^2 - h * (1 + γ * (pt[i] + pt[j])) * (abs(qt[k])^α)
+      end
+    end
 
     return cx
   end
-  lvar = T[
-    0.0,
-    0.0,
-    0.0,
-    0.0,
-    0.0,
-    0.0,
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-    0.0,
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-    1.0e-16,
-    1.0e-16,
-    1.0e-16,
-    1.0e-16,
-    1.0e-16,
-    1.0e-16,
-    1.0e-16,
-    0.0,
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-    1.0,
-    1.0,
-    1.0,
-    0.0,
-    0.0,
-    0.0,
-    1.0,
-    1.0,
-    1.0,
-    0.0,
-    0.0,
-    0.0,
-    1.0,
-    1.0,
-    1.0,
-    0.0,
-    0.0,
-    0.0,
-    1.0,
-    1.0,
-    1.0,
-    0.0,
-    0.0,
-    0.0,
-    1.0,
-    1.0,
-    1.0,
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-    0.0,
-    0.0,
-    0.0,
-    0.0,
-    0.0,
-    0.0,
-  ]
-  uvar = T[
-    Inf,
-    Inf,
-    Inf,
-    Inf,
-    Inf,
-    Inf,
-    Inf,
-    Inf,
-    Inf,
-    Inf,
-    Inf,
-    Inf,
-    Inf,
-    Inf,
-    Inf,
-    Inf,
-    Inf,
-    Inf,
-    Inf,
-    Inf,
-    Inf,
-    Inf,
-    Inf,
-    Inf,
-    Inf,
-    Inf,
-    Inf,
-    Inf,
-    Inf,
-    Inf,
-    Inf,
-    Inf,
-    Inf,
-    Inf,
-    Inf,
-    Inf,
-    Inf,
-    Inf,
-    Inf,
-    Inf,
-    Inf,
-    Inf,
-    Inf,
-    Inf,
-    Inf,
-    Inf,
-    Inf,
-    Inf,
-    Inf,
-    Inf,
-    Inf,
-    Inf,
-    Inf,
-    Inf,
-    Inf,
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-  ]
+  lvar = vcat(  #
+    zeros(T, 23 * 9),  # p
+    fill(1e-16, 19 * 9),  # q
+    repeat(vcat(zeros(T, 3), ones(T, 3)), 8),  # f and r
+  )
+  uvar = vcat(  #
+    fill(typemax(T), 23 * 9),  # p
+    fill(typemax(T), 19 * 9),  # q
+    repeat(vcat(fill(typemax(T), 3), 10 .* ones(T, 3)), 8)fill(typemax(T), 3 * 8),
+  )
   lcon = zeros(T, 360)
   ucon = zeros(T, 360)