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800 second compile time on ForwardDiff example #27488

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ChrisRackauckas opened this issue Jun 8, 2018 · 15 comments
Closed

800 second compile time on ForwardDiff example #27488

ChrisRackauckas opened this issue Jun 8, 2018 · 15 comments
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compiler:latency Compiler latency

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@ChrisRackauckas
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I isolated the issue SciML/DifferentialEquations.jl#303 at least down to ForwardDiff on a large nonlinear function.

P2D2c = function(dy,y,pars,t)
    Dbulk = pars[1]
    Dsn = pars[2]
    Dsp = pars[3]
    F = 96487.000000
    R = 8.314300
    Rpn = pars[4]
    Rpp = pars[5]
    Tr = 298.150000
    brugn = pars[6]
    brugp = pars[7]
    brugs = pars[8]
    c0 = pars[9]
    ctn = pars[10]
    ctp = pars[11]
    efn = pars[12]
    efp = pars[13]
    en = pars[14]
    ep = pars[15]
    es = pars[16]
    kn = pars[17]
    kp = pars[18]
    ln1 = pars[19]
    lp = pars[20]
    ls = pars[21]
    sigmn = pars[22]
    sigmp = pars[23]
    socn = pars[24]
    socp = pars[25]
    t1 = pars[26]


    current = -1.0
    capacity=17.5
    rate=-2.
    iapp=capacity*rate
    up=[0.,0.]
    Kr = pars[27]


    ap = 3/Rpp*(1-ep-efp)

    an = 3/Rpn*(1-en-efn)

    sigmap = sigmp*(1-ep-efp)

    sigman = sigmn*(1-en-efn)

    D2pos = ep^brugp*Dbulk

    D2sep = es^brugs*Dbulk

    D2neg = en^brugn*Dbulk

    dy[1] = 1/ep*(64.*D2pos/lp^2*(y[60]-2.*y[1]+y[2])+2.*ap*(1.-1.*t1)*kp*(y[1]*c0)^.5*(-1.*y[110]*ctp+ctp)^.5*(y[110]*ctp)^.5*sinh(.5*F/R/Tr*(y[86]-1.*y[65]-1.*ocp_cathode(y[110],up)))/c0)
    dy[2] = 1/ep*(64.*D2pos/lp^2*(y[1]-2.*y[2]+y[3])+2.*ap*(1.-1.*t1)*kp*(y[2]*c0)^.5*(-1.*y[111]*ctp+ctp)^.5*(y[111]*ctp)^.5*sinh(.5*F/R/Tr*(y[87]-1.*y[66]-1.*ocp_cathode(y[111],up)))/c0)
    dy[3] = 1/ep*(64.*D2pos/lp^2*(y[2]-2.*y[3]+y[4])+2.*ap*(1.-1.*t1)*kp*(y[3]*c0)^.5*(-1.*y[112]*ctp+ctp)^.5*(y[112]*ctp)^.5*sinh(.5*F/R/Tr*(y[88]-1.*y[67]-1.*ocp_cathode(y[112],up)))/c0)
    dy[4] = 1/ep*(64.*D2pos/lp^2*(y[3]-2.*y[4]+y[5])+2.*ap*(1.-1.*t1)*kp*(y[4]*c0)^.5*(-1.*y[113]*ctp+ctp)^.5*(y[113]*ctp)^.5*sinh(.5*F/R/Tr*(y[89]-1.*y[68]-1.*ocp_cathode(y[113],up)))/c0)
    dy[5] = 1/ep*(64.*D2pos/lp^2*(y[4]-2.*y[5]+y[6])+2.*ap*(1.-1.*t1)*kp*(y[5]*c0)^.5*(-1.*y[114]*ctp+ctp)^.5*(y[114]*ctp)^.5*sinh(.5*F/R/Tr*(y[90]-1.*y[69]-1.*ocp_cathode(y[114],up)))/c0)
    dy[6] = 1/ep*(64.*D2pos/lp^2*(y[5]-2.*y[6]+y[7])+2.*ap*(1.-1.*t1)*kp*(y[6]*c0)^.5*(-1.*y[115]*ctp+ctp)^.5*(y[115]*ctp)^.5*sinh(.5*F/R/Tr*(y[91]-1.*y[70]-1.*ocp_cathode(y[115],up)))/c0)
    dy[7] = 1/ep*(64.*D2pos/lp^2*(y[6]-2.*y[7]+y[61])+2.*ap*(1.-1.*t1)*kp*(y[7]*c0)^.5*(-1.*y[116]*ctp+ctp)^.5*(y[116]*ctp)^.5*sinh(.5*F/R/Tr*(y[92]-1.*y[71]-1.*ocp_cathode(y[116],up)))/c0)
    dy[8] = 16./es*D2sep/ls^2*(y[61]-2.*y[8]+y[9])
    dy[9] = 16./es*D2sep/ls^2*(y[8]-2.*y[9]+y[10])
    dy[10] = 16./es*D2sep/ls^2*(y[9]-2.*y[10]+y[62])
    dy[11] = 1/en*(64.*D2neg/ln1^2*(y[62]-2.*y[11]+y[12])+2.*an*(1.-1.*t1)*kn*(y[11]*c0)^.5*(-1.*y[124]*ctn+ctn)^.5*(y[124]*ctn)^.5*sinh(.5*F/R/Tr*(y[95]-1.*y[77]+.5e-1-2.325*exp(-100.*y[124]^1.15)+.1721*tanh(20.000000*y[124]-21.000000)+.25e-2*tanh(39.347962*y[124]-37.241379)+.34e-1*tanh(89.411765*y[124]-6.0294118)+.2e-2*tanh(7.0422535*y[124]-1.3661972)+.155e-1*tanh(77.519380*y[124]-8.1395349)))/c0)
    dy[12] = 1/en*(64.*D2neg/ln1^2*(y[11]-2.*y[12]+y[13])+2.*an*(1.-1.*t1)*kn*(y[12]*c0)^.5*(-1.*y[125]*ctn+ctn)^.5*(y[125]*ctn)^.5*sinh(.5*F/R/Tr*(y[96]-1.*y[78]+.5e-1-2.325*exp(-100.*y[125]^1.15)+.1721*tanh(20.000000*y[125]-21.000000)+.25e-2*tanh(39.347962*y[125]-37.241379)+.34e-1*tanh(89.411765*y[125]-6.0294118)+.2e-2*tanh(7.0422535*y[125]-1.3661972)+.155e-1*tanh(77.519380*y[125]-8.1395349)))/c0)
    dy[13] = 1/en*(64.*D2neg/ln1^2*(y[12]-2.*y[13]+y[14])+2.*an*(1.-1.*t1)*kn*(y[13]*c0)^.5*(-1.*y[126]*ctn+ctn)^.5*(y[126]*ctn)^.5*sinh(.5*F/R/Tr*(y[97]-1.*y[79]+.5e-1-2.325*exp(-100.*y[126]^1.15)+.1721*tanh(20.000000*y[126]-21.000000)+.25e-2*tanh(39.347962*y[126]-37.241379)+.34e-1*tanh(89.411765*y[126]-6.0294118)+.2e-2*tanh(7.0422535*y[126]-1.3661972)+.155e-1*tanh(77.519380*y[126]-8.1395349)))/c0)
    dy[14] = 1/en*(64.*D2neg/ln1^2*(y[13]-2.*y[14]+y[15])+2.*an*(1.-1.*t1)*kn*(y[14]*c0)^.5*(-1.*y[127]*ctn+ctn)^.5*(y[127]*ctn)^.5*sinh(.5*F/R/Tr*(y[98]-1.*y[80]+.5e-1-2.325*exp(-100.*y[127]^1.15)+.1721*tanh(20.000000*y[127]-21.000000)+.25e-2*tanh(39.347962*y[127]-37.241379)+.34e-1*tanh(89.411765*y[127]-6.0294118)+.2e-2*tanh(7.0422535*y[127]-1.3661972)+.155e-1*tanh(77.519380*y[127]-8.1395349)))/c0)
    dy[15] = 1/en*(64.*D2neg/ln1^2*(y[14]-2.*y[15]+y[16])+2.*an*(1.-1.*t1)*kn*(y[15]*c0)^.5*(-1.*y[128]*ctn+ctn)^.5*(y[128]*ctn)^.5*sinh(.5*F/R/Tr*(y[99]-1.*y[81]+.5e-1-2.325*exp(-100.*y[128]^1.15)+.1721*tanh(20.000000*y[128]-21.000000)+.25e-2*tanh(39.347962*y[128]-37.241379)+.34e-1*tanh(89.411765*y[128]-6.0294118)+.2e-2*tanh(7.0422535*y[128]-1.3661972)+.155e-1*tanh(77.519380*y[128]-8.1395349)))/c0)
    dy[16] = 1/en*(64.*D2neg/ln1^2*(y[15]-2.*y[16]+y[17])+2.*an*(1.-1.*t1)*kn*(y[16]*c0)^.5*(-1.*y[129]*ctn+ctn)^.5*(y[129]*ctn)^.5*sinh(.5*F/R/Tr*(y[100]-1.*y[82]+.5e-1-2.325*exp(-100.*y[129]^1.15)+.1721*tanh(20.000000*y[129]-21.000000)+.25e-2*tanh(39.347962*y[129]-37.241379)+.34e-1*tanh(89.411765*y[129]-6.0294118)+.2e-2*tanh(7.0422535*y[129]-1.3661972)+.155e-1*tanh(77.519380*y[129]-8.1395349)))/c0)
    dy[17] = 1/en*(64.*D2neg/ln1^2*(y[16]-2.*y[17]+y[63])+2.*an*(1.-1.*t1)*kn*(y[17]*c0)^.5*(-1.*y[130]*ctn+ctn)^.5*(y[130]*ctn)^.5*sinh(.5*F/R/Tr*(y[101]-1.*y[83]+.5e-1-2.325*exp(-100.*y[130]^1.15)+.1721*tanh(20.000000*y[130]-21.000000)+.25e-2*tanh(39.347962*y[130]-37.241379)+.34e-1*tanh(89.411765*y[130]-6.0294118)+.2e-2*tanh(7.0422535*y[130]-1.3661972)+.155e-1*tanh(77.519380*y[130]-8.1395349)))/c0)
    dy[18] = 16.*(Dsp*(y[25]-1.*y[103])+Dsp*(y[103]-2.*y[18]+y[25]))/Rpp^2
    dy[19] = 16.*(Dsp*(y[26]-1.*y[104])+Dsp*(y[104]-2.*y[19]+y[26]))/Rpp^2
    dy[20] = 16.*(Dsp*(y[27]-1.*y[105])+Dsp*(y[105]-2.*y[20]+y[27]))/Rpp^2
    dy[21] = 16.*(Dsp*(y[28]-1.*y[106])+Dsp*(y[106]-2.*y[21]+y[28]))/Rpp^2
    dy[22] = 16.*(Dsp*(y[29]-1.*y[107])+Dsp*(y[107]-2.*y[22]+y[29]))/Rpp^2
    dy[23] = 16.*(Dsp*(y[30]-1.*y[108])+Dsp*(y[108]-2.*y[23]+y[30]))/Rpp^2
    dy[24] = 16.*(Dsp*(y[31]-1.*y[109])+Dsp*(y[109]-2.*y[24]+y[31]))/Rpp^2
    dy[25] = 4.*(2.*Dsp*(y[32]-1.*y[18])+4.*Dsp*(y[18]-2.*y[25]+y[32]))/Rpp^2
    dy[26] = 4.*(2.*Dsp*(y[33]-1.*y[19])+4.*Dsp*(y[19]-2.*y[26]+y[33]))/Rpp^2
    dy[27] = 4.*(2.*Dsp*(y[34]-1.*y[20])+4.*Dsp*(y[20]-2.*y[27]+y[34]))/Rpp^2
    dy[28] = 4.*(2.*Dsp*(y[35]-1.*y[21])+4.*Dsp*(y[21]-2.*y[28]+y[35]))/Rpp^2
    dy[29] = 4.*(2.*Dsp*(y[36]-1.*y[22])+4.*Dsp*(y[22]-2.*y[29]+y[36]))/Rpp^2
    dy[30] = 4.*(2.*Dsp*(y[37]-1.*y[23])+4.*Dsp*(y[23]-2.*y[30]+y[37]))/Rpp^2
    dy[31] = 4.*(2.*Dsp*(y[38]-1.*y[24])+4.*Dsp*(y[24]-2.*y[31]+y[38]))/Rpp^2
    dy[32] = 1.777777778*(3.*Dsp*(y[110]-1.*y[25])+9.*Dsp*(y[25]-2.*y[32]+y[110]))/Rpp^2
    dy[33] = 1.777777778*(3.*Dsp*(y[111]-1.*y[26])+9.*Dsp*(y[26]-2.*y[33]+y[111]))/Rpp^2
    dy[34] = 1.777777778*(3.*Dsp*(y[112]-1.*y[27])+9.*Dsp*(y[27]-2.*y[34]+y[112]))/Rpp^2
    dy[35] = 1.777777778*(3.*Dsp*(y[113]-1.*y[28])+9.*Dsp*(y[28]-2.*y[35]+y[113]))/Rpp^2
    dy[36] = 1.777777778*(3.*Dsp*(y[114]-1.*y[29])+9.*Dsp*(y[29]-2.*y[36]+y[114]))/Rpp^2
    dy[37] = 1.777777778*(3.*Dsp*(y[115]-1.*y[30])+9.*Dsp*(y[30]-2.*y[37]+y[115]))/Rpp^2
    dy[38] = 1.777777778*(3.*Dsp*(y[116]-1.*y[31])+9.*Dsp*(y[31]-2.*y[38]+y[116]))/Rpp^2
    dy[39] = 16.*Dsn*(2.*y[46]-2.*y[39])/Rpn^2
    dy[40] = 16.*Dsn*(2.*y[47]-2.*y[40])/Rpn^2
    dy[41] = 16.*Dsn*(2.*y[48]-2.*y[41])/Rpn^2
    dy[42] = 16.*Dsn*(2.*y[49]-2.*y[42])/Rpn^2
    dy[43] = 16.*Dsn*(2.*y[50]-2.*y[43])/Rpn^2
    dy[44] = 16.*Dsn*(2.*y[51]-2.*y[44])/Rpn^2
    dy[45] = 16.*Dsn*(2.*y[52]-2.*y[45])/Rpn^2
    dy[46] = 4.*Dsn*(6.*y[53]+2.*y[39]-8.*y[46])/Rpn^2
    dy[47] = 4.*Dsn*(6.*y[54]+2.*y[40]-8.*y[47])/Rpn^2
    dy[48] = 4.*Dsn*(6.*y[55]+2.*y[41]-8.*y[48])/Rpn^2
    dy[49] = 4.*Dsn*(6.*y[56]+2.*y[42]-8.*y[49])/Rpn^2
    dy[50] = 4.*Dsn*(6.*y[57]+2.*y[43]-8.*y[50])/Rpn^2
    dy[51] = 4.*Dsn*(6.*y[58]+2.*y[44]-8.*y[51])/Rpn^2
    dy[52] = 4.*Dsn*(6.*y[59]+2.*y[45]-8.*y[52])/Rpn^2
    dy[53] = 1.777777778*Dsn*(12.*y[124]+6.*y[46]-18.*y[53])/Rpn^2
    dy[54] = 1.777777778*Dsn*(12.*y[125]+6.*y[47]-18.*y[54])/Rpn^2
    dy[55] = 1.777777778*Dsn*(12.*y[126]+6.*y[48]-18.*y[55])/Rpn^2
    dy[56] = 1.777777778*Dsn*(12.*y[127]+6.*y[49]-18.*y[56])/Rpn^2
    dy[57] = 1.777777778*Dsn*(12.*y[128]+6.*y[50]-18.*y[57])/Rpn^2
    dy[58] = 1.777777778*Dsn*(12.*y[129]+6.*y[51]-18.*y[58])/Rpn^2
    dy[59] = 1.777777778*Dsn*(12.*y[130]+6.*y[52]-18.*y[59])/Rpn^2
    dy[60] = 4.*D2pos*(-1.*y[2]-3.*y[60]+4.*y[1])/lp
    dy[61] = 4.*D2pos*(y[6]+3.*y[61]-4.*y[7])/lp-2.*D2sep*(-1.*y[9]-3.*y[61]+4.*y[8])/ls
    dy[62] = 2.*D2sep*(y[9]+3.*y[62]-4.*y[10])/ls-4.*D2neg*(-1.*y[12]-3.*y[62]+4.*y[11])/ln1
    dy[63] = 4.*D2neg*(y[16]+3.*y[63]-4.*y[17])/ln1
    dy[64] = 4.*(-1.*y[66]-3.*y[64]+4.*y[65])/lp
    dy[65] = -4.*sigmap/lp*(y[87]-1.*y[85])-4.*ep^brugp*(.41253e-1+.5007e-3*y[1]-.47212e-6*y[1]^2+.15904e-9*y[1]^3-.16018e-13*y[1]^4)/lp*(y[66]-1.*y[64])+8.*ep^brugp*(.41253e-1+.5007e-3*y[1]-.47212e-6*y[1]^2+.15904e-9*y[1]^3-.16018e-13*y[1]^4)*R*Tr/F*(1.-1.*t1)/lp*(y[2]-1.*y[60])/y[1]-iapp
    dy[66] = -4.*sigmap/lp*(y[88]-1.*y[86])-4.*ep^brugp*(.41253e-1+.5007e-3*y[2]-.47212e-6*y[2]^2+.15904e-9*y[2]^3-.16018e-13*y[2]^4)/lp*(y[67]-1.*y[65])+8.*ep^brugp*(.41253e-1+.5007e-3*y[2]-.47212e-6*y[2]^2+.15904e-9*y[2]^3-.16018e-13*y[2]^4)*R*Tr/F*(1.-1.*t1)/lp*(y[3]-1.*y[1])/y[2]-iapp
    dy[67] = -4.*sigmap/lp*(y[89]-1.*y[87])-4.*ep^brugp*(.41253e-1+.5007e-3*y[3]-.47212e-6*y[3]^2+.15904e-9*y[3]^3-.16018e-13*y[3]^4)/lp*(y[68]-1.*y[66])+8.*ep^brugp*(.41253e-1+.5007e-3*y[3]-.47212e-6*y[3]^2+.15904e-9*y[3]^3-.16018e-13*y[3]^4)*R*Tr/F*(1.-1.*t1)/lp*(y[4]-1.*y[2])/y[3]-iapp
    dy[68] = -4.*sigmap/lp*(y[90]-1.*y[88])-4.*ep^brugp*(.41253e-1+.5007e-3*y[4]-.47212e-6*y[4]^2+.15904e-9*y[4]^3-.16018e-13*y[4]^4)/lp*(y[69]-1.*y[67])+8.*ep^brugp*(.41253e-1+.5007e-3*y[4]-.47212e-6*y[4]^2+.15904e-9*y[4]^3-.16018e-13*y[4]^4)*R*Tr/F*(1.-1.*t1)/lp*(y[5]-1.*y[3])/y[4]-iapp
    dy[69] = -4.*sigmap/lp*(y[91]-1.*y[89])-4.*ep^brugp*(.41253e-1+.5007e-3*y[5]-.47212e-6*y[5]^2+.15904e-9*y[5]^3-.16018e-13*y[5]^4)/lp*(y[70]-1.*y[68])+8.*ep^brugp*(.41253e-1+.5007e-3*y[5]-.47212e-6*y[5]^2+.15904e-9*y[5]^3-.16018e-13*y[5]^4)*R*Tr/F*(1.-1.*t1)/lp*(y[6]-1.*y[4])/y[5]-iapp
    dy[70] = -4.*sigmap/lp*(y[92]-1.*y[90])-4.*ep^brugp*(.41253e-1+.5007e-3*y[6]-.47212e-6*y[6]^2+.15904e-9*y[6]^3-.16018e-13*y[6]^4)/lp*(y[71]-1.*y[69])+8.*ep^brugp*(.41253e-1+.5007e-3*y[6]-.47212e-6*y[6]^2+.15904e-9*y[6]^3-.16018e-13*y[6]^4)*R*Tr/F*(1.-1.*t1)/lp*(y[7]-1.*y[5])/y[6]-iapp
    dy[71] = -4.*sigmap/lp*(y[93]-1.*y[91])-4.*ep^brugp*(.41253e-1+.5007e-3*y[7]-.47212e-6*y[7]^2+.15904e-9*y[7]^3-.16018e-13*y[7]^4)/lp*(y[72]-1.*y[70])+8.*ep^brugp*(.41253e-1+.5007e-3*y[7]-.47212e-6*y[7]^2+.15904e-9*y[7]^3-.16018e-13*y[7]^4)*R*Tr/F*(1.-1.*t1)/lp*(y[61]-1.*y[6])/y[7]-iapp
    dy[72] = 4.*ep^brugp*(.41253e-1+.5007e-3*y[61]-.47212e-6*y[61]^2+.15904e-9*y[61]^3-.16018e-13*y[61]^4)*(y[70]+3.*y[72]-4.*y[71])/lp-2.*es^brugs*(.41253e-1+.5007e-3*y[61]-.47212e-6*y[61]^2+.15904e-9*y[61]^3-.16018e-13*y[61]^4)*(-1.*y[74]-3.*y[72]+4.*y[73])/ls
    dy[73] = -2.*es^brugs*(.41253e-1+.5007e-3*y[8]-.47212e-6*y[8]^2+.15904e-9*y[8]^3-.16018e-13*y[8]^4)/ls*(y[74]-1.*y[72])+4.*es^brugs*(.41253e-1+.5007e-3*y[8]-.47212e-6*y[8]^2+.15904e-9*y[8]^3-.16018e-13*y[8]^4)*R*Tr/F*(1.-1.*t1)/ls*(y[9]-1.*y[61])/y[8]-iapp
    dy[74] = -2.*es^brugs*(.41253e-1+.5007e-3*y[9]-.47212e-6*y[9]^2+.15904e-9*y[9]^3-.16018e-13*y[9]^4)/ls*(y[75]-1.*y[73])+4.*es^brugs*(.41253e-1+.5007e-3*y[9]-.47212e-6*y[9]^2+.15904e-9*y[9]^3-.16018e-13*y[9]^4)*R*Tr/F*(1.-1.*t1)/ls*(y[10]-1.*y[8])/y[9]-iapp
    dy[75] = -2.*es^brugs*(.41253e-1+.5007e-3*y[10]-.47212e-6*y[10]^2+.15904e-9*y[10]^3-.16018e-13*y[10]^4)/ls*(y[76]-1.*y[74])+4.*es^brugs*(.41253e-1+.5007e-3*y[10]-.47212e-6*y[10]^2+.15904e-9*y[10]^3-.16018e-13*y[10]^4)*R*Tr/F*(1.-1.*t1)/ls*(y[62]-1.*y[9])/y[10]-iapp
    dy[76] = 2.*es^brugs*(.41253e-1+.5007e-3*y[62]-.47212e-6*y[62]^2+.15904e-9*y[62]^3-.16018e-13*y[62]^4)*(y[74]+3.*y[76]-4.*y[75])/ls-4.*en^brugn*(.41253e-1+.5007e-3*y[62]-.47212e-6*y[62]^2+.15904e-9*y[62]^3-.16018e-13*y[62]^4)*(-1.*y[78]-3.*y[76]+4.*y[77])/ln1
    dy[77] = -4.*sigman/ln1*(y[96]-1.*y[94])-4.*en^brugn*(.41253e-1+.5007e-3*y[11]-.47212e-6*y[11]^2+.15904e-9*y[11]^3-.16018e-13*y[11]^4)/ln1*(y[78]-1.*y[76])+8.*en^brugn*(.41253e-1+.5007e-3*y[11]-.47212e-6*y[11]^2+.15904e-9*y[11]^3-.16018e-13*y[11]^4)*R*Tr/F*(1.-1.*t1)/ln1*(y[12]-1.*y[62])/y[11]-iapp
    dy[78] = -4.*sigman/ln1*(y[97]-1.*y[95])-4.*en^brugn*(.41253e-1+.5007e-3*y[12]-.47212e-6*y[12]^2+.15904e-9*y[12]^3-.16018e-13*y[12]^4)/ln1*(y[79]-1.*y[77])+8.*en^brugn*(.41253e-1+.5007e-3*y[12]-.47212e-6*y[12]^2+.15904e-9*y[12]^3-.16018e-13*y[12]^4)*R*Tr/F*(1.-1.*t1)/ln1*(y[13]-1.*y[11])/y[12]-iapp
    dy[79] = -4.*sigman/ln1*(y[98]-1.*y[96])-4.*en^brugn*(.41253e-1+.5007e-3*y[13]-.47212e-6*y[13]^2+.15904e-9*y[13]^3-.16018e-13*y[13]^4)/ln1*(y[80]-1.*y[78])+8.*en^brugn*(.41253e-1+.5007e-3*y[13]-.47212e-6*y[13]^2+.15904e-9*y[13]^3-.16018e-13*y[13]^4)*R*Tr/F*(1.-1.*t1)/ln1*(y[14]-1.*y[12])/y[13]-iapp
    dy[80] = -4.*sigman/ln1*(y[99]-1.*y[97])-4.*en^brugn*(.41253e-1+.5007e-3*y[14]-.47212e-6*y[14]^2+.15904e-9*y[14]^3-.16018e-13*y[14]^4)/ln1*(y[81]-1.*y[79])+8.*en^brugn*(.41253e-1+.5007e-3*y[14]-.47212e-6*y[14]^2+.15904e-9*y[14]^3-.16018e-13*y[14]^4)*R*Tr/F*(1.-1.*t1)/ln1*(y[15]-1.*y[13])/y[14]-iapp
    dy[81] = -4.*sigman/ln1*(y[100]-1.*y[98])-4.*en^brugn*(.41253e-1+.5007e-3*y[15]-.47212e-6*y[15]^2+.15904e-9*y[15]^3-.16018e-13*y[15]^4)/ln1*(y[82]-1.*y[80])+8.*en^brugn*(.41253e-1+.5007e-3*y[15]-.47212e-6*y[15]^2+.15904e-9*y[15]^3-.16018e-13*y[15]^4)*R*Tr/F*(1.-1.*t1)/ln1*(y[16]-1.*y[14])/y[15]-iapp
    dy[82] = -4.*sigman/ln1*(y[101]-1.*y[99])-4.*en^brugn*(.41253e-1+.5007e-3*y[16]-.47212e-6*y[16]^2+.15904e-9*y[16]^3-.16018e-13*y[16]^4)/ln1*(y[83]-1.*y[81])+8.*en^brugn*(.41253e-1+.5007e-3*y[16]-.47212e-6*y[16]^2+.15904e-9*y[16]^3-.16018e-13*y[16]^4)*R*Tr/F*(1.-1.*t1)/ln1*(y[17]-1.*y[15])/y[16]-iapp
    dy[83] = -4.*sigman/ln1*(y[102]-1.*y[100])-4.*en^brugn*(.41253e-1+.5007e-3*y[17]-.47212e-6*y[17]^2+.15904e-9*y[17]^3-.16018e-13*y[17]^4)/ln1*(y[84]-1.*y[82])+8.*en^brugn*(.41253e-1+.5007e-3*y[17]-.47212e-6*y[17]^2+.15904e-9*y[17]^3-.16018e-13*y[17]^4)*R*Tr/F*(1.-1.*t1)/ln1*(y[63]-1.*y[16])/y[17]-iapp
    dy[84] = y[84]
    dy[85] = 4.*(-1.*y[87]-3.*y[85]+4.*y[86])/lp+1.*iapp/sigmap
    dy[86] = 64.*sigmap/lp^2*(y[85]-2.*y[86]+y[87])-2.*ap*F*kp*(y[1]*c0)^.5*(-1.*y[110]*ctp+ctp)^.5*(y[110]*ctp)^.5*sinh(.5*F/R/Tr*(y[86]-1.*y[65]-1.*ocp_cathode(y[110],up)))
    dy[87] = 64.*sigmap/lp^2*(y[86]-2.*y[87]+y[88])-2.*ap*F*kp*(y[2]*c0)^.5*(-1.*y[111]*ctp+ctp)^.5*(y[111]*ctp)^.5*sinh(.5*F/R/Tr*(y[87]-1.*y[66]-1.*ocp_cathode(y[111],up)))
    dy[88] = 64.*sigmap/lp^2*(y[87]-2.*y[88]+y[89])-2.*ap*F*kp*(y[3]*c0)^.5*(-1.*y[112]*ctp+ctp)^.5*(y[112]*ctp)^.5*sinh(.5*F/R/Tr*(y[88]-1.*y[67]-1.*ocp_cathode(y[112],up)))
    dy[89] = 64.*sigmap/lp^2*(y[88]-2.*y[89]+y[90])-2.*ap*F*kp*(y[4]*c0)^.5*(-1.*y[113]*ctp+ctp)^.5*(y[113]*ctp)^.5*sinh(.5*F/R/Tr*(y[89]-1.*y[68]-1.*ocp_cathode(y[113],up)))
    dy[90] = 64.*sigmap/lp^2*(y[89]-2.*y[90]+y[91])-2.*ap*F*kp*(y[5]*c0)^.5*(-1.*y[114]*ctp+ctp)^.5*(y[114]*ctp)^.5*sinh(.5*F/R/Tr*(y[90]-1.*y[69]-1.*ocp_cathode(y[114],up)))
    dy[91] = 64.*sigmap/lp^2*(y[90]-2.*y[91]+y[92])-2.*ap*F*kp*(y[6]*c0)^.5*(-1.*y[115]*ctp+ctp)^.5*(y[115]*ctp)^.5*sinh(.5*F/R/Tr*(y[91]-1.*y[70]-1.*ocp_cathode(y[115],up)))
    dy[92] = 64.*sigmap/lp^2*(y[91]-2.*y[92]+y[93])-2.*ap*F*kp*(y[7]*c0)^.5*(-1.*y[116]*ctp+ctp)^.5*(y[116]*ctp)^.5*sinh(.5*F/R/Tr*(y[92]-1.*y[71]-1.*ocp_cathode(y[116],up)))
    dy[93] = 4.*(y[91]+3.*y[93]-4.*y[92])/lp
    dy[94] = 4.*(-1.*y[96]-3.*y[94]+4.*y[95])/ln1
    dy[95] = 64.*sigman/ln1^2*(y[94]-2.*y[95]+y[96])-2.*an*F*kn*(y[11]*c0)^.5*(-1.*y[124]*ctn+ctn)^.5*(y[124]*ctn)^.5*sinh(.5*F/R/Tr*(y[95]-1.*y[77]+.5e-1-2.325*exp(-100.*y[124]^1.15)+.1721*tanh(20.000000*y[124]-21.000000)+.25e-2*tanh(39.347962*y[124]-37.241379)+.34e-1*tanh(89.411765*y[124]-6.0294118)+.2e-2*tanh(7.0422535*y[124]-1.3661972)+.155e-1*tanh(77.519380*y[124]-8.1395349)))
    dy[96] = 64.*sigman/ln1^2*(y[95]-2.*y[96]+y[97])-2.*an*F*kn*(y[12]*c0)^.5*(-1.*y[125]*ctn+ctn)^.5*(y[125]*ctn)^.5*sinh(.5*F/R/Tr*(y[96]-1.*y[78]+.5e-1-2.325*exp(-100.*y[125]^1.15)+.1721*tanh(20.000000*y[125]-21.000000)+.25e-2*tanh(39.347962*y[125]-37.241379)+.34e-1*tanh(89.411765*y[125]-6.0294118)+.2e-2*tanh(7.0422535*y[125]-1.3661972)+.155e-1*tanh(77.519380*y[125]-8.1395349)))
    dy[97] = 64.*sigman/ln1^2*(y[96]-2.*y[97]+y[98])-2.*an*F*kn*(y[13]*c0)^.5*(-1.*y[126]*ctn+ctn)^.5*(y[126]*ctn)^.5*sinh(.5*F/R/Tr*(y[97]-1.*y[79]+.5e-1-2.325*exp(-100.*y[126]^1.15)+.1721*tanh(20.000000*y[126]-21.000000)+.25e-2*tanh(39.347962*y[126]-37.241379)+.34e-1*tanh(89.411765*y[126]-6.0294118)+.2e-2*tanh(7.0422535*y[126]-1.3661972)+.155e-1*tanh(77.519380*y[126]-8.1395349)))
    dy[98] = 64.*sigman/ln1^2*(y[97]-2.*y[98]+y[99])-2.*an*F*kn*(y[14]*c0)^.5*(-1.*y[127]*ctn+ctn)^.5*(y[127]*ctn)^.5*sinh(.5*F/R/Tr*(y[98]-1.*y[80]+.5e-1-2.325*exp(-100.*y[127]^1.15)+.1721*tanh(20.000000*y[127]-21.000000)+.25e-2*tanh(39.347962*y[127]-37.241379)+.34e-1*tanh(89.411765*y[127]-6.0294118)+.2e-2*tanh(7.0422535*y[127]-1.3661972)+.155e-1*tanh(77.519380*y[127]-8.1395349)))
    dy[99] = 64.*sigman/ln1^2*(y[98]-2.*y[99]+y[100])-2.*an*F*kn*(y[15]*c0)^.5*(-1.*y[128]*ctn+ctn)^.5*(y[128]*ctn)^.5*sinh(.5*F/R/Tr*(y[99]-1.*y[81]+.5e-1-2.325*exp(-100.*y[128]^1.15)+.1721*tanh(20.000000*y[128]-21.000000)+.25e-2*tanh(39.347962*y[128]-37.241379)+.34e-1*tanh(89.411765*y[128]-6.0294118)+.2e-2*tanh(7.0422535*y[128]-1.3661972)+.155e-1*tanh(77.519380*y[128]-8.1395349)))
    dy[100] = 64.*sigman/ln1^2*(y[99]-2.*y[100]+y[101])-2.*an*F*kn*(y[16]*c0)^.5*(-1.*y[129]*ctn+ctn)^.5*(y[129]*ctn)^.5*sinh(.5*F/R/Tr*(y[100]-1.*y[82]+.5e-1-2.325*exp(-100.*y[129]^1.15)+.1721*tanh(20.000000*y[129]-21.000000)+.25e-2*tanh(39.347962*y[129]-37.241379)+.34e-1*tanh(89.411765*y[129]-6.0294118)+.2e-2*tanh(7.0422535*y[129]-1.3661972)+.155e-1*tanh(77.519380*y[129]-8.1395349)))
    dy[101] = 64.*sigman/ln1^2*(y[100]-2.*y[101]+y[102])-2.*an*F*kn*(y[17]*c0)^.5*(-1.*y[130]*ctn+ctn)^.5*(y[130]*ctn)^.5*sinh(.5*F/R/Tr*(y[101]-1.*y[83]+.5e-1-2.325*exp(-100.*y[130]^1.15)+.1721*tanh(20.000000*y[130]-21.000000)+.25e-2*tanh(39.347962*y[130]-37.241379)+.34e-1*tanh(89.411765*y[130]-6.0294118)+.2e-2*tanh(7.0422535*y[130]-1.3661972)+.155e-1*tanh(77.519380*y[130]-8.1395349)))
    dy[102] = 4.*(y[100]+3.*y[102]-4.*y[101])/ln1+1.*iapp/sigman
    dy[103] = -2.*(-1.*y[25]-3.*y[103]+4.*y[18])/Rpp
    dy[104] = -2.*(-1.*y[26]-3.*y[104]+4.*y[19])/Rpp
    dy[105] = -2.*(-1.*y[27]-3.*y[105]+4.*y[20])/Rpp
    dy[106] = -2.*(-1.*y[28]-3.*y[106]+4.*y[21])/Rpp
    dy[107] = -2.*(-1.*y[29]-3.*y[107]+4.*y[22])/Rpp
    dy[108] = -2.*(-1.*y[30]-3.*y[108]+4.*y[23])/Rpp
    dy[109] = -2.*(-1.*y[31]-3.*y[109]+4.*y[24])/Rpp
    dy[110] = 2.*Dsp*(y[25]+3.*y[110]-4.*y[32])/Rpp+2.*kp*(y[1]*c0)^.5*(-1.*y[110]*ctp+ctp)^.5*(y[110]*ctp)^.5*sinh(.5*F/R/Tr*(y[86]-1.*y[65]-1.*ocp_cathode(y[110],up)))/ctp
    dy[111] = 2.*Dsp*(y[26]+3.*y[111]-4.*y[33])/Rpp+2.*kp*(y[2]*c0)^.5*(-1.*y[111]*ctp+ctp)^.5*(y[111]*ctp)^.5*sinh(.5*F/R/Tr*(y[87]-1.*y[66]-1.*ocp_cathode(y[111],up)))/ctp
    dy[112] = 2.*Dsp*(y[27]+3.*y[112]-4.*y[34])/Rpp+2.*kp*(y[3]*c0)^.5*(-1.*y[112]*ctp+ctp)^.5*(y[112]*ctp)^.5*sinh(.5*F/R/Tr*(y[88]-1.*y[67]-1.*ocp_cathode(y[112],up)))/ctp
    dy[113] = 2.*Dsp*(y[28]+3.*y[113]-4.*y[35])/Rpp+2.*kp*(y[4]*c0)^.5*(-1.*y[113]*ctp+ctp)^.5*(y[113]*ctp)^.5*sinh(.5*F/R/Tr*(y[89]-1.*y[68]-1.*ocp_cathode(y[113],up)))/ctp
    dy[114] = 2.*Dsp*(y[29]+3.*y[114]-4.*y[36])/Rpp+2.*kp*(y[5]*c0)^.5*(-1.*y[114]*ctp+ctp)^.5*(y[114]*ctp)^.5*sinh(.5*F/R/Tr*(y[90]-1.*y[69]-1.*ocp_cathode(y[114],up)))/ctp
    dy[115] = 2.*Dsp*(y[30]+3.*y[115]-4.*y[37])/Rpp+2.*kp*(y[6]*c0)^.5*(-1.*y[115]*ctp+ctp)^.5*(y[115]*ctp)^.5*sinh(.5*F/R/Tr*(y[91]-1.*y[70]-1.*ocp_cathode(y[115],up)))/ctp
    dy[116] = 2.*Dsp*(y[31]+3.*y[116]-4.*y[38])/Rpp+2.*kp*(y[7]*c0)^.5*(-1.*y[116]*ctp+ctp)^.5*(y[116]*ctp)^.5*sinh(.5*F/R/Tr*(y[92]-1.*y[71]-1.*ocp_cathode(y[116],up)))/ctp
    dy[117] = -2.*(-1.*y[46]-3.*y[117]+4.*y[39])/Rpn
    dy[118] = -2.*(-1.*y[47]-3.*y[118]+4.*y[40])/Rpn
    dy[119] = -2.*(-1.*y[48]-3.*y[119]+4.*y[41])/Rpn
    dy[120] = -2.*(-1.*y[49]-3.*y[120]+4.*y[42])/Rpn
    dy[121] = -2.*(-1.*y[50]-3.*y[121]+4.*y[43])/Rpn
    dy[122] = -2.*(-1.*y[51]-3.*y[122]+4.*y[44])/Rpn
    dy[123] = -2.*(-1.*y[52]-3.*y[123]+4.*y[45])/Rpn
    dy[124] = 2.*Dsn*(y[46]+3.*y[124]-4.*y[53])/Rpn+2.*kn*(y[11]*c0)^.5*(-1.*y[124]*ctn+ctn)^.5*(y[124]*ctn)^.5*sinh(.5*F/R/Tr*(y[95]-1.*y[77]+.5e-1-2.325*exp(-100.*y[124]^1.15)+.1721*tanh(20.000000*y[124]-21.000000)+.25e-2*tanh(39.347962*y[124]-37.241379)+.34e-1*tanh(89.411765*y[124]-6.0294118)+.2e-2*tanh(7.0422535*y[124]-1.3661972)+.155e-1*tanh(77.519380*y[124]-8.1395349)))/ctn
    dy[125] = 2.*Dsn*(y[47]+3.*y[125]-4.*y[54])/Rpn+2.*kn*(y[12]*c0)^.5*(-1.*y[125]*ctn+ctn)^.5*(y[125]*ctn)^.5*sinh(.5*F/R/Tr*(y[96]-1.*y[78]+.5e-1-2.325*exp(-100.*y[125]^1.15)+.1721*tanh(20.000000*y[125]-21.000000)+.25e-2*tanh(39.347962*y[125]-37.241379)+.34e-1*tanh(89.411765*y[125]-6.0294118)+.2e-2*tanh(7.0422535*y[125]-1.3661972)+.155e-1*tanh(77.519380*y[125]-8.1395349)))/ctn
    dy[126] = 2.*Dsn*(y[48]+3.*y[126]-4.*y[55])/Rpn+2.*kn*(y[13]*c0)^.5*(-1.*y[126]*ctn+ctn)^.5*(y[126]*ctn)^.5*sinh(.5*F/R/Tr*(y[97]-1.*y[79]+.5e-1-2.325*exp(-100.*y[126]^1.15)+.1721*tanh(20.000000*y[126]-21.000000)+.25e-2*tanh(39.347962*y[126]-37.241379)+.34e-1*tanh(89.411765*y[126]-6.0294118)+.2e-2*tanh(7.0422535*y[126]-1.3661972)+.155e-1*tanh(77.519380*y[126]-8.1395349)))/ctn
    dy[127] = 2.*Dsn*(y[49]+3.*y[127]-4.*y[56])/Rpn+2.*kn*(y[14]*c0)^.5*(-1.*y[127]*ctn+ctn)^.5*(y[127]*ctn)^.5*sinh(.5*F/R/Tr*(y[98]-1.*y[80]+.5e-1-2.325*exp(-100.*y[127]^1.15)+.1721*tanh(20.000000*y[127]-21.000000)+.25e-2*tanh(39.347962*y[127]-37.241379)+.34e-1*tanh(89.411765*y[127]-6.0294118)+.2e-2*tanh(7.0422535*y[127]-1.3661972)+.155e-1*tanh(77.519380*y[127]-8.1395349)))/ctn
    dy[128] = 2.*Dsn*(y[50]+3.*y[128]-4.*y[57])/Rpn+2.*kn*(y[15]*c0)^.5*(-1.*y[128]*ctn+ctn)^.5*(y[128]*ctn)^.5*sinh(.5*F/R/Tr*(y[99]-1.*y[81]+.5e-1-2.325*exp(-100.*y[128]^1.15)+.1721*tanh(20.000000*y[128]-21.000000)+.25e-2*tanh(39.347962*y[128]-37.241379)+.34e-1*tanh(89.411765*y[128]-6.0294118)+.2e-2*tanh(7.0422535*y[128]-1.3661972)+.155e-1*tanh(77.519380*y[128]-8.1395349)))/ctn
    dy[129] = 2.*Dsn*(y[51]+3.*y[129]-4.*y[58])/Rpn+2.*kn*(y[16]*c0)^.5*(-1.*y[129]*ctn+ctn)^.5*(y[129]*ctn)^.5*sinh(.5*F/R/Tr*(y[100]-1.*y[82]+.5e-1-2.325*exp(-100.*y[129]^1.15)+.1721*tanh(20.000000*y[129]-21.000000)+.25e-2*tanh(39.347962*y[129]-37.241379)+.34e-1*tanh(89.411765*y[129]-6.0294118)+.2e-2*tanh(7.0422535*y[129]-1.3661972)+.155e-1*tanh(77.519380*y[129]-8.1395349)))/ctn
    dy[130] = 2.*Dsn*(y[52]+3.*y[130]-4.*y[59])/Rpn+2.*kn*(y[17]*c0)^.5*(-1.*y[130]*ctn+ctn)^.5*(y[130]*ctn)^.5*sinh(.5*F/R/Tr*(y[101]-1.*y[83]+.5e-1-2.325*exp(-100.*y[130]^1.15)+.1721*tanh(20.000000*y[130]-21.000000)+.25e-2*tanh(39.347962*y[130]-37.241379)+.34e-1*tanh(89.411765*y[130]-6.0294118)+.2e-2*tanh(7.0422535*y[130]-1.3661972)+.155e-1*tanh(77.519380*y[130]-8.1395349)))/ctn
    dy[131] = y[131]-y[85]+y[102]+ (current*Kr)

end
function ocp_cathode(theta_p,up)
    Up = (-5.057-13.6*theta_p^2+121.6*theta_p^4-185.1*theta_p^6-45.43*theta_p^8+127.7*theta_p^10)/(-1-5.04*theta_p^2+32.3*theta_p^4-40.95*theta_p^6-25.94*theta_p^8+40.63*theta_p^10)

end
yyy = function(pars::Array{Float64})
    socn=pars[24]
    socp=pars[25]
    y0 = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,socp,socp,socp,socp,socp,socp,socp,socp,socp,socp,socp,socp,socp,socp,socp,socp,socp,socp,socp,socp,socp,socn,socn,socn,socn,socn,socn,socn,socn,socn,socn,socn,socn,socn,socn,socn,socn,socn,socn,socn,socn,socn,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,(-0.5057e1 - 0.136e2 * socp ^ 2 + 0.1216e3 * socp ^ 4 - 0.1851e3 * socp ^ 6 - 0.4543e2 * socp ^ 8 + 0.1277e3 * socp ^ 10) / (-0.1e1 - 0.504e1 * socp ^ 2 + 0.323e2 * socp ^ 4 - 0.4095e2 * socp ^ 6 - 0.2594e2 * socp ^ 8 + 0.4063e2 * socp ^ 10),(-0.5057e1 - 0.136e2 * socp ^ 2 + 0.1216e3 * socp ^ 4 - 0.1851e3 * socp ^ 6 - 0.4543e2 * socp ^ 8 + 0.1277e3 * socp ^ 10) / (-0.1e1 - 0.504e1 * socp ^ 2 + 0.323e2 * socp ^ 4 - 0.4095e2 * socp ^ 6 - 0.2594e2 * socp ^ 8 + 0.4063e2 * socp ^ 10),(-0.5057e1 - 0.136e2 * socp ^ 2 + 0.1216e3 * socp ^ 4 - 0.1851e3 * socp ^ 6 - 0.4543e2 * socp ^ 8 + 0.1277e3 * socp ^ 10) / (-0.1e1 - 0.504e1 * socp ^ 2 + 0.323e2 * socp ^ 4 - 0.4095e2 * socp ^ 6 - 0.2594e2 * socp ^ 8 + 0.4063e2 * socp ^ 10),(-0.5057e1 - 0.136e2 * socp ^ 2 + 0.1216e3 * socp ^ 4 - 0.1851e3 * socp ^ 6 - 0.4543e2 * socp ^ 8 + 0.1277e3 * socp ^ 10) / (-0.1e1 - 0.504e1 * socp ^ 2 + 0.323e2 * socp ^ 4 - 0.4095e2 * socp ^ 6 - 0.2594e2 * socp ^ 8 + 0.4063e2 * socp ^ 10),(-0.5057e1 - 0.136e2 * socp ^ 2 + 0.1216e3 * socp ^ 4 - 0.1851e3 * socp ^ 6 - 0.4543e2 * socp ^ 8 + 0.1277e3 * socp ^ 10) / (-0.1e1 - 0.504e1 * socp ^ 2 + 0.323e2 * socp ^ 4 - 0.4095e2 * socp ^ 6 - 0.2594e2 * socp ^ 8 + 0.4063e2 * socp ^ 10),(-0.5057e1 - 0.136e2 * socp ^ 2 + 0.1216e3 * socp ^ 4 - 0.1851e3 * socp ^ 6 - 0.4543e2 * socp ^ 8 + 0.1277e3 * socp ^ 10) / (-0.1e1 - 0.504e1 * socp ^ 2 + 0.323e2 * socp ^ 4 - 0.4095e2 * socp ^ 6 - 0.2594e2 * socp ^ 8 + 0.4063e2 * socp ^ 10),(-0.5057e1 - 0.136e2 * socp ^ 2 + 0.1216e3 * socp ^ 4 - 0.1851e3 * socp ^ 6 - 0.4543e2 * socp ^ 8 + 0.1277e3 * socp ^ 10) / (-0.1e1 - 0.504e1 * socp ^ 2 + 0.323e2 * socp ^ 4 - 0.4095e2 * socp ^ 6 - 0.2594e2 * socp ^ 8 + 0.4063e2 * socp ^ 10),(-0.5057e1 - 0.136e2 * socp ^ 2 + 0.1216e3 * socp ^ 4 - 0.1851e3 * socp ^ 6 - 0.4543e2 * socp ^ 8 + 0.1277e3 * socp ^ 10) / (-0.1e1 - 0.504e1 * socp ^ 2 + 0.323e2 * socp ^ 4 - 0.4095e2 * socp ^ 6 - 0.2594e2 * socp ^ 8 + 0.4063e2 * socp ^ 10),(-0.5057e1 - 0.136e2 * socp ^ 2 + 0.1216e3 * socp ^ 4 - 0.1851e3 * socp ^ 6 - 0.4543e2 * socp ^ 8 + 0.1277e3 * socp ^ 10) / (-0.1e1 - 0.504e1 * socp ^ 2 + 0.323e2 * socp ^ 4 - 0.4095e2 * socp ^ 6 - 0.2594e2 * socp ^ 8 + 0.4063e2 * socp ^ 10),-0.5e-1 + 0.2325e1 * exp(-0.100e3 * socn ^ 0.115e1) - 0.1721e0 * tanh(0.20000000e2 * socn - 0.21000000e2) - 0.25e-2 * tanh(0.39347962e2 * socn - 0.37241379e2) - 0.34e-1 * tanh(0.89411765e2 * socn - 0.60294118e1) - 0.2e-2 * tanh(0.70422535e1 * socn - 0.13661972e1) - 0.155e-1 * tanh(0.77519380e2 * socn - 0.81395349e1),-0.5e-1 + 0.2325e1 * exp(-0.100e3 * socn ^ 0.115e1) - 0.1721e0 * tanh(0.20000000e2 * socn - 0.21000000e2) - 0.25e-2 * tanh(0.39347962e2 * socn - 0.37241379e2) - 0.34e-1 * tanh(0.89411765e2 * socn - 0.60294118e1) - 0.2e-2 * tanh(0.70422535e1 * socn - 0.13661972e1) - 0.155e-1 * tanh(0.77519380e2 * socn - 0.81395349e1),-0.5e-1 + 0.2325e1 * exp(-0.100e3 * socn ^ 0.115e1) - 0.1721e0 * tanh(0.20000000e2 * socn - 0.21000000e2) - 0.25e-2 * tanh(0.39347962e2 * socn - 0.37241379e2) - 0.34e-1 * tanh(0.89411765e2 * socn - 0.60294118e1) - 0.2e-2 * tanh(0.70422535e1 * socn - 0.13661972e1) - 0.155e-1 * tanh(0.77519380e2 * socn - 0.81395349e1),-0.5e-1 + 0.2325e1 * exp(-0.100e3 * socn ^ 0.115e1) - 0.1721e0 * tanh(0.20000000e2 * socn - 0.21000000e2) - 0.25e-2 * tanh(0.39347962e2 * socn - 0.37241379e2) - 0.34e-1 * tanh(0.89411765e2 * socn - 0.60294118e1) - 0.2e-2 * tanh(0.70422535e1 * socn - 0.13661972e1) - 0.155e-1 * tanh(0.77519380e2 * socn - 0.81395349e1),-0.5e-1 + 0.2325e1 * exp(-0.100e3 * socn ^ 0.115e1) - 0.1721e0 * tanh(0.20000000e2 * socn - 0.21000000e2) - 0.25e-2 * tanh(0.39347962e2 * socn - 0.37241379e2) - 0.34e-1 * tanh(0.89411765e2 * socn - 0.60294118e1) - 0.2e-2 * tanh(0.70422535e1 * socn - 0.13661972e1) - 0.155e-1 * tanh(0.77519380e2 * socn - 0.81395349e1),-0.5e-1 + 0.2325e1 * exp(-0.100e3 * socn ^ 0.115e1) - 0.1721e0 * tanh(0.20000000e2 * socn - 0.21000000e2) - 0.25e-2 * tanh(0.39347962e2 * socn - 0.37241379e2) - 0.34e-1 * tanh(0.89411765e2 * socn - 0.60294118e1) - 0.2e-2 * tanh(0.70422535e1 * socn - 0.13661972e1) - 0.155e-1 * tanh(0.77519380e2 * socn - 0.81395349e1),-0.5e-1 + 0.2325e1 * exp(-0.100e3 * socn ^ 0.115e1) - 0.1721e0 * tanh(0.20000000e2 * socn - 0.21000000e2) - 0.25e-2 * tanh(0.39347962e2 * socn - 0.37241379e2) - 0.34e-1 * tanh(0.89411765e2 * socn - 0.60294118e1) - 0.2e-2 * tanh(0.70422535e1 * socn - 0.13661972e1) - 0.155e-1 * tanh(0.77519380e2 * socn - 0.81395349e1),-0.5e-1 + 0.2325e1 * exp(-0.100e3 * socn ^ 0.115e1) - 0.1721e0 * tanh(0.20000000e2 * socn - 0.21000000e2) - 0.25e-2 * tanh(0.39347962e2 * socn - 0.37241379e2) - 0.34e-1 * tanh(0.89411765e2 * socn - 0.60294118e1) - 0.2e-2 * tanh(0.70422535e1 * socn - 0.13661972e1) - 0.155e-1 * tanh(0.77519380e2 * socn - 0.81395349e1),-0.5e-1 + 0.2325e1 * exp(-0.100e3 * socn ^ 0.115e1) - 0.1721e0 * tanh(0.20000000e2 * socn - 0.21000000e2) - 0.25e-2 * tanh(0.39347962e2 * socn - 0.37241379e2) - 0.34e-1 * tanh(0.89411765e2 * socn - 0.60294118e1) - 0.2e-2 * tanh(0.70422535e1 * socn - 0.13661972e1) - 0.155e-1 * tanh(0.77519380e2 * socn - 0.81395349e1),socp,socp,socp,socp,socp,socp,socp,socp,socp,socp,socp,socp,socp,socp,socn,socn,socn,socn,socn,socn,socn,socn,socn,socn,socn,socn,socn,socn,(-0.5057e1 - 0.136e2 * socp ^ 2 + 0.1216e3 * socp ^ 4 - 0.1851e3 * socp ^ 6 - 0.4543e2 * socp ^ 8 + 0.1277e3 * socp ^ 10) / (-0.1e1 - 0.504e1 * socp ^ 2 + 0.323e2 * socp ^ 4 - 0.4095e2 * socp ^ 6 - 0.2594e2 * socp ^ 8 + 0.4063e2 * socp ^ 10) + 0.5e-1 - 0.2325e1 * exp(-0.100e3 * socn ^ 0.115e1) + 0.1721e0 * tanh(0.20000000e2 * socn - 0.21000000e2) + 0.25e-2 * tanh(0.39347962e2 * socn - 0.37241379e2) + 0.34e-1 * tanh(0.89411765e2 * socn - 0.60294118e1) + 0.2e-2 * tanh(0.70422535e1 * socn - 0.13661972e1) + 0.155e-1 * tanh(0.77519380e2 * socn - 0.81395349e1)]

end
y0=zeros(131)

n=length(y0)
MM=zeros((n,n))
node = 59

for i in 1:node
    MM[i,i]=1.
end

pars = [7.33234842e-08,6.40146313e-12,1.56954148e-13,1.65301662e-06,
  1.28277079e-05,1.39115369e+00,1.70413971e+00,1.93944836e+00,
  1.15245117e+03,3.46144727e+04,4.02951641e+04,3.24118063e-02,
  2.70097144e-02,5.20209372e-01,3.74625146e-01,4.16417062e-01,
  5.51529622e-09,6.95793778e-09,4.91284482e-05,4.88584483e-05,
  1.28054144e-05,1.38146591e+02,9.15019798e+00,9.78830695e-01,
  4.58723247e-01,4.32648301e-01,0.02]
y0 = yyy(pars)
dy = zeros(n)
f = (dy,y) -> P2D2c(zeros(n),y,pars,0.)
using ForwardDiff

# Really long compile time
ForwardDiff.jacobian(f,dy,y0)
@ChrisRackauckas ChrisRackauckas mentioned this issue Jun 8, 2018
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@jrevels
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jrevels commented Jun 8, 2018 •
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ForwardDiff definitely is written in a way that's pretty mean to the compiler. It's great at triggering crazy compile times since it injects Tuples of partial derivatives into a large portion of a target program's scalar computations, and then does a lot of unrolling and specialization on those tuples. Here's another ForwardDiff compilation nightmare example: JuliaDiff/ForwardDiff.jl#278

@ChrisRackauckas
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So is this a max tuple length being too small kind of thing? #22370

@dlfivefifty
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BandedMatrices.jl also had an almost 100x slowdown (see "bug-slowmul" branch):

julia> A = brand(5,5,1,1); b = randn(5); @time A*b # v0.6.2
  0.375991 seconds (335.46 k allocations: 16.421 MiB)

VS

julia> A = brand(5,5,1,1); b = randn(5); @time A*b  # v0.7, branch "bug-slowmul"
 24.676427 seconds (57.04 M allocations: 5.038 GiB, 3.76% gc time)

I sped this up to "only" 15x slowdown on master by making the code type stable:

julia> A = brand(5,5,1,1); b = randn(5); @time A*b # v0.7, branch "master"
  5.644144 seconds (16.42 M allocations: 1.252 GiB, 4.54% gc time)

@ChrisRackauckas
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That seems unrelated. This is true on v0.6.3 and is not related to v0.7 regressions.

@dlfivefifty
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dlfivefifty commented Jun 8, 2018 •
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I'm not sure what you mean:

julia> A = brand(5,5,1,1); b = randn(5); @time A*b  # v0.6.3
  0.418718 seconds (557.03 k allocations: 25.756 MiB, 13.73% gc time)

Edit: OHH, your issue is true on v0.6.3

@ViralBShah ViralBShah added the compiler:latency Compiler latency label Jun 8, 2018
@ViralBShah ViralBShah modified the milestone: 1.0 Jun 8, 2018
@tknopp
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tknopp commented Jun 9, 2018

I sped this up to "only" 15x slowdown on master by making the code type stable

This is where nobody has a concrete answer for:
https://discourse.julialang.org/t/does-compile-time-depend-on-type-stability/6548/4

My feeling also was that type stable code is faster to compile whereas type unstable code might lead to very long compilation times. According to https://discourse.julialang.org/t/meaning-type-piracy-and-method-merging/11003/44 this is not true though.

@ChrisRackauckas
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ChrisRackauckas commented Jun 9, 2018 •
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I'm not sure this is related though. This is type-stable and was tracked down to issues with large NTuples.

@dlfivefifty
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I filed a separate issue #27512

@ChrisRackauckas ChrisRackauckas mentioned this issue Aug 25, 2018
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@ChrisRackauckas
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ChrisRackauckas commented Aug 25, 2018 •
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Here's the example updated to work on v1.0.

P2D2c = function(dy,y,pars,t)
    Dbulk = pars[1]
    Dsn = pars[2]
    Dsp = pars[3]
    F = 96487.000000
    R = 8.314300
    Rpn = pars[4]
    Rpp = pars[5]
    Tr = 298.150000
    brugn = pars[6]
    brugp = pars[7]
    brugs = pars[8]
    c0 = pars[9]
    ctn = pars[10]
    ctp = pars[11]
    efn = pars[12]
    efp = pars[13]
    en = pars[14]
    ep = pars[15]
    es = pars[16]
    kn = pars[17]
    kp = pars[18]
    ln1 = pars[19]
    lp = pars[20]
    ls = pars[21]
    sigmn = pars[22]
    sigmp = pars[23]
    socn = pars[24]
    socp = pars[25]
    t1 = pars[26]


    current = -1.0
    capacity=17.5
    rate=-2.
    iapp=capacity*rate
    up=[0.,0.]
    Kr = pars[27]


    ap = 3/Rpp*(1-ep-efp)

    an = 3/Rpn*(1-en-efn)

    sigmap = sigmp*(1-ep-efp)

    sigman = sigmn*(1-en-efn)

    D2pos = ep^brugp*Dbulk

    D2sep = es^brugs*Dbulk

    D2neg = en^brugn*Dbulk

    dy[1] = 1/ep*(64.0*D2pos/lp^2*(y[60]-2.0*y[1]+y[2])+2.0*ap*(1.0-1.0*t1)*kp*(y[1]*c0)^.5*(-1.0*y[110]*ctp+ctp)^.5*(y[110]*ctp)^.5*sinh(.5*F/R/Tr*(y[86]-1.0*y[65]-1.0*ocp_cathode(y[110],up)))/c0)
    dy[2] = 1/ep*(64.0*D2pos/lp^2*(y[1]-2.0*y[2]+y[3])+2.0*ap*(1.0-1.0*t1)*kp*(y[2]*c0)^.5*(-1.0*y[111]*ctp+ctp)^.5*(y[111]*ctp)^.5*sinh(.5*F/R/Tr*(y[87]-1.0*y[66]-1.0*ocp_cathode(y[111],up)))/c0)
    dy[3] = 1/ep*(64.0*D2pos/lp^2*(y[2]-2.0*y[3]+y[4])+2.0*ap*(1.0-1.0*t1)*kp*(y[3]*c0)^.5*(-1.0*y[112]*ctp+ctp)^.5*(y[112]*ctp)^.5*sinh(.5*F/R/Tr*(y[88]-1.0*y[67]-1.0*ocp_cathode(y[112],up)))/c0)
    dy[4] = 1/ep*(64.0*D2pos/lp^2*(y[3]-2.0*y[4]+y[5])+2.0*ap*(1.0-1.0*t1)*kp*(y[4]*c0)^.5*(-1.0*y[113]*ctp+ctp)^.5*(y[113]*ctp)^.5*sinh(.5*F/R/Tr*(y[89]-1.0*y[68]-1.0*ocp_cathode(y[113],up)))/c0)
    dy[5] = 1/ep*(64.0*D2pos/lp^2*(y[4]-2.0*y[5]+y[6])+2.0*ap*(1.0-1.0*t1)*kp*(y[5]*c0)^.5*(-1.0*y[114]*ctp+ctp)^.5*(y[114]*ctp)^.5*sinh(.5*F/R/Tr*(y[90]-1.0*y[69]-1.0*ocp_cathode(y[114],up)))/c0)
    dy[6] = 1/ep*(64.0*D2pos/lp^2*(y[5]-2.0*y[6]+y[7])+2.0*ap*(1.0-1.0*t1)*kp*(y[6]*c0)^.5*(-1.0*y[115]*ctp+ctp)^.5*(y[115]*ctp)^.5*sinh(.5*F/R/Tr*(y[91]-1.0*y[70]-1.0*ocp_cathode(y[115],up)))/c0)
    dy[7] = 1/ep*(64.0*D2pos/lp^2*(y[6]-2.0*y[7]+y[61])+2.0*ap*(1.0-1.0*t1)*kp*(y[7]*c0)^.5*(-1.0*y[116]*ctp+ctp)^.5*(y[116]*ctp)^.5*sinh(.5*F/R/Tr*(y[92]-1.0*y[71]-1.0*ocp_cathode(y[116],up)))/c0)
    dy[8] = 16.0/es*D2sep/ls^2*(y[61]-2.0*y[8]+y[9])
    dy[9] = 16.0/es*D2sep/ls^2*(y[8]-2.0*y[9]+y[10])
    dy[10] = 16.0/es*D2sep/ls^2*(y[9]-2.0*y[10]+y[62])
    dy[11] = 1/en*(64.0*D2neg/ln1^2*(y[62]-2.0*y[11]+y[12])+2.0*an*(1.0-1.0*t1)*kn*(y[11]*c0)^.5*(-1.0*y[124]*ctn+ctn)^.5*(y[124]*ctn)^.5*sinh(.5*F/R/Tr*(y[95]-1.0*y[77]+.5e-1-2.325*exp(-100.0*y[124]^1.15)+.1721*tanh(20.000000*y[124]-21.000000)+.25e-2*tanh(39.347962*y[124]-37.241379)+.34e-1*tanh(89.411765*y[124]-6.0294118)+.2e-2*tanh(7.0422535*y[124]-1.3661972)+.155e-1*tanh(77.519380*y[124]-8.1395349)))/c0)
    dy[12] = 1/en*(64.0*D2neg/ln1^2*(y[11]-2.0*y[12]+y[13])+2.0*an*(1.0-1.0*t1)*kn*(y[12]*c0)^.5*(-1.0*y[125]*ctn+ctn)^.5*(y[125]*ctn)^.5*sinh(.5*F/R/Tr*(y[96]-1.0*y[78]+.5e-1-2.325*exp(-100.0*y[125]^1.15)+.1721*tanh(20.000000*y[125]-21.000000)+.25e-2*tanh(39.347962*y[125]-37.241379)+.34e-1*tanh(89.411765*y[125]-6.0294118)+.2e-2*tanh(7.0422535*y[125]-1.3661972)+.155e-1*tanh(77.519380*y[125]-8.1395349)))/c0)
    dy[13] = 1/en*(64.0*D2neg/ln1^2*(y[12]-2.0*y[13]+y[14])+2.0*an*(1.0-1.0*t1)*kn*(y[13]*c0)^.5*(-1.0*y[126]*ctn+ctn)^.5*(y[126]*ctn)^.5*sinh(.5*F/R/Tr*(y[97]-1.0*y[79]+.5e-1-2.325*exp(-100.0*y[126]^1.15)+.1721*tanh(20.000000*y[126]-21.000000)+.25e-2*tanh(39.347962*y[126]-37.241379)+.34e-1*tanh(89.411765*y[126]-6.0294118)+.2e-2*tanh(7.0422535*y[126]-1.3661972)+.155e-1*tanh(77.519380*y[126]-8.1395349)))/c0)
    dy[14] = 1/en*(64.0*D2neg/ln1^2*(y[13]-2.0*y[14]+y[15])+2.0*an*(1.0-1.0*t1)*kn*(y[14]*c0)^.5*(-1.0*y[127]*ctn+ctn)^.5*(y[127]*ctn)^.5*sinh(.5*F/R/Tr*(y[98]-1.0*y[80]+.5e-1-2.325*exp(-100.0*y[127]^1.15)+.1721*tanh(20.000000*y[127]-21.000000)+.25e-2*tanh(39.347962*y[127]-37.241379)+.34e-1*tanh(89.411765*y[127]-6.0294118)+.2e-2*tanh(7.0422535*y[127]-1.3661972)+.155e-1*tanh(77.519380*y[127]-8.1395349)))/c0)
    dy[15] = 1/en*(64.0*D2neg/ln1^2*(y[14]-2.0*y[15]+y[16])+2.0*an*(1.0-1.0*t1)*kn*(y[15]*c0)^.5*(-1.0*y[128]*ctn+ctn)^.5*(y[128]*ctn)^.5*sinh(.5*F/R/Tr*(y[99]-1.0*y[81]+.5e-1-2.325*exp(-100.0*y[128]^1.15)+.1721*tanh(20.000000*y[128]-21.000000)+.25e-2*tanh(39.347962*y[128]-37.241379)+.34e-1*tanh(89.411765*y[128]-6.0294118)+.2e-2*tanh(7.0422535*y[128]-1.3661972)+.155e-1*tanh(77.519380*y[128]-8.1395349)))/c0)
    dy[16] = 1/en*(64.0*D2neg/ln1^2*(y[15]-2.0*y[16]+y[17])+2.0*an*(1.0-1.0*t1)*kn*(y[16]*c0)^.5*(-1.0*y[129]*ctn+ctn)^.5*(y[129]*ctn)^.5*sinh(.5*F/R/Tr*(y[100]-1.0*y[82]+.5e-1-2.325*exp(-100.0*y[129]^1.15)+.1721*tanh(20.000000*y[129]-21.000000)+.25e-2*tanh(39.347962*y[129]-37.241379)+.34e-1*tanh(89.411765*y[129]-6.0294118)+.2e-2*tanh(7.0422535*y[129]-1.3661972)+.155e-1*tanh(77.519380*y[129]-8.1395349)))/c0)
    dy[17] = 1/en*(64.0*D2neg/ln1^2*(y[16]-2.0*y[17]+y[63])+2.0*an*(1.0-1.0*t1)*kn*(y[17]*c0)^.5*(-1.0*y[130]*ctn+ctn)^.5*(y[130]*ctn)^.5*sinh(.5*F/R/Tr*(y[101]-1.0*y[83]+.5e-1-2.325*exp(-100.0*y[130]^1.15)+.1721*tanh(20.000000*y[130]-21.000000)+.25e-2*tanh(39.347962*y[130]-37.241379)+.34e-1*tanh(89.411765*y[130]-6.0294118)+.2e-2*tanh(7.0422535*y[130]-1.3661972)+.155e-1*tanh(77.519380*y[130]-8.1395349)))/c0)
    dy[18] = 16.0*(Dsp*(y[25]-1.0*y[103])+Dsp*(y[103]-2.0*y[18]+y[25]))/Rpp^2
    dy[19] = 16.0*(Dsp*(y[26]-1.0*y[104])+Dsp*(y[104]-2.0*y[19]+y[26]))/Rpp^2
    dy[20] = 16.0*(Dsp*(y[27]-1.0*y[105])+Dsp*(y[105]-2.0*y[20]+y[27]))/Rpp^2
    dy[21] = 16.0*(Dsp*(y[28]-1.0*y[106])+Dsp*(y[106]-2.0*y[21]+y[28]))/Rpp^2
    dy[22] = 16.0*(Dsp*(y[29]-1.0*y[107])+Dsp*(y[107]-2.0*y[22]+y[29]))/Rpp^2
    dy[23] = 16.0*(Dsp*(y[30]-1.0*y[108])+Dsp*(y[108]-2.0*y[23]+y[30]))/Rpp^2
    dy[24] = 16.0*(Dsp*(y[31]-1.0*y[109])+Dsp*(y[109]-2.0*y[24]+y[31]))/Rpp^2
    dy[25] = 4.0*(2.0*Dsp*(y[32]-1.0*y[18])+4.0*Dsp*(y[18]-2.0*y[25]+y[32]))/Rpp^2
    dy[26] = 4.0*(2.0*Dsp*(y[33]-1.0*y[19])+4.0*Dsp*(y[19]-2.0*y[26]+y[33]))/Rpp^2
    dy[27] = 4.0*(2.0*Dsp*(y[34]-1.0*y[20])+4.0*Dsp*(y[20]-2.0*y[27]+y[34]))/Rpp^2
    dy[28] = 4.0*(2.0*Dsp*(y[35]-1.0*y[21])+4.0*Dsp*(y[21]-2.0*y[28]+y[35]))/Rpp^2
    dy[29] = 4.0*(2.0*Dsp*(y[36]-1.0*y[22])+4.0*Dsp*(y[22]-2.0*y[29]+y[36]))/Rpp^2
    dy[30] = 4.0*(2.0*Dsp*(y[37]-1.0*y[23])+4.0*Dsp*(y[23]-2.0*y[30]+y[37]))/Rpp^2
    dy[31] = 4.0*(2.0*Dsp*(y[38]-1.0*y[24])+4.0*Dsp*(y[24]-2.0*y[31]+y[38]))/Rpp^2
    dy[32] = 1.777777778*(3.0*Dsp*(y[110]-1.0*y[25])+9.0*Dsp*(y[25]-2.0*y[32]+y[110]))/Rpp^2
    dy[33] = 1.777777778*(3.0*Dsp*(y[111]-1.0*y[26])+9.0*Dsp*(y[26]-2.0*y[33]+y[111]))/Rpp^2
    dy[34] = 1.777777778*(3.0*Dsp*(y[112]-1.0*y[27])+9.0*Dsp*(y[27]-2.0*y[34]+y[112]))/Rpp^2
    dy[35] = 1.777777778*(3.0*Dsp*(y[113]-1.0*y[28])+9.0*Dsp*(y[28]-2.0*y[35]+y[113]))/Rpp^2
    dy[36] = 1.777777778*(3.0*Dsp*(y[114]-1.0*y[29])+9.0*Dsp*(y[29]-2.0*y[36]+y[114]))/Rpp^2
    dy[37] = 1.777777778*(3.0*Dsp*(y[115]-1.0*y[30])+9.0*Dsp*(y[30]-2.0*y[37]+y[115]))/Rpp^2
    dy[38] = 1.777777778*(3.0*Dsp*(y[116]-1.0*y[31])+9.0*Dsp*(y[31]-2.0*y[38]+y[116]))/Rpp^2
    dy[39] = 16.0*Dsn*(2.0*y[46]-2.0*y[39])/Rpn^2
    dy[40] = 16.0*Dsn*(2.0*y[47]-2.0*y[40])/Rpn^2
    dy[41] = 16.0*Dsn*(2.0*y[48]-2.0*y[41])/Rpn^2
    dy[42] = 16.0*Dsn*(2.0*y[49]-2.0*y[42])/Rpn^2
    dy[43] = 16.0*Dsn*(2.0*y[50]-2.0*y[43])/Rpn^2
    dy[44] = 16.0*Dsn*(2.0*y[51]-2.0*y[44])/Rpn^2
    dy[45] = 16.0*Dsn*(2.0*y[52]-2.0*y[45])/Rpn^2
    dy[46] = 4.0*Dsn*(6.0*y[53]+2.0*y[39]-8.0*y[46])/Rpn^2
    dy[47] = 4.0*Dsn*(6.0*y[54]+2.0*y[40]-8.0*y[47])/Rpn^2
    dy[48] = 4.0*Dsn*(6.0*y[55]+2.0*y[41]-8.0*y[48])/Rpn^2
    dy[49] = 4.0*Dsn*(6.0*y[56]+2.0*y[42]-8.0*y[49])/Rpn^2
    dy[50] = 4.0*Dsn*(6.0*y[57]+2.0*y[43]-8.0*y[50])/Rpn^2
    dy[51] = 4.0*Dsn*(6.0*y[58]+2.0*y[44]-8.0*y[51])/Rpn^2
    dy[52] = 4.0*Dsn*(6.0*y[59]+2.0*y[45]-8.0*y[52])/Rpn^2
    dy[53] = 1.777777778*Dsn*(12.0*y[124]+6.0*y[46]-18.0*y[53])/Rpn^2
    dy[54] = 1.777777778*Dsn*(12.0*y[125]+6.0*y[47]-18.0*y[54])/Rpn^2
    dy[55] = 1.777777778*Dsn*(12.0*y[126]+6.0*y[48]-18.0*y[55])/Rpn^2
    dy[56] = 1.777777778*Dsn*(12.0*y[127]+6.0*y[49]-18.0*y[56])/Rpn^2
    dy[57] = 1.777777778*Dsn*(12.0*y[128]+6.0*y[50]-18.0*y[57])/Rpn^2
    dy[58] = 1.777777778*Dsn*(12.0*y[129]+6.0*y[51]-18.0*y[58])/Rpn^2
    dy[59] = 1.777777778*Dsn*(12.0*y[130]+6.0*y[52]-18.0*y[59])/Rpn^2
    dy[60] = 4.0*D2pos*(-1.0*y[2]-3.0*y[60]+4.0*y[1])/lp
    dy[61] = 4.0*D2pos*(y[6]+3.0*y[61]-4.0*y[7])/lp-2.0*D2sep*(-1.0*y[9]-3.0*y[61]+4.0*y[8])/ls
    dy[62] = 2.0*D2sep*(y[9]+3.0*y[62]-4.0*y[10])/ls-4.0*D2neg*(-1.0*y[12]-3.0*y[62]+4.0*y[11])/ln1
    dy[63] = 4.0*D2neg*(y[16]+3.0*y[63]-4.0*y[17])/ln1
    dy[64] = 4.0*(-1.0*y[66]-3.0*y[64]+4.0*y[65])/lp
    dy[65] = -4.0*sigmap/lp*(y[87]-1.0*y[85])-4.0*ep^brugp*(.41253e-1+.5007e-3*y[1]-.47212e-6*y[1]^2+.15904e-9*y[1]^3-.16018e-13*y[1]^4)/lp*(y[66]-1.0*y[64])+8.0*ep^brugp*(.41253e-1+.5007e-3*y[1]-.47212e-6*y[1]^2+.15904e-9*y[1]^3-.16018e-13*y[1]^4)*R*Tr/F*(1.0-1.0*t1)/lp*(y[2]-1.0*y[60])/y[1]-iapp
    dy[66] = -4.0*sigmap/lp*(y[88]-1.0*y[86])-4.0*ep^brugp*(.41253e-1+.5007e-3*y[2]-.47212e-6*y[2]^2+.15904e-9*y[2]^3-.16018e-13*y[2]^4)/lp*(y[67]-1.0*y[65])+8.0*ep^brugp*(.41253e-1+.5007e-3*y[2]-.47212e-6*y[2]^2+.15904e-9*y[2]^3-.16018e-13*y[2]^4)*R*Tr/F*(1.0-1.0*t1)/lp*(y[3]-1.0*y[1])/y[2]-iapp
    dy[67] = -4.0*sigmap/lp*(y[89]-1.0*y[87])-4.0*ep^brugp*(.41253e-1+.5007e-3*y[3]-.47212e-6*y[3]^2+.15904e-9*y[3]^3-.16018e-13*y[3]^4)/lp*(y[68]-1.0*y[66])+8.0*ep^brugp*(.41253e-1+.5007e-3*y[3]-.47212e-6*y[3]^2+.15904e-9*y[3]^3-.16018e-13*y[3]^4)*R*Tr/F*(1.0-1.0*t1)/lp*(y[4]-1.0*y[2])/y[3]-iapp
    dy[68] = -4.0*sigmap/lp*(y[90]-1.0*y[88])-4.0*ep^brugp*(.41253e-1+.5007e-3*y[4]-.47212e-6*y[4]^2+.15904e-9*y[4]^3-.16018e-13*y[4]^4)/lp*(y[69]-1.0*y[67])+8.0*ep^brugp*(.41253e-1+.5007e-3*y[4]-.47212e-6*y[4]^2+.15904e-9*y[4]^3-.16018e-13*y[4]^4)*R*Tr/F*(1.0-1.0*t1)/lp*(y[5]-1.0*y[3])/y[4]-iapp
    dy[69] = -4.0*sigmap/lp*(y[91]-1.0*y[89])-4.0*ep^brugp*(.41253e-1+.5007e-3*y[5]-.47212e-6*y[5]^2+.15904e-9*y[5]^3-.16018e-13*y[5]^4)/lp*(y[70]-1.0*y[68])+8.0*ep^brugp*(.41253e-1+.5007e-3*y[5]-.47212e-6*y[5]^2+.15904e-9*y[5]^3-.16018e-13*y[5]^4)*R*Tr/F*(1.0-1.0*t1)/lp*(y[6]-1.0*y[4])/y[5]-iapp
    dy[70] = -4.0*sigmap/lp*(y[92]-1.0*y[90])-4.0*ep^brugp*(.41253e-1+.5007e-3*y[6]-.47212e-6*y[6]^2+.15904e-9*y[6]^3-.16018e-13*y[6]^4)/lp*(y[71]-1.0*y[69])+8.0*ep^brugp*(.41253e-1+.5007e-3*y[6]-.47212e-6*y[6]^2+.15904e-9*y[6]^3-.16018e-13*y[6]^4)*R*Tr/F*(1.0-1.0*t1)/lp*(y[7]-1.0*y[5])/y[6]-iapp
    dy[71] = -4.0*sigmap/lp*(y[93]-1.0*y[91])-4.0*ep^brugp*(.41253e-1+.5007e-3*y[7]-.47212e-6*y[7]^2+.15904e-9*y[7]^3-.16018e-13*y[7]^4)/lp*(y[72]-1.0*y[70])+8.0*ep^brugp*(.41253e-1+.5007e-3*y[7]-.47212e-6*y[7]^2+.15904e-9*y[7]^3-.16018e-13*y[7]^4)*R*Tr/F*(1.0-1.0*t1)/lp*(y[61]-1.0*y[6])/y[7]-iapp
    dy[72] = 4.0*ep^brugp*(.41253e-1+.5007e-3*y[61]-.47212e-6*y[61]^2+.15904e-9*y[61]^3-.16018e-13*y[61]^4)*(y[70]+3.0*y[72]-4.0*y[71])/lp-2.0*es^brugs*(.41253e-1+.5007e-3*y[61]-.47212e-6*y[61]^2+.15904e-9*y[61]^3-.16018e-13*y[61]^4)*(-1.0*y[74]-3.0*y[72]+4.0*y[73])/ls
    dy[73] = -2.0*es^brugs*(.41253e-1+.5007e-3*y[8]-.47212e-6*y[8]^2+.15904e-9*y[8]^3-.16018e-13*y[8]^4)/ls*(y[74]-1.0*y[72])+4.0*es^brugs*(.41253e-1+.5007e-3*y[8]-.47212e-6*y[8]^2+.15904e-9*y[8]^3-.16018e-13*y[8]^4)*R*Tr/F*(1.0-1.0*t1)/ls*(y[9]-1.0*y[61])/y[8]-iapp
    dy[74] = -2.0*es^brugs*(.41253e-1+.5007e-3*y[9]-.47212e-6*y[9]^2+.15904e-9*y[9]^3-.16018e-13*y[9]^4)/ls*(y[75]-1.0*y[73])+4.0*es^brugs*(.41253e-1+.5007e-3*y[9]-.47212e-6*y[9]^2+.15904e-9*y[9]^3-.16018e-13*y[9]^4)*R*Tr/F*(1.0-1.0*t1)/ls*(y[10]-1.0*y[8])/y[9]-iapp
    dy[75] = -2.0*es^brugs*(.41253e-1+.5007e-3*y[10]-.47212e-6*y[10]^2+.15904e-9*y[10]^3-.16018e-13*y[10]^4)/ls*(y[76]-1.0*y[74])+4.0*es^brugs*(.41253e-1+.5007e-3*y[10]-.47212e-6*y[10]^2+.15904e-9*y[10]^3-.16018e-13*y[10]^4)*R*Tr/F*(1.0-1.0*t1)/ls*(y[62]-1.0*y[9])/y[10]-iapp
    dy[76] = 2.0*es^brugs*(.41253e-1+.5007e-3*y[62]-.47212e-6*y[62]^2+.15904e-9*y[62]^3-.16018e-13*y[62]^4)*(y[74]+3.0*y[76]-4.0*y[75])/ls-4.0*en^brugn*(.41253e-1+.5007e-3*y[62]-.47212e-6*y[62]^2+.15904e-9*y[62]^3-.16018e-13*y[62]^4)*(-1.0*y[78]-3.0*y[76]+4.0*y[77])/ln1
    dy[77] = -4.0*sigman/ln1*(y[96]-1.0*y[94])-4.0*en^brugn*(.41253e-1+.5007e-3*y[11]-.47212e-6*y[11]^2+.15904e-9*y[11]^3-.16018e-13*y[11]^4)/ln1*(y[78]-1.0*y[76])+8.0*en^brugn*(.41253e-1+.5007e-3*y[11]-.47212e-6*y[11]^2+.15904e-9*y[11]^3-.16018e-13*y[11]^4)*R*Tr/F*(1.0-1.0*t1)/ln1*(y[12]-1.0*y[62])/y[11]-iapp
    dy[78] = -4.0*sigman/ln1*(y[97]-1.0*y[95])-4.0*en^brugn*(.41253e-1+.5007e-3*y[12]-.47212e-6*y[12]^2+.15904e-9*y[12]^3-.16018e-13*y[12]^4)/ln1*(y[79]-1.0*y[77])+8.0*en^brugn*(.41253e-1+.5007e-3*y[12]-.47212e-6*y[12]^2+.15904e-9*y[12]^3-.16018e-13*y[12]^4)*R*Tr/F*(1.0-1.0*t1)/ln1*(y[13]-1.0*y[11])/y[12]-iapp
    dy[79] = -4.0*sigman/ln1*(y[98]-1.0*y[96])-4.0*en^brugn*(.41253e-1+.5007e-3*y[13]-.47212e-6*y[13]^2+.15904e-9*y[13]^3-.16018e-13*y[13]^4)/ln1*(y[80]-1.0*y[78])+8.0*en^brugn*(.41253e-1+.5007e-3*y[13]-.47212e-6*y[13]^2+.15904e-9*y[13]^3-.16018e-13*y[13]^4)*R*Tr/F*(1.0-1.0*t1)/ln1*(y[14]-1.0*y[12])/y[13]-iapp
    dy[80] = -4.0*sigman/ln1*(y[99]-1.0*y[97])-4.0*en^brugn*(.41253e-1+.5007e-3*y[14]-.47212e-6*y[14]^2+.15904e-9*y[14]^3-.16018e-13*y[14]^4)/ln1*(y[81]-1.0*y[79])+8.0*en^brugn*(.41253e-1+.5007e-3*y[14]-.47212e-6*y[14]^2+.15904e-9*y[14]^3-.16018e-13*y[14]^4)*R*Tr/F*(1.0-1.0*t1)/ln1*(y[15]-1.0*y[13])/y[14]-iapp
    dy[81] = -4.0*sigman/ln1*(y[100]-1.0*y[98])-4.0*en^brugn*(.41253e-1+.5007e-3*y[15]-.47212e-6*y[15]^2+.15904e-9*y[15]^3-.16018e-13*y[15]^4)/ln1*(y[82]-1.0*y[80])+8.0*en^brugn*(.41253e-1+.5007e-3*y[15]-.47212e-6*y[15]^2+.15904e-9*y[15]^3-.16018e-13*y[15]^4)*R*Tr/F*(1.0-1.0*t1)/ln1*(y[16]-1.0*y[14])/y[15]-iapp
    dy[82] = -4.0*sigman/ln1*(y[101]-1.0*y[99])-4.0*en^brugn*(.41253e-1+.5007e-3*y[16]-.47212e-6*y[16]^2+.15904e-9*y[16]^3-.16018e-13*y[16]^4)/ln1*(y[83]-1.0*y[81])+8.0*en^brugn*(.41253e-1+.5007e-3*y[16]-.47212e-6*y[16]^2+.15904e-9*y[16]^3-.16018e-13*y[16]^4)*R*Tr/F*(1.0-1.0*t1)/ln1*(y[17]-1.0*y[15])/y[16]-iapp
    dy[83] = -4.0*sigman/ln1*(y[102]-1.0*y[100])-4.0*en^brugn*(.41253e-1+.5007e-3*y[17]-.47212e-6*y[17]^2+.15904e-9*y[17]^3-.16018e-13*y[17]^4)/ln1*(y[84]-1.0*y[82])+8.0*en^brugn*(.41253e-1+.5007e-3*y[17]-.47212e-6*y[17]^2+.15904e-9*y[17]^3-.16018e-13*y[17]^4)*R*Tr/F*(1.0-1.0*t1)/ln1*(y[63]-1.0*y[16])/y[17]-iapp
    dy[84] = y[84]
    dy[85] = 4.0*(-1.0*y[87]-3.0*y[85]+4.0*y[86])/lp+1.0*iapp/sigmap
    dy[86] = 64.0*sigmap/lp^2*(y[85]-2.0*y[86]+y[87])-2.0*ap*F*kp*(y[1]*c0)^.5*(-1.0*y[110]*ctp+ctp)^.5*(y[110]*ctp)^.5*sinh(.5*F/R/Tr*(y[86]-1.0*y[65]-1.0*ocp_cathode(y[110],up)))
    dy[87] = 64.0*sigmap/lp^2*(y[86]-2.0*y[87]+y[88])-2.0*ap*F*kp*(y[2]*c0)^.5*(-1.0*y[111]*ctp+ctp)^.5*(y[111]*ctp)^.5*sinh(.5*F/R/Tr*(y[87]-1.0*y[66]-1.0*ocp_cathode(y[111],up)))
    dy[88] = 64.0*sigmap/lp^2*(y[87]-2.0*y[88]+y[89])-2.0*ap*F*kp*(y[3]*c0)^.5*(-1.0*y[112]*ctp+ctp)^.5*(y[112]*ctp)^.5*sinh(.5*F/R/Tr*(y[88]-1.0*y[67]-1.0*ocp_cathode(y[112],up)))
    dy[89] = 64.0*sigmap/lp^2*(y[88]-2.0*y[89]+y[90])-2.0*ap*F*kp*(y[4]*c0)^.5*(-1.0*y[113]*ctp+ctp)^.5*(y[113]*ctp)^.5*sinh(.5*F/R/Tr*(y[89]-1.0*y[68]-1.0*ocp_cathode(y[113],up)))
    dy[90] = 64.0*sigmap/lp^2*(y[89]-2.0*y[90]+y[91])-2.0*ap*F*kp*(y[5]*c0)^.5*(-1.0*y[114]*ctp+ctp)^.5*(y[114]*ctp)^.5*sinh(.5*F/R/Tr*(y[90]-1.0*y[69]-1.0*ocp_cathode(y[114],up)))
    dy[91] = 64.0*sigmap/lp^2*(y[90]-2.0*y[91]+y[92])-2.0*ap*F*kp*(y[6]*c0)^.5*(-1.0*y[115]*ctp+ctp)^.5*(y[115]*ctp)^.5*sinh(.5*F/R/Tr*(y[91]-1.0*y[70]-1.0*ocp_cathode(y[115],up)))
    dy[92] = 64.0*sigmap/lp^2*(y[91]-2.0*y[92]+y[93])-2.0*ap*F*kp*(y[7]*c0)^.5*(-1.0*y[116]*ctp+ctp)^.5*(y[116]*ctp)^.5*sinh(.5*F/R/Tr*(y[92]-1.0*y[71]-1.0*ocp_cathode(y[116],up)))
    dy[93] = 4.0*(y[91]+3.0*y[93]-4.0*y[92])/lp
    dy[94] = 4.0*(-1.0*y[96]-3.0*y[94]+4.0*y[95])/ln1
    dy[95] = 64.0*sigman/ln1^2*(y[94]-2.0*y[95]+y[96])-2.0*an*F*kn*(y[11]*c0)^.5*(-1.0*y[124]*ctn+ctn)^.5*(y[124]*ctn)^.5*sinh(.5*F/R/Tr*(y[95]-1.0*y[77]+.5e-1-2.325*exp(-100.0*y[124]^1.15)+.1721*tanh(20.000000*y[124]-21.000000)+.25e-2*tanh(39.347962*y[124]-37.241379)+.34e-1*tanh(89.411765*y[124]-6.0294118)+.2e-2*tanh(7.0422535*y[124]-1.3661972)+.155e-1*tanh(77.519380*y[124]-8.1395349)))
    dy[96] = 64.0*sigman/ln1^2*(y[95]-2.0*y[96]+y[97])-2.0*an*F*kn*(y[12]*c0)^.5*(-1.0*y[125]*ctn+ctn)^.5*(y[125]*ctn)^.5*sinh(.5*F/R/Tr*(y[96]-1.0*y[78]+.5e-1-2.325*exp(-100.0*y[125]^1.15)+.1721*tanh(20.000000*y[125]-21.000000)+.25e-2*tanh(39.347962*y[125]-37.241379)+.34e-1*tanh(89.411765*y[125]-6.0294118)+.2e-2*tanh(7.0422535*y[125]-1.3661972)+.155e-1*tanh(77.519380*y[125]-8.1395349)))
    dy[97] = 64.0*sigman/ln1^2*(y[96]-2.0*y[97]+y[98])-2.0*an*F*kn*(y[13]*c0)^.5*(-1.0*y[126]*ctn+ctn)^.5*(y[126]*ctn)^.5*sinh(.5*F/R/Tr*(y[97]-1.0*y[79]+.5e-1-2.325*exp(-100.0*y[126]^1.15)+.1721*tanh(20.000000*y[126]-21.000000)+.25e-2*tanh(39.347962*y[126]-37.241379)+.34e-1*tanh(89.411765*y[126]-6.0294118)+.2e-2*tanh(7.0422535*y[126]-1.3661972)+.155e-1*tanh(77.519380*y[126]-8.1395349)))
    dy[98] = 64.0*sigman/ln1^2*(y[97]-2.0*y[98]+y[99])-2.0*an*F*kn*(y[14]*c0)^.5*(-1.0*y[127]*ctn+ctn)^.5*(y[127]*ctn)^.5*sinh(.5*F/R/Tr*(y[98]-1.0*y[80]+.5e-1-2.325*exp(-100.0*y[127]^1.15)+.1721*tanh(20.000000*y[127]-21.000000)+.25e-2*tanh(39.347962*y[127]-37.241379)+.34e-1*tanh(89.411765*y[127]-6.0294118)+.2e-2*tanh(7.0422535*y[127]-1.3661972)+.155e-1*tanh(77.519380*y[127]-8.1395349)))
    dy[99] = 64.0*sigman/ln1^2*(y[98]-2.0*y[99]+y[100])-2.0*an*F*kn*(y[15]*c0)^.5*(-1.0*y[128]*ctn+ctn)^.5*(y[128]*ctn)^.5*sinh(.5*F/R/Tr*(y[99]-1.0*y[81]+.5e-1-2.325*exp(-100.0*y[128]^1.15)+.1721*tanh(20.000000*y[128]-21.000000)+.25e-2*tanh(39.347962*y[128]-37.241379)+.34e-1*tanh(89.411765*y[128]-6.0294118)+.2e-2*tanh(7.0422535*y[128]-1.3661972)+.155e-1*tanh(77.519380*y[128]-8.1395349)))
    dy[100] = 64.0*sigman/ln1^2*(y[99]-2.0*y[100]+y[101])-2.0*an*F*kn*(y[16]*c0)^.5*(-1.0*y[129]*ctn+ctn)^.5*(y[129]*ctn)^.5*sinh(.5*F/R/Tr*(y[100]-1.0*y[82]+.5e-1-2.325*exp(-100.0*y[129]^1.15)+.1721*tanh(20.000000*y[129]-21.000000)+.25e-2*tanh(39.347962*y[129]-37.241379)+.34e-1*tanh(89.411765*y[129]-6.0294118)+.2e-2*tanh(7.0422535*y[129]-1.3661972)+.155e-1*tanh(77.519380*y[129]-8.1395349)))
    dy[101] = 64.0*sigman/ln1^2*(y[100]-2.0*y[101]+y[102])-2.0*an*F*kn*(y[17]*c0)^.5*(-1.0*y[130]*ctn+ctn)^.5*(y[130]*ctn)^.5*sinh(.5*F/R/Tr*(y[101]-1.0*y[83]+.5e-1-2.325*exp(-100.0*y[130]^1.15)+.1721*tanh(20.000000*y[130]-21.000000)+.25e-2*tanh(39.347962*y[130]-37.241379)+.34e-1*tanh(89.411765*y[130]-6.0294118)+.2e-2*tanh(7.0422535*y[130]-1.3661972)+.155e-1*tanh(77.519380*y[130]-8.1395349)))
    dy[102] = 4.0*(y[100]+3.0*y[102]-4.0*y[101])/ln1+1.0*iapp/sigman
    dy[103] = -2.0*(-1.0*y[25]-3.0*y[103]+4.0*y[18])/Rpp
    dy[104] = -2.0*(-1.0*y[26]-3.0*y[104]+4.0*y[19])/Rpp
    dy[105] = -2.0*(-1.0*y[27]-3.0*y[105]+4.0*y[20])/Rpp
    dy[106] = -2.0*(-1.0*y[28]-3.0*y[106]+4.0*y[21])/Rpp
    dy[107] = -2.0*(-1.0*y[29]-3.0*y[107]+4.0*y[22])/Rpp
    dy[108] = -2.0*(-1.0*y[30]-3.0*y[108]+4.0*y[23])/Rpp
    dy[109] = -2.0*(-1.0*y[31]-3.0*y[109]+4.0*y[24])/Rpp
    dy[110] = 2.0*Dsp*(y[25]+3.0*y[110]-4.0*y[32])/Rpp+2.0*kp*(y[1]*c0)^.5*(-1.0*y[110]*ctp+ctp)^.5*(y[110]*ctp)^.5*sinh(.5*F/R/Tr*(y[86]-1.0*y[65]-1.0*ocp_cathode(y[110],up)))/ctp
    dy[111] = 2.0*Dsp*(y[26]+3.0*y[111]-4.0*y[33])/Rpp+2.0*kp*(y[2]*c0)^.5*(-1.0*y[111]*ctp+ctp)^.5*(y[111]*ctp)^.5*sinh(.5*F/R/Tr*(y[87]-1.0*y[66]-1.0*ocp_cathode(y[111],up)))/ctp
    dy[112] = 2.0*Dsp*(y[27]+3.0*y[112]-4.0*y[34])/Rpp+2.0*kp*(y[3]*c0)^.5*(-1.0*y[112]*ctp+ctp)^.5*(y[112]*ctp)^.5*sinh(.5*F/R/Tr*(y[88]-1.0*y[67]-1.0*ocp_cathode(y[112],up)))/ctp
    dy[113] = 2.0*Dsp*(y[28]+3.0*y[113]-4.0*y[35])/Rpp+2.0*kp*(y[4]*c0)^.5*(-1.0*y[113]*ctp+ctp)^.5*(y[113]*ctp)^.5*sinh(.5*F/R/Tr*(y[89]-1.0*y[68]-1.0*ocp_cathode(y[113],up)))/ctp
    dy[114] = 2.0*Dsp*(y[29]+3.0*y[114]-4.0*y[36])/Rpp+2.0*kp*(y[5]*c0)^.5*(-1.0*y[114]*ctp+ctp)^.5*(y[114]*ctp)^.5*sinh(.5*F/R/Tr*(y[90]-1.0*y[69]-1.0*ocp_cathode(y[114],up)))/ctp
    dy[115] = 2.0*Dsp*(y[30]+3.0*y[115]-4.0*y[37])/Rpp+2.0*kp*(y[6]*c0)^.5*(-1.0*y[115]*ctp+ctp)^.5*(y[115]*ctp)^.5*sinh(.5*F/R/Tr*(y[91]-1.0*y[70]-1.0*ocp_cathode(y[115],up)))/ctp
    dy[116] = 2.0*Dsp*(y[31]+3.0*y[116]-4.0*y[38])/Rpp+2.0*kp*(y[7]*c0)^.5*(-1.0*y[116]*ctp+ctp)^.5*(y[116]*ctp)^.5*sinh(.5*F/R/Tr*(y[92]-1.0*y[71]-1.0*ocp_cathode(y[116],up)))/ctp
    dy[117] = -2.0*(-1.0*y[46]-3.0*y[117]+4.0*y[39])/Rpn
    dy[118] = -2.0*(-1.0*y[47]-3.0*y[118]+4.0*y[40])/Rpn
    dy[119] = -2.0*(-1.0*y[48]-3.0*y[119]+4.0*y[41])/Rpn
    dy[120] = -2.0*(-1.0*y[49]-3.0*y[120]+4.0*y[42])/Rpn
    dy[121] = -2.0*(-1.0*y[50]-3.0*y[121]+4.0*y[43])/Rpn
    dy[122] = -2.0*(-1.0*y[51]-3.0*y[122]+4.0*y[44])/Rpn
    dy[123] = -2.0*(-1.0*y[52]-3.0*y[123]+4.0*y[45])/Rpn
    dy[124] = 2.0*Dsn*(y[46]+3.0*y[124]-4.0*y[53])/Rpn+2.0*kn*(y[11]*c0)^.5*(-1.0*y[124]*ctn+ctn)^.5*(y[124]*ctn)^.5*sinh(.5*F/R/Tr*(y[95]-1.0*y[77]+.5e-1-2.325*exp(-100.0*y[124]^1.15)+.1721*tanh(20.000000*y[124]-21.000000)+.25e-2*tanh(39.347962*y[124]-37.241379)+.34e-1*tanh(89.411765*y[124]-6.0294118)+.2e-2*tanh(7.0422535*y[124]-1.3661972)+.155e-1*tanh(77.519380*y[124]-8.1395349)))/ctn
    dy[125] = 2.0*Dsn*(y[47]+3.0*y[125]-4.0*y[54])/Rpn+2.0*kn*(y[12]*c0)^.5*(-1.0*y[125]*ctn+ctn)^.5*(y[125]*ctn)^.5*sinh(.5*F/R/Tr*(y[96]-1.0*y[78]+.5e-1-2.325*exp(-100.0*y[125]^1.15)+.1721*tanh(20.000000*y[125]-21.000000)+.25e-2*tanh(39.347962*y[125]-37.241379)+.34e-1*tanh(89.411765*y[125]-6.0294118)+.2e-2*tanh(7.0422535*y[125]-1.3661972)+.155e-1*tanh(77.519380*y[125]-8.1395349)))/ctn
    dy[126] = 2.0*Dsn*(y[48]+3.0*y[126]-4.0*y[55])/Rpn+2.0*kn*(y[13]*c0)^.5*(-1.0*y[126]*ctn+ctn)^.5*(y[126]*ctn)^.5*sinh(.5*F/R/Tr*(y[97]-1.0*y[79]+.5e-1-2.325*exp(-100.0*y[126]^1.15)+.1721*tanh(20.000000*y[126]-21.000000)+.25e-2*tanh(39.347962*y[126]-37.241379)+.34e-1*tanh(89.411765*y[126]-6.0294118)+.2e-2*tanh(7.0422535*y[126]-1.3661972)+.155e-1*tanh(77.519380*y[126]-8.1395349)))/ctn
    dy[127] = 2.0*Dsn*(y[49]+3.0*y[127]-4.0*y[56])/Rpn+2.0*kn*(y[14]*c0)^.5*(-1.0*y[127]*ctn+ctn)^.5*(y[127]*ctn)^.5*sinh(.5*F/R/Tr*(y[98]-1.0*y[80]+.5e-1-2.325*exp(-100.0*y[127]^1.15)+.1721*tanh(20.000000*y[127]-21.000000)+.25e-2*tanh(39.347962*y[127]-37.241379)+.34e-1*tanh(89.411765*y[127]-6.0294118)+.2e-2*tanh(7.0422535*y[127]-1.3661972)+.155e-1*tanh(77.519380*y[127]-8.1395349)))/ctn
    dy[128] = 2.0*Dsn*(y[50]+3.0*y[128]-4.0*y[57])/Rpn+2.0*kn*(y[15]*c0)^.5*(-1.0*y[128]*ctn+ctn)^.5*(y[128]*ctn)^.5*sinh(.5*F/R/Tr*(y[99]-1.0*y[81]+.5e-1-2.325*exp(-100.0*y[128]^1.15)+.1721*tanh(20.000000*y[128]-21.000000)+.25e-2*tanh(39.347962*y[128]-37.241379)+.34e-1*tanh(89.411765*y[128]-6.0294118)+.2e-2*tanh(7.0422535*y[128]-1.3661972)+.155e-1*tanh(77.519380*y[128]-8.1395349)))/ctn
    dy[129] = 2.0*Dsn*(y[51]+3.0*y[129]-4.0*y[58])/Rpn+2.0*kn*(y[16]*c0)^.5*(-1.0*y[129]*ctn+ctn)^.5*(y[129]*ctn)^.5*sinh(.5*F/R/Tr*(y[100]-1.0*y[82]+.5e-1-2.325*exp(-100.0*y[129]^1.15)+.1721*tanh(20.000000*y[129]-21.000000)+.25e-2*tanh(39.347962*y[129]-37.241379)+.34e-1*tanh(89.411765*y[129]-6.0294118)+.2e-2*tanh(7.0422535*y[129]-1.3661972)+.155e-1*tanh(77.519380*y[129]-8.1395349)))/ctn
    dy[130] = 2.0*Dsn*(y[52]+3.0*y[130]-4.0*y[59])/Rpn+2.0*kn*(y[17]*c0)^.5*(-1.0*y[130]*ctn+ctn)^.5*(y[130]*ctn)^.5*sinh(.5*F/R/Tr*(y[101]-1.0*y[83]+.5e-1-2.325*exp(-100.0*y[130]^1.15)+.1721*tanh(20.000000*y[130]-21.000000)+.25e-2*tanh(39.347962*y[130]-37.241379)+.34e-1*tanh(89.411765*y[130]-6.0294118)+.2e-2*tanh(7.0422535*y[130]-1.3661972)+.155e-1*tanh(77.519380*y[130]-8.1395349)))/ctn
    dy[131] = y[131]-y[85]+y[102]+ (current*Kr)

end
function ocp_cathode(theta_p,up)
    Up = (-5.057-13.6*theta_p^2+121.6*theta_p^4-185.1*theta_p^6-45.43*theta_p^8+127.7*theta_p^10)/(-1-5.04*theta_p^2+32.3*theta_p^4-40.95*theta_p^6-25.94*theta_p^8+40.63*theta_p^10)

end
yyy = function(pars::Array{Float64})
    socn=pars[24]
    socp=pars[25]
    y0 = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,socp,socp,socp,socp,socp,socp,socp,socp,socp,socp,socp,socp,socp,socp,socp,socp,socp,socp,socp,socp,socp,socn,socn,socn,socn,socn,socn,socn,socn,socn,socn,socn,socn,socn,socn,socn,socn,socn,socn,socn,socn,socn,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,(-0.5057e1 - 0.136e2 * socp ^ 2 + 0.1216e3 * socp ^ 4 - 0.1851e3 * socp ^ 6 - 0.4543e2 * socp ^ 8 + 0.1277e3 * socp ^ 10) / (-0.1e1 - 0.504e1 * socp ^ 2 + 0.323e2 * socp ^ 4 - 0.4095e2 * socp ^ 6 - 0.2594e2 * socp ^ 8 + 0.4063e2 * socp ^ 10),(-0.5057e1 - 0.136e2 * socp ^ 2 + 0.1216e3 * socp ^ 4 - 0.1851e3 * socp ^ 6 - 0.4543e2 * socp ^ 8 + 0.1277e3 * socp ^ 10) / (-0.1e1 - 0.504e1 * socp ^ 2 + 0.323e2 * socp ^ 4 - 0.4095e2 * socp ^ 6 - 0.2594e2 * socp ^ 8 + 0.4063e2 * socp ^ 10),(-0.5057e1 - 0.136e2 * socp ^ 2 + 0.1216e3 * socp ^ 4 - 0.1851e3 * socp ^ 6 - 0.4543e2 * socp ^ 8 + 0.1277e3 * socp ^ 10) / (-0.1e1 - 0.504e1 * socp ^ 2 + 0.323e2 * socp ^ 4 - 0.4095e2 * socp ^ 6 - 0.2594e2 * socp ^ 8 + 0.4063e2 * socp ^ 10),(-0.5057e1 - 0.136e2 * socp ^ 2 + 0.1216e3 * socp ^ 4 - 0.1851e3 * socp ^ 6 - 0.4543e2 * socp ^ 8 + 0.1277e3 * socp ^ 10) / (-0.1e1 - 0.504e1 * socp ^ 2 + 0.323e2 * socp ^ 4 - 0.4095e2 * socp ^ 6 - 0.2594e2 * socp ^ 8 + 0.4063e2 * socp ^ 10),(-0.5057e1 - 0.136e2 * socp ^ 2 + 0.1216e3 * socp ^ 4 - 0.1851e3 * socp ^ 6 - 0.4543e2 * socp ^ 8 + 0.1277e3 * socp ^ 10) / (-0.1e1 - 0.504e1 * socp ^ 2 + 0.323e2 * socp ^ 4 - 0.4095e2 * socp ^ 6 - 0.2594e2 * socp ^ 8 + 0.4063e2 * socp ^ 10),(-0.5057e1 - 0.136e2 * socp ^ 2 + 0.1216e3 * socp ^ 4 - 0.1851e3 * socp ^ 6 - 0.4543e2 * socp ^ 8 + 0.1277e3 * socp ^ 10) / (-0.1e1 - 0.504e1 * socp ^ 2 + 0.323e2 * socp ^ 4 - 0.4095e2 * socp ^ 6 - 0.2594e2 * socp ^ 8 + 0.4063e2 * socp ^ 10),(-0.5057e1 - 0.136e2 * socp ^ 2 + 0.1216e3 * socp ^ 4 - 0.1851e3 * socp ^ 6 - 0.4543e2 * socp ^ 8 + 0.1277e3 * socp ^ 10) / (-0.1e1 - 0.504e1 * socp ^ 2 + 0.323e2 * socp ^ 4 - 0.4095e2 * socp ^ 6 - 0.2594e2 * socp ^ 8 + 0.4063e2 * socp ^ 10),(-0.5057e1 - 0.136e2 * socp ^ 2 + 0.1216e3 * socp ^ 4 - 0.1851e3 * socp ^ 6 - 0.4543e2 * socp ^ 8 + 0.1277e3 * socp ^ 10) / (-0.1e1 - 0.504e1 * socp ^ 2 + 0.323e2 * socp ^ 4 - 0.4095e2 * socp ^ 6 - 0.2594e2 * socp ^ 8 + 0.4063e2 * socp ^ 10),(-0.5057e1 - 0.136e2 * socp ^ 2 + 0.1216e3 * socp ^ 4 - 0.1851e3 * socp ^ 6 - 0.4543e2 * socp ^ 8 + 0.1277e3 * socp ^ 10) / (-0.1e1 - 0.504e1 * socp ^ 2 + 0.323e2 * socp ^ 4 - 0.4095e2 * socp ^ 6 - 0.2594e2 * socp ^ 8 + 0.4063e2 * socp ^ 10),-0.5e-1 + 0.2325e1 * exp(-0.100e3 * socn ^ 0.115e1) - 0.1721e0 * tanh(0.20000000e2 * socn - 0.21000000e2) - 0.25e-2 * tanh(0.39347962e2 * socn - 0.37241379e2) - 0.34e-1 * tanh(0.89411765e2 * socn - 0.60294118e1) - 0.2e-2 * tanh(0.70422535e1 * socn - 0.13661972e1) - 0.155e-1 * tanh(0.77519380e2 * socn - 0.81395349e1),-0.5e-1 + 0.2325e1 * exp(-0.100e3 * socn ^ 0.115e1) - 0.1721e0 * tanh(0.20000000e2 * socn - 0.21000000e2) - 0.25e-2 * tanh(0.39347962e2 * socn - 0.37241379e2) - 0.34e-1 * tanh(0.89411765e2 * socn - 0.60294118e1) - 0.2e-2 * tanh(0.70422535e1 * socn - 0.13661972e1) - 0.155e-1 * tanh(0.77519380e2 * socn - 0.81395349e1),-0.5e-1 + 0.2325e1 * exp(-0.100e3 * socn ^ 0.115e1) - 0.1721e0 * tanh(0.20000000e2 * socn - 0.21000000e2) - 0.25e-2 * tanh(0.39347962e2 * socn - 0.37241379e2) - 0.34e-1 * tanh(0.89411765e2 * socn - 0.60294118e1) - 0.2e-2 * tanh(0.70422535e1 * socn - 0.13661972e1) - 0.155e-1 * tanh(0.77519380e2 * socn - 0.81395349e1),-0.5e-1 + 0.2325e1 * exp(-0.100e3 * socn ^ 0.115e1) - 0.1721e0 * tanh(0.20000000e2 * socn - 0.21000000e2) - 0.25e-2 * tanh(0.39347962e2 * socn - 0.37241379e2) - 0.34e-1 * tanh(0.89411765e2 * socn - 0.60294118e1) - 0.2e-2 * tanh(0.70422535e1 * socn - 0.13661972e1) - 0.155e-1 * tanh(0.77519380e2 * socn - 0.81395349e1),-0.5e-1 + 0.2325e1 * exp(-0.100e3 * socn ^ 0.115e1) - 0.1721e0 * tanh(0.20000000e2 * socn - 0.21000000e2) - 0.25e-2 * tanh(0.39347962e2 * socn - 0.37241379e2) - 0.34e-1 * tanh(0.89411765e2 * socn - 0.60294118e1) - 0.2e-2 * tanh(0.70422535e1 * socn - 0.13661972e1) - 0.155e-1 * tanh(0.77519380e2 * socn - 0.81395349e1),-0.5e-1 + 0.2325e1 * exp(-0.100e3 * socn ^ 0.115e1) - 0.1721e0 * tanh(0.20000000e2 * socn - 0.21000000e2) - 0.25e-2 * tanh(0.39347962e2 * socn - 0.37241379e2) - 0.34e-1 * tanh(0.89411765e2 * socn - 0.60294118e1) - 0.2e-2 * tanh(0.70422535e1 * socn - 0.13661972e1) - 0.155e-1 * tanh(0.77519380e2 * socn - 0.81395349e1),-0.5e-1 + 0.2325e1 * exp(-0.100e3 * socn ^ 0.115e1) - 0.1721e0 * tanh(0.20000000e2 * socn - 0.21000000e2) - 0.25e-2 * tanh(0.39347962e2 * socn - 0.37241379e2) - 0.34e-1 * tanh(0.89411765e2 * socn - 0.60294118e1) - 0.2e-2 * tanh(0.70422535e1 * socn - 0.13661972e1) - 0.155e-1 * tanh(0.77519380e2 * socn - 0.81395349e1),-0.5e-1 + 0.2325e1 * exp(-0.100e3 * socn ^ 0.115e1) - 0.1721e0 * tanh(0.20000000e2 * socn - 0.21000000e2) - 0.25e-2 * tanh(0.39347962e2 * socn - 0.37241379e2) - 0.34e-1 * tanh(0.89411765e2 * socn - 0.60294118e1) - 0.2e-2 * tanh(0.70422535e1 * socn - 0.13661972e1) - 0.155e-1 * tanh(0.77519380e2 * socn - 0.81395349e1),-0.5e-1 + 0.2325e1 * exp(-0.100e3 * socn ^ 0.115e1) - 0.1721e0 * tanh(0.20000000e2 * socn - 0.21000000e2) - 0.25e-2 * tanh(0.39347962e2 * socn - 0.37241379e2) - 0.34e-1 * tanh(0.89411765e2 * socn - 0.60294118e1) - 0.2e-2 * tanh(0.70422535e1 * socn - 0.13661972e1) - 0.155e-1 * tanh(0.77519380e2 * socn - 0.81395349e1),socp,socp,socp,socp,socp,socp,socp,socp,socp,socp,socp,socp,socp,socp,socn,socn,socn,socn,socn,socn,socn,socn,socn,socn,socn,socn,socn,socn,(-0.5057e1 - 0.136e2 * socp ^ 2 + 0.1216e3 * socp ^ 4 - 0.1851e3 * socp ^ 6 - 0.4543e2 * socp ^ 8 + 0.1277e3 * socp ^ 10) / (-0.1e1 - 0.504e1 * socp ^ 2 + 0.323e2 * socp ^ 4 - 0.4095e2 * socp ^ 6 - 0.2594e2 * socp ^ 8 + 0.4063e2 * socp ^ 10) + 0.5e-1 - 0.2325e1 * exp(-0.100e3 * socn ^ 0.115e1) + 0.1721e0 * tanh(0.20000000e2 * socn - 0.21000000e2) + 0.25e-2 * tanh(0.39347962e2 * socn - 0.37241379e2) + 0.34e-1 * tanh(0.89411765e2 * socn - 0.60294118e1) + 0.2e-2 * tanh(0.70422535e1 * socn - 0.13661972e1) + 0.155e-1 * tanh(0.77519380e2 * socn - 0.81395349e1)]

end
y0=zeros(131)

n=length(y0)
MM=zeros((n,n))
node = 59

for i in 1:node
    MM[i,i]=1.
end

pars = [7.33234842e-08,6.40146313e-12,1.56954148e-13,1.65301662e-06,
  1.28277079e-05,1.39115369e+00,1.70413971e+00,1.93944836e+00,
  1.15245117e+03,3.46144727e+04,4.02951641e+04,3.24118063e-02,
  2.70097144e-02,5.20209372e-01,3.74625146e-01,4.16417062e-01,
  5.51529622e-09,6.95793778e-09,4.91284482e-05,4.88584483e-05,
  1.28054144e-05,1.38146591e+02,9.15019798e+00,9.78830695e-01,
  4.58723247e-01,4.32648301e-01,0.02]
y0 = yyy(pars)
dy = zeros(n)
f = (dy,y) -> P2D2c(zero(y),y,pars,0.)
using ForwardDiff

# Really long compile time
ForwardDiff.jacobian(f,dy,y0)

and I haven't been able to have the compilation finish.

Edit: This regressed to 800 seconds.

842.944606 seconds (15.81 M allocations: 1.411 GiB, 0.08% gc time)

@ChrisRackauckas ChrisRackauckas changed the title 500 second compile time on ForwardDiff example 800 second compile time on ForwardDiff example Aug 25, 2018
@timholy
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timholy commented Aug 25, 2018

Almost surely a duplicate of #25927? Take a @profile and see if construct_domtree! is the major bottleneck during compilation. If so, put a link to this issue in #25927 and then close this.

If it's not construct_domtree!, leave this open (preferably with info from the profile about where the bottleneck is).

@ChrisRackauckas
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# Really long compile time
using Profile
Profile.init(n = 10^6, delay = 1.0)
@profile ForwardDiff.jacobian(f,dy,y0)

Profile.print(format=:flat)
 Warning: The profile data buffer is full; profiling probably terminated
│ before your program finished. To profile for longer runs, call
│ `Profile.init()` with a larger buffer and/or larger delay.
└ @ Profile C:\cygwin\home\Administrator\buildbot\worker\package_win64\build\usr\share\julia\stdlib\v1.0\Profile\src\Profile.jl:312
 Count File                          Line Function
    15 .\abstractarray.jl             649 copyto!(::Array{Int64,1}, ::Core.Compil...    62 .\abstractarray.jl             650 copyto!(::Array{Int64,1}, ::Core.Compil...    14 .\abstractarray.jl            1835 foreach
     1 .\abstractarray.jl             841 isempty
     1 .\abstractarray.jl            1980 map!(::getfield(Core.Compiler, Symbol("...     1 .\abstractarray.jl            1981 map!
    39 .\abstractarray.jl             617 similar
    39 .\abstractarray.jl             618 similar
     1 .\abstractdict.jl              512 Type
     4 .\array.jl                    1024 Type
     1 .\array.jl                     523 _collect(::Type{Int64}, ::Core.Compiler...   105 .\array.jl                     563 _collect(::Core.Compiler.UnitRange{Int6...    14 .\array.jl                     814 _growend!
     1 .\array.jl                     532 _similar_for
     1 .\array.jl                     898 cfg_inline_item!(::Core.Compiler.Inlini...     1 .\array.jl                     518 collect
   105 .\array.jl                     557 collect
     1 .\array.jl                     557 collect(::Core.Compiler.Iterators.Filte...     7 .\array.jl                     274 copyto!(::Array{Int64,1}, ::Int64, ::Ar...     6 .\array.jl                     277 copyto!
     3 .\array.jl                     416 fill
     3 .\array.jl                     418 fill
    13 .\array.jl                     365 getindex
     1 .\array.jl                     366 getindex
  1875 .\array.jl                     731 getindex
   528 .\array.jl                     707 iterate
     1 .\array.jl                     707 iterate(::Array{Any,1})
     2 .\array.jl                     707 iterate
     1 .\array.jl                     707 iterate(::Array{Any,1})
    75 .\array.jl                     707 iterate
     4 .\array.jl                     199 length
     5 .\array.jl                     856 push!
     2 .\array.jl                     862 push!
     7 .\array.jl                    1006 resize!
   130 .\array.jl                     769 setindex!
     1 .\array.jl                    1024 sizehint!
     7 .\array.jl                     225 unsafe_copyto!
     7 .\array.jl                     244 unsafe_copyto!(::Array{UInt64,1}, ::Int...     3 .\array.jl                     464 zeros
     3 .\array.jl                     467 zeros
    14 .\bitarray.jl                   85 _div64
     8 .\bitarray.jl                 1356 unsafe_bitfindnext(::Array{UInt64,1}, :...     1 .\bitarray.jl                 1358 unsafe_bitfindnext(::Array{UInt64,1}, :...     7 .\bitarray.jl                 1361 unsafe_bitfindnext(::Array{UInt64,1}, :...     9 .\bitarray.jl                 1362 unsafe_bitfindnext(::Array{UInt64,1}, :...     3 .\bitset.jl                     18 Type
     1 .\bitset.jl                     29 Type
     6 .\bitset.jl                     76 _bits_findnext
    43 .\bitset.jl                     77 _bits_findnext
     6 .\bitset.jl                     78 _bits_findnext
  3286 .\bitset.jl                     67 _bits_getindex
   273 .\bitset.jl                     68 _bits_getindex
    28 .\bitset.jl                     69 _bits_getindex
    16 .\bitset.jl                     46 copy(::Core.Compiler.BitSet)
     6 .\bitset.jl                     58 copy!
     6 .\bitset.jl                     59 copy!
     1 .\bitset.jl                     18 find_ssavalue_uses(::Array{Any,1}, ::In...  3708 .\bitset.jl                    300 in
    56 .\bitset.jl                    304 iterate
     4 .\bitset.jl                    305 iterate
     1 .\bitset.jl                    322 length
   161 .\boot.jl                      506 (::Core.GeneratedFunctionStub)(::Any, :...    21 .\boot.jl                      221 Type
     1 .\boot.jl                      368 Type
     7 .\boot.jl                      372 Type
    72 .\boot.jl                      394 Type
    44 .\boot.jl                      403 Type
     1 .\boot.jl                      408 Type
    39 .\boot.jl                      411 Type
    16 .\boot.jl                      413 Type
    26 .\boot.jl                      394 _similar_for
     3 .\compiler/ssair\domtree.jl     10 Type
     1 .\compiler/ssair\domtree.jl     61 construct_domtree(::Core.Compiler.CFG)
    11 .\compiler/ssair\domtree.jl     62 construct_domtree(::Core.Compiler.CFG)
     2 .\compiler/ssair\domtree.jl     67 construct_domtree(::Core.Compiler.CFG)
     6 .\compiler/ssair\domtree.jl     69 construct_domtree(::Core.Compiler.CFG)
     2 .\compiler/ssair\domtree.jl     79 construct_domtree(::Core.Compiler.CFG)
   105 .\compiler/ssair\domtree.jl     81 construct_domtree(::Core.Compiler.CFG)
     5 .\compiler/ssair\domtree.jl     83 construct_domtree(::Core.Compiler.CFG)
    39 .\compiler/ssair\domtree.jl     85 construct_domtree(::Core.Compiler.CFG)
 21636 .\compiler/ssair\domtree.jl     86 construct_domtree(::Core.Compiler.CFG)
   548 .\compiler/ssair\domtree.jl     87 construct_domtree(::Core.Compiler.CFG)
   113 .\compiler/ssair\domtree.jl     91 construct_domtree(::Core.Compiler.CFG)
     3 .\compiler/ssair\domtree.jl    102 construct_domtree(::Core.Compiler.CFG)
     8 .\compiler/ssair\driver.jl     103 just_construct_ssa(::Core.CodeInfo, ::A...     4 .\compiler/ssair\driver.jl     104 just_construct_ssa(::Core.CodeInfo, ::A...    25 .\compiler/ssair\driver.jl     109 just_construct_ssa(::Core.CodeInfo, ::A...    41 .\compiler/ssair\driver.jl     114 run_passes(::Core.CodeInfo, ::Int64, ::...     3 .\compiler/ssair\driver.jl     117 run_passes(::Core.CodeInfo, ::Int64, ::...   368 .\compiler/ssair\driver.jl     118 run_passes(::Core.CodeInfo, ::Int64, ::... 22470 .\compiler/ssair\driver.jl     120 run_passes(::Core.CodeInfo, ::Int64, ::...     4 .\compiler/ssair\driver.jl     121 run_passes(::Core.CodeInfo, ::Int64, ::...    17 .\compiler/ssair\driver.jl     123 run_passes(::Core.CodeInfo, ::Int64, ::...     6 .\compiler/ssair\driver.jl     126 run_passes(::Core.CodeInfo, ::Int64, ::...     1 .\compiler/ssair\driver.jl     128 run_passes(::Core.CodeInfo, ::Int64, ::...     9 .\compiler/ssair\driver.jl     129 run_passes(::Core.CodeInfo, ::Int64, ::...     2 .\compiler/ssair\inlining.jl    10 Core.Compiler.InliningTodo(::Int64, ::B...     1 .\compiler/ssair\inlining.jl    79 Core.Compiler.CFGInliningState(::Core.C...     1 .\compiler/ssair\inlining.jl   621 analyze_method!(::Int64, ::Any, ::Any, ...     4 .\compiler/ssair\inlining.jl   644 analyze_method!(::Int64, ::Any, ::Any, ...     1 .\compiler/ssair\inlining.jl   652 analyze_method!(::Int64, ::Any, ::Any, ...     7 .\compiler/ssair\inlining.jl   655 analyze_method!(::Int64, ::Any, ::Any, ...    12 .\compiler/ssair\inlining.jl   675 analyze_method!(::Int64, ::Any, ::Any, ...    11 .\compiler/ssair\inlining.jl   677 analyze_method!(::Int64, ::Any, ::Any, ...    75 .\compiler/ssair\inlining.jl   682 analyze_method!(::Int64, ::Any, ::Any, ...     6 .\compiler/ssair\inlining.jl   686 analyze_method!(::Int64, ::Any, ::Any, ...     1 .\compiler/ssair\inlining.jl   767 assemble_inline_todo!(::Core.Compiler.I...     1 .\compiler/ssair\inlining.jl   773 assemble_inline_todo!(::Core.Compiler.I...     3 .\compiler/ssair\inlining.jl   776 assemble_inline_todo!(::Core.Compiler.I...     1 .\compiler/ssair\inlining.jl   777 assemble_inline_todo!(::Core.Compiler.I...     1 .\compiler/ssair\inlining.jl   779 assemble_inline_todo!(::Core.Compiler.I...     2 .\compiler/ssair\inlining.jl   785 assemble_inline_todo!(::Core.Compiler.I...     1 .\compiler/ssair\inlining.jl   791 assemble_inline_todo!(::Core.Compiler.I...    10 .\compiler/ssair\inlining.jl   840 assemble_inline_todo!(::Core.Compiler.I...     1 .\compiler/ssair\inlining.jl   850 assemble_inline_todo!(::Core.Compiler.I...    66 .\compiler/ssair\inlining.jl   869 assemble_inline_todo!(::Core.Compiler.I...     9 .\compiler/ssair\inlining.jl   877 assemble_inline_todo!(::Core.Compiler.I...     3 .\compiler/ssair\inlining.jl   883 assemble_inline_todo!(::Core.Compiler.I...     1 .\compiler/ssair\inlining.jl   884 assemble_inline_todo!(::Core.Compiler.I...   116 .\compiler/ssair\inlining.jl   889 assemble_inline_todo!(::Core.Compiler.I...     3 .\compiler/ssair\inlining.jl   937 assemble_inline_todo!(::Core.Compiler.I...     2 .\compiler/ssair\inlining.jl   946 assemble_inline_todo!(::Core.Compiler.I...     1 .\compiler/ssair\inlining.jl   950 assemble_inline_todo!(::Core.Compiler.I...     1 .\compiler/ssair\inlining.jl   464 batch_inline!(::Array{Any,1}, ::Core.Co...    13 .\compiler/ssair\inlining.jl   472 batch_inline!(::Array{Any,1}, ::Core.Co...     1 .\compiler/ssair\inlining.jl   475 batch_inline!(::Array{Any,1}, ::Core.Co...     3 .\compiler/ssair\inlining.jl   507 batch_inline!(::Array{Any,1}, ::Core.Co...    91 .\compiler/ssair\inlining.jl   515 batch_inline!(::Array{Any,1}, ::Core.Co...     1 .\compiler/ssair\inlining.jl   517 batch_inline!(::Array{Any,1}, ::Core.Co...     3 .\compiler/ssair\inlining.jl   534 batch_inline!(::Array{Any,1}, ::Core.Co...    32 .\compiler/ssair\inlining.jl   538 batch_inline!(::Array{Any,1}, ::Core.Co...    13 .\compiler/ssair\inlining.jl   106 cfg_inline_item!
     6 .\compiler/ssair\inlining.jl   148 cfg_inline_item!(::Core.Compiler.Inlini...     3 .\compiler/ssair\inlining.jl   156 cfg_inline_item!(::Core.Compiler.Inlini...     2 .\compiler/ssair\inlining.jl   159 cfg_inline_item!(::Core.Compiler.Inlini...     1 .\compiler/ssair\inlining.jl   165 cfg_inline_item!(::Core.Compiler.Inlini...     1 .\compiler/ssair\inlining.jl  1025 early_inline_special_case(::Core.Compil...     7 .\compiler/ssair\inlining.jl  1144 find_inferred(::Core.MethodInstance, ::...     1 .\compiler/ssair\inlining.jl   262 finish_cfg_inline!(::Core.Compiler.CFGI...     1 .\compiler/ssair\inlining.jl   741 handle_single_case!(::Core.Compiler.IRC...     1 .\compiler/ssair\inlining.jl   752 handle_single_case!(::Core.Compiler.IRC...     1 .\compiler/ssair\inlining.jl   277 ir_inline_item!(::Core.Compiler.Increme...     7 .\compiler/ssair\inlining.jl   278 ir_inline_item!(::Core.Compiler.Increme...     3 .\compiler/ssair\inlining.jl   299 ir_inline_item!(::Core.Compiler.Increme...     1 .\compiler/ssair\inlining.jl   300 ir_inline_item!(::Core.Compiler.Increme...     1 .\compiler/ssair\inlining.jl   307 ir_inline_item!(::Core.Compiler.Increme...     2 .\compiler/ssair\inlining.jl   316 ir_inline_item!(::Core.Compiler.Increme...     1 .\compiler/ssair\inlining.jl   330 ir_inline_item!(::Core.Compiler.Increme...    11 .\compiler/ssair\inlining.jl   331 ir_inline_item!(::Core.Compiler.Increme...    18 .\compiler/ssair\inlining.jl   332 ir_inline_item!(::Core.Compiler.Increme...    45 .\compiler/ssair\inlining.jl   363 ir_inline_item!(::Core.Compiler.Increme...     1 .\compiler/ssair\inlining.jl   371 ir_inline_item!(::Core.Compiler.Increme...     1 .\compiler/ssair\inlining.jl   430 ir_inline_unionsplit!(::Core.Compiler.I...     1 .\compiler/ssair\inlining.jl  1002 ispuretopfunction(::Any)
   223 .\compiler/ssair\inlining.jl    60 ssa_inlining_pass!
   145 .\compiler/ssair\inlining.jl    63 ssa_inlining_pass!
     1 .\compiler/ssair\inlining.jl  1079 ssa_substitute!
    17 .\compiler/ssair\inlining.jl  1081 ssa_substitute!
     1 .\compiler/ssair\inlining.jl  1092 ssa_substitute_op!(::Any, ::Array{Any,1...     1 .\compiler/ssair\inlining.jl  1107 ssa_substitute_op!(::Any, ::Array{Any,1...     4 .\compiler/ssair\inlining.jl  1124 ssa_substitute_op!(::Any, ::Array{Any,1...     5 .\compiler/ssair\inlining.jl  1125 ssa_substitute_op!(::Any, ::Array{Any,1...    11 .\compiler/ssair\inlining.jl  1126 ssa_substitute_op!(::Any, ::Array{Any,1...     1 .\compiler/ssair\inlining.jl  1128 ssa_substitute_op!(::Any, ::Array{Any,1...     1 .\compiler/ssair\ir.jl          39 Type
     1 .\compiler/ssair\ir.jl         207 Type
    33 .\compiler/ssair\ir.jl         245 Type
    46 .\compiler/ssair\ir.jl         250 Type
     1 .\compiler/ssair\ir.jl         469 Core.Compiler.IncrementalCompact(::Core...     1 .\compiler/ssair\ir.jl         474 Core.Compiler.IncrementalCompact(::Core...     1 .\compiler/ssair\ir.jl         477 Core.Compiler.IncrementalCompact(::Core...     2 .\compiler/ssair\ir.jl         490 Core.Compiler.IncrementalCompact(::Core...     1 .\compiler/ssair\ir.jl         491 Core.Compiler.IncrementalCompact(::Core...     1 .\compiler/ssair\ir.jl        1024 compact!(::Core.Compiler.IRCode)
    14 .\compiler/ssair\ir.jl        1026 compact!(::Core.Compiler.IRCode)
     1 .\compiler/ssair\ir.jl        1027 compact!(::Core.Compiler.IRCode)
     1 .\compiler/ssair\ir.jl         116 compute_basic_blocks(::Array{Any,1})
     1 .\compiler/ssair\ir.jl         119 compute_basic_blocks(::Array{Any,1})
     5 .\compiler/ssair\ir.jl         542 count_added_node!(::Core.Compiler.Incre...     1 .\compiler/ssair\ir.jl         543 count_added_node!(::Core.Compiler.Incre...     3 .\compiler/ssair\ir.jl         547 count_added_node!(::Core.Compiler.Incre...     1 .\compiler/ssair\ir.jl         551 count_added_node!(::Core.Compiler.Incre...    33 .\compiler/ssair\ir.jl        1014 finish
     1 .\compiler/ssair\ir.jl         823 finish_current_bb!(::Core.Compiler.Incr...     1 .\compiler/ssair\ir.jl         252 getindex
     8 .\compiler/ssair\ir.jl         267 getindex(::Core.Compiler.UseRef)
     1 .\compiler/ssair\ir.jl         268 getindex(::Core.Compiler.UseRef)
     1 .\compiler/ssair\ir.jl         277 getindex(::Core.Compiler.UseRef)
     2 .\compiler/ssair\ir.jl         279 getindex(::Core.Compiler.UseRef)
     2 .\compiler/ssair\ir.jl         280 getindex(::Core.Compiler.UseRef)
     2 .\compiler/ssair\ir.jl         303 getindex(::Core.Compiler.UseRef)
     2 .\compiler/ssair\ir.jl         305 getindex(::Core.Compiler.UseRef)
     2 .\compiler/ssair\ir.jl         310 is_relevant_expr
    15 .\compiler/ssair\ir.jl         367 iterate
    13 .\compiler/ssair\ir.jl         369 iterate(::Core.Compiler.UseRefIterator,...     1 .\compiler/ssair\ir.jl         372 iterate(::Core.Compiler.UseRefIterator,...    12 .\compiler/ssair\ir.jl         373 iterate(::Core.Compiler.UseRefIterator,...     2 .\compiler/ssair\ir.jl         375 iterate(::Core.Compiler.UseRefIterator,...     2 .\compiler/ssair\ir.jl         853 iterate
     1 .\compiler/ssair\ir.jl         853 iterate(::Core.Compiler.IncrementalComp...     1 .\compiler/ssair\ir.jl         858 iterate(::Core.Compiler.IncrementalComp...     1 .\compiler/ssair\ir.jl         881 iterate(::Core.Compiler.IncrementalComp...    54 .\compiler/ssair\ir.jl         882 iterate(::Core.Compiler.IncrementalComp...     1 .\compiler/ssair\ir.jl         887 iterate(::Core.Compiler.IncrementalComp...     5 .\compiler/ssair\ir.jl         889 iterate(::Core.Compiler.IncrementalComp...     4 .\compiler/ssair\ir.jl         894 iterate(::Core.Compiler.IncrementalComp...    33 .\compiler/ssair\ir.jl         898 maybe_erase_unused!
     3 .\compiler/ssair\ir.jl         903 maybe_erase_unused!(::Array{Int64,1}, :...    30 .\compiler/ssair\ir.jl         906 maybe_erase_unused!(::Array{Int64,1}, :...     2 .\compiler/ssair\ir.jl         760 process_node!(::Array{Any,1}, ::Int64, ...     1 .\compiler/ssair\ir.jl         763 process_node!(::Array{Any,1}, ::Int64, ...    51 .\compiler/ssair\ir.jl         769 process_node!(::Array{Any,1}, ::Int64, ...    54 .\compiler/ssair\ir.jl         790 process_node!
     1 .\compiler/ssair\ir.jl         726 renumber_ssa2(::Core.SSAValue, ::Array{...     8 .\compiler/ssair\ir.jl         734 renumber_ssa2(::Core.SSAValue, ::Array{...    25 .\compiler/ssair\ir.jl         740 renumber_ssa2!(::Any, ::Array{Any,1}, :...     6 .\compiler/ssair\ir.jl         741 renumber_ssa2!(::Any, ::Array{Any,1}, :...     3 .\compiler/ssair\ir.jl         742 renumber_ssa2!(::Any, ::Array{Any,1}, :...     1 .\compiler/ssair\ir.jl         743 renumber_ssa2!(::Any, ::Array{Any,1}, :...    10 .\compiler/ssair\ir.jl         747 renumber_ssa2!(::Any, ::Array{Any,1}, :...     5 .\compiler/ssair\ir.jl         752 renumber_ssa2!(::Any, ::Array{Any,1}, :...     1 .\compiler/ssair\ir.jl         754 renumber_ssa2!(::Any, ::Array{Any,1}, :...     1 .\compiler/ssair\ir.jl         801 resize!(::Core.Compiler.IncrementalComp...     1 .\compiler/ssair\ir.jl         319 setindex!(::Core.Compiler.UseRef, ::Any)
     2 .\compiler/ssair\ir.jl         333 setindex!(::Core.Compiler.UseRef, ::Any)
     1 .\compiler/ssair\ir.jl         345 setindex!(::Core.Compiler.UseRef, ::Any)
     1 .\compiler/ssair\ir.jl         636 setindex!(::Core.Compiler.IncrementalCo...     5 .\compiler/ssair\ir.jl         639 setindex!(::Core.Compiler.IncrementalCo...     1 .\compiler/ssair\ir.jl         640 setindex!(::Core.Compiler.IncrementalCo...     1 .\compiler/ssair\ir.jl         641 setindex!(::Core.Compiler.IncrementalCo...     1 .\compiler/ssair\ir.jl         643 setindex!(::Core.Compiler.IncrementalCo...    10 .\compiler/ssair\ir.jl         648 setindex!(::Core.Compiler.IncrementalCo...    19 .\compiler/ssair\ir.jl         655 setindex!
     2 .\compiler/ssair\ir.jl         987 simple_dce!(::Core.Compiler.Incremental...    31 .\compiler/ssair\ir.jl         991 simple_dce!(::Core.Compiler.Incremental...     1 .\compiler/ssair\ir.jl         409 ssamap(::getfield(Core.Compiler, Symbol...     1 .\compiler/ssair\ir.jl         411 ssamap(::getfield(Core.Compiler, Symbol...    23 .\compiler/ssair\ir.jl         245 userefs
     2 .\compiler/ssair\ir.jl         361 userefs
    46 .\compiler/ssair\ir.jl         364 userefs
    11 .\compiler/ssair\legacy.jl       8 inflate_ir(::Core.CodeInfo, ::Core.Meth...    64 .\compiler/ssair\legacy.jl      12 inflate_ir(::Core.CodeInfo, ::Core.Meth...    54 .\compiler/ssair\legacy.jl      16 inflate_ir(::Core.CodeInfo, ::Core.Simp...     2 .\compiler/ssair\legacy.jl      22 inflate_ir(::Core.CodeInfo, ::Core.Simp...     2 .\compiler/ssair\legacy.jl      25 inflate_ir(::Core.CodeInfo, ::Core.Simp...     1 .\compiler/ssair\legacy.jl      26 inflate_ir(::Core.CodeInfo, ::Core.Simp...     2 .\compiler/ssair\legacy.jl      29 inflate_ir(::Core.CodeInfo, ::Core.Simp...     2 .\compiler/ssair\legacy.jl      39 inflate_ir(::Core.CodeInfo, ::Core.Simp...     1 .\compiler/ssair\legacy.jl      48 inflate_ir(::Core.CodeInfo, ::Core.Simp...     3 .\compiler/ssair\legacy.jl      67 replace_code_newstyle!(::Core.CodeInfo,...     1 .\compiler/ssair\legacy.jl      71 replace_code_newstyle!(::Core.CodeInfo,...     1 .\compiler/ssair\legacy.jl      80 replace_code_newstyle!(::Core.CodeInfo,...     1 .\compiler/ssair\legacy.jl      83 replace_code_newstyle!(::Core.CodeInfo,...     1 .\compiler/ssair\passes.jl     197 (::getfield(Core.Compiler, Symbol("##27...     2 .\compiler/ssair\passes.jl     812 adce_erase!
     1 .\compiler/ssair\passes.jl     841 adce_pass!(::Core.Compiler.IRCode)
     1 .\compiler/ssair\passes.jl     843 adce_pass!(::Core.Compiler.IRCode)
     1 .\compiler/ssair\passes.jl     846 adce_pass!(::Core.Compiler.IRCode)
     1 .\compiler/ssair\passes.jl     854 adce_pass!(::Core.Compiler.IRCode)
     2 .\compiler/ssair\passes.jl     858 adce_pass!(::Core.Compiler.IRCode)
     1 .\compiler/ssair\passes.jl     506 getfield_elim_pass!(::Core.Compiler.IRC...     1 .\compiler/ssair\passes.jl     521 getfield_elim_pass!(::Core.Compiler.IRC...     1 .\compiler/ssair\passes.jl     523 getfield_elim_pass!(::Core.Compiler.IRC...     1 .\compiler/ssair\passes.jl     547 getfield_elim_pass!(::Core.Compiler.IRC...     2 .\compiler/ssair\passes.jl     554 getfield_elim_pass!(::Core.Compiler.IRC...     1 .\compiler/ssair\passes.jl     610 getfield_elim_pass!(::Core.Compiler.IRC...     1 .\compiler/ssair\passes.jl     612 getfield_elim_pass!(::Core.Compiler.IRC...     2 .\compiler/ssair\passes.jl     645 getfield_elim_pass!(::Core.Compiler.IRC...     2 .\compiler/ssair\passes.jl     652 getfield_elim_pass!(::Core.Compiler.IRC...     2 .\compiler/ssair\passes.jl     671 getfield_elim_pass!(::Core.Compiler.IRC...     3 .\compiler/ssair\passes.jl     688 getfield_elim_pass!(::Core.Compiler.IRC...     1 .\compiler/ssair\passes.jl     397 lift_comparison!(::Core.Compiler.Increm...     1 .\compiler/ssair\passes.jl     402 lift_comparison!(::Core.Compiler.Increm...     1 .\compiler/ssair\passes.jl     264 lift_leaves(::Core.Compiler.Incremental...     1 .\compiler/ssair\passes.jl     268 lift_leaves(::Core.Compiler.Incremental...     1 .\compiler/ssair\passes.jl     453 perform_lifting!(::Core.Compiler.Increm...     1 .\compiler/ssair\passes.jl     454 perform_lifting!(::Core.Compiler.Increm...     2 .\compiler/ssair\passes.jl     169 walk_to_defs(::Core.Compiler.Incrementa...     1 .\compiler/ssair\passes.jl     191 walk_to_defs(::Core.Compiler.Incrementa...     3 .\compiler/ssair\queries.jl     67 compact_exprtype
     3 .\compiler/ssair\queries.jl     76 is_known_call
     3 .\compiler/ssair\queries.jl      7 stmt_effect_free(::Any, ::Any, ::Core.C...     1 .\compiler/ssair\slot2ssa.jl     8 Type
     1 .\compiler/ssair\slot2ssa.jl   520 compute_live_ins(::Core.Compiler.CFG, :...     1 .\compiler/ssair\slot2ssa.jl   522 compute_live_ins(::Core.Compiler.CFG, :...     1 .\compiler/ssair\slot2ssa.jl   598 construct_ssa!(::Core.CodeInfo, ::Array...     2 .\compiler/ssair\slot2ssa.jl   628 construct_ssa!(::Core.CodeInfo, ::Array...     1 .\compiler/ssair\slot2ssa.jl   654 construct_ssa!(::Core.CodeInfo, ::Array...     1 .\compiler/ssair\slot2ssa.jl   670 construct_ssa!(::Core.CodeInfo, ::Array...     1 .\compiler/ssair\slot2ssa.jl   732 construct_ssa!(::Core.CodeInfo, ::Array...     6 .\compiler/ssair\slot2ssa.jl   740 construct_ssa!(::Core.CodeInfo, ::Array...     1 .\compiler/ssair\slot2ssa.jl   768 construct_ssa!(::Core.CodeInfo, ::Array...     1 .\compiler/ssair\slot2ssa.jl   775 construct_ssa!(::Core.CodeInfo, ::Array...     3 .\compiler/ssair\slot2ssa.jl   791 construct_ssa!(::Core.CodeInfo, ::Array...     1 .\compiler/ssair\slot2ssa.jl   813 construct_ssa!(::Core.CodeInfo, ::Array...     3 .\compiler/ssair\slot2ssa.jl   862 construct_ssa!(::Core.CodeInfo, ::Array...     1 .\compiler/ssair\slot2ssa.jl   864 construct_ssa!(::Core.CodeInfo, ::Array...     3 .\compiler/ssair\slot2ssa.jl   869 construct_ssa!(::Core.CodeInfo, ::Array...     2 .\compiler/ssair\slot2ssa.jl   494 domsort_ssa!(::Core.Compiler.IRCode, ::...     1 .\compiler/ssair\slot2ssa.jl   499 domsort_ssa!(::Core.Compiler.IRCode, ::...     2 .\compiler/ssair\slot2ssa.jl   122 fixemup!(::getfield(Core.Compiler, Symb...     3 .\compiler/ssair\slot2ssa.jl   126 fixemup!(::getfield(Core.Compiler, Symb...     1 .\compiler/ssair\slot2ssa.jl   159 fixemup!(::getfield(Core.Compiler, Symb...     1 .\compiler/ssair\slot2ssa.jl   160 fixemup!(::getfield(Core.Compiler, Symb...     1 .\compiler/ssair\slot2ssa.jl   163 fixemup!(::getfield(Core.Compiler, Symb...     1 .\compiler/ssair\slot2ssa.jl    94 new_to_regular(::Any, ::Int64)
     1 .\compiler/ssair\slot2ssa.jl    98 new_to_regular(::Any, ::Int64)
     6 .\compiler/ssair\slot2ssa.jl   182 rename_uses!(::Core.Compiler.IRCode, ::...     1 .\compiler/ssair\slot2ssa.jl    73 renumber_ssa!
     1 .\compiler/ssair\slot2ssa.jl    73 renumber_ssa!(::Any, ::Array{Any,1})
     2 .\compiler/ssair\slot2ssa.jl    74 renumber_ssa!
     2 .\compiler/ssair\slot2ssa.jl    23 scan_entry!(::Array{Core.Compiler.SlotI...     3 .\compiler/ssair\slot2ssa.jl    24 scan_entry!(::Array{Core.Compiler.SlotI...     1 .\compiler/ssair\slot2ssa.jl    29 scan_entry!(::Array{Core.Compiler.SlotI...     1 .\compiler/ssair\slot2ssa.jl    49 scan_slot_def_use(::Int64, ::Core.CodeI...     1 .\compiler/ssair\slot2ssa.jl    52 scan_slot_def_use(::Int64, ::Core.CodeI...     6 .\compiler/ssair\slot2ssa.jl    55 scan_slot_def_use(::Int64, ::Core.CodeI...     3 ...abstractinterpretation.jl   470 abstract_apply(::Any, ::Array{Any,1}, :...    68 ...abstractinterpretation.jl   487 abstract_apply(::Any, ::Array{Any,1}, :...    71 ...abstractinterpretation.jl   535 abstract_call(::Any, ::Array{Any,1}, ::...     5 ...abstractinterpretation.jl   561 abstract_call(::Any, ::Array{Any,1}, ::...     2 ...abstractinterpretation.jl   563 abstract_call(::Any, ::Array{Any,1}, ::...     3 ...abstractinterpretation.jl   708 abstract_call(::Any, ::Array{Any,1}, ::...     5 ...abstractinterpretation.jl   754 abstract_call(::Any, ::Tuple{}, ::Array...     6 ...abstractinterpretation.jl   755 abstract_call(::Any, ::Array{Any,1}, ::...     3 ...abstractinterpretation.jl   765 abstract_call(::Any, ::Array{Any,1}, ::...  2026 ...abstractinterpretation.jl   779 abstract_call(::Any, ::Tuple{}, ::Array...     1 ...abstractinterpretation.jl    17 abstract_call_gf_by_type(::Any, ::Array...     1 ...abstractinterpretation.jl    33 abstract_call_gf_by_type(::Any, ::Array...    74 ...abstractinterpretation.jl    45 abstract_call_gf_by_type(::Any, ::Array...  1649 ...abstractinterpretation.jl    79 abstract_call_gf_by_type(::Any, ::Array...     1 ...abstractinterpretation.jl    81 abstract_call_gf_by_type(::Any, ::Array...     3 ...abstractinterpretation.jl    83 abstract_call_gf_by_type(::Any, ::Array...   368 ...abstractinterpretation.jl    91 abstract_call_gf_by_type(::Any, ::Array...     1 ...abstractinterpretation.jl    99 abstract_call_gf_by_type(::Any, ::Array...    11 ...abstractinterpretation.jl   105 abstract_call_gf_by_type(::Any, ::Array...  1646 ...abstractinterpretation.jl   331 abstract_call_method(::Method, ::Any, :...     3 ...abstractinterpretation.jl   335 abstract_call_method(::Method, ::Any, :...     2 ...abstractinterpretation.jl   127 abstract_call_method_with_const_args(::...    13 ...abstractinterpretation.jl   166 abstract_call_method_with_const_args(::...     1 ...abstractinterpretation.jl   182 abstract_call_method_with_const_args(::...    12 ...abstractinterpretation.jl   187 abstract_call_method_with_const_args(::...     1 ...abstractinterpretation.jl   189 abstract_call_method_with_const_args(::...   338 ...abstractinterpretation.jl   191 abstract_call_method_with_const_args(::...     1 ...abstractinterpretation.jl   195 abstract_call_method_with_const_args(::...     1 ...abstractinterpretation.jl   879 abstract_eval(::Any, ::Array{Any,1}, ::...     1 ...abstractinterpretation.jl   880 abstract_eval(::Any, ::Array{Any,1}, ::...     1 ...abstractinterpretation.jl   882 abstract_eval(::Any, ::Array{Any,1}, ::...     1 ...abstractinterpretation.jl   884 abstract_eval(::Any, ::Array{Any,1}, ::...     1 ...abstractinterpretation.jl   892 abstract_eval(::Any, ::Array{Any,1}, ::...  2132 ...abstractinterpretation.jl   893 abstract_eval(::Any, ::Array{Any,1}, ::...    83 ...abstractinterpretation.jl   806 abstract_eval_call(::Array{Any,1}, ::Ar...  2049 ...abstractinterpretation.jl   808 abstract_eval_call(::Array{Any,1}, ::Ar...     4 ...abstractinterpretation.jl   973 abstract_eval_global
     2 ...abstractinterpretation.jl   974 abstract_eval_global
     1 ...abstractinterpretation.jl   980 abstract_eval_ssavalue(::Core.SSAValue,...     1 ...abstractinterpretation.jl   409 abstract_iteration(::Any, ::Array{Any,1...     3 ...abstractinterpretation.jl   356 precise_container_type(::Any, ::Any, ::...     1 ...abstractinterpretation.jl   394 precise_container_type(::Any, ::Any, ::...     1 ...abstractinterpretation.jl   399 precise_container_type(::Any, ::Any, ::...     6 ...abstractinterpretation.jl   512 pure_eval_call(::Any, ::Array{Any,1}, :...     1 ...abstractinterpretation.jl  1014 typeinf_local(::Core.Compiler.Inference...     1 ...abstractinterpretation.jl  1027 typeinf_local(::Core.Compiler.Inference...     1 ...abstractinterpretation.jl  1032 typeinf_local(::Core.Compiler.Inference...   171 ...abstractinterpretation.jl  1103 typeinf_local(::Core.Compiler.Inference...  1964 ...abstractinterpretation.jl  1117 typeinf_local(::Core.Compiler.Inference...     1 ...abstractinterpretation.jl  1120 typeinf_local(::Core.Compiler.Inference...     1 ...abstractinterpretation.jl  1141 typeinf_local(::Core.Compiler.Inference...     1 ...abstractinterpretation.jl  1146 typeinf_local(::Core.Compiler.Inference...  2141 ...abstractinterpretation.jl  1173 typeinf_nocycle(::Core.Compiler.Inferen...     1 ...mpiler\inferenceresult.jl   116 cache_lookup(::Core.MethodInstance, ::A...     2 ...mpiler\inferenceresult.jl   123 cache_lookup(::Core.MethodInstance, ::A...    12 ...mpiler\inferenceresult.jl   126 cache_lookup(::Core.MethodInstance, ::A...     5 ...mpiler\inferenceresult.jl   129 cache_lookup(::Core.MethodInstance, ::A...     1 ...mpiler\inferenceresult.jl    25 get_argtypes
     1 ...mpiler\inferenceresult.jl    36 get_argtypes(::Core.MethodInstance)
     8 ...mpiler\inferenceresult.jl    37 get_argtypes(::Core.MethodInstance)
     1 ...mpiler\inferenceresult.jl    63 get_argtypes(::Core.MethodInstance)
     1 ...mpiler\inferenceresult.jl    92 get_argtypes(::Core.MethodInstance)
     1 ...mpiler\inferenceresult.jl    97 get_argtypes(::Core.MethodInstance)
     1 .\compiler\inferencestate.jl    62 Core.Compiler.InferenceState(::Core.Com...     2 .\compiler\inferencestate.jl    73 Core.Compiler.InferenceState(::Core.Com...     1 .\compiler\inferencestate.jl    77 Core.Compiler.InferenceState(::Core.Com...   176 .\compiler\inferencestate.jl   117 Type
     4 .\compiler\inferencestate.jl   120 Type
     2 .\compiler\inferencestate.jl   213 add_backedge!(::Core.MethodInstance, ::...     1 .\compiler\inferencestate.jl   185 record_ssa_assign(::Int64, ::Any, ::Cor...     1 .\compiler\optimize.jl         373 inline_worthy
     1 .\compiler\optimize.jl         140 isinlineable(::Method, ::Core.Compiler.... 22918 .\compiler\optimize.jl         162 optimize(::Core.Compiler.OptimizationSt...     6 .\compiler\optimize.jl         208 optimize(::Core.Compiler.OptimizationSt...     1 .\compiler\optimize.jl         241 optimize(::Core.Compiler.OptimizationSt...     1 .\compiler\optimize.jl         284 statement_cost(::Expr, ::Int64, ::Core....     1 .\compiler\tfuncs.jl           398 (::getfield(Core.Compiler, Symbol("##19...     1 .\compiler\tfuncs.jl           927 apply_type_tfunc(::Any, ::Any)
     5 .\compiler\tfuncs.jl          1073 builtin_tfunction(::Any, ::Array{Any,1}...     1 .\compiler\tfuncs.jl          1152 builtin_tfunction(::Any, ::Array{Any,1}...     4 .\compiler\tfuncs.jl          1164 builtin_tfunction(::Any, ::Array{Any,1}...     1 .\compiler\tfuncs.jl           220 egal_tfunc(::Any, ::Any)
     1 .\compiler\tfuncs.jl            60 instanceof_tfunc(::Any)
     1 .\compiler\tfuncs.jl            86 math_tfunc(::Any, ::Any)
     3 .\compiler\tfuncs.jl          1185 return_type_tfunc(::Array{Any,1}, ::Arr...     1 .\compiler\typeinfer.jl        250 annotate_slot_load!(::Expr, ::Array{Any...     1 .\compiler\typeinfer.jl        251 annotate_slot_load!(::Expr, ::Array{Any...     4 .\compiler\typeinfer.jl        124 cache_result(::Core.Compiler.InferenceR...     1 .\compiler\typeinfer.jl        133 cache_result(::Core.Compiler.InferenceR...     5 .\compiler\typeinfer.jl        155 finish
     1 .\compiler\typeinfer.jl        170 finish
     1 .\compiler\typeinfer.jl        226 maybe_widen_conditional(::Any)
     1 .\compiler\typeinfer.jl        202 store_backedges(::Core.Compiler.Inferen...     1 .\compiler\typeinfer.jl        311 type_annotate!(::Core.Compiler.Inferenc...     1 .\compiler\typeinfer.jl        312 type_annotate!(::Core.Compiler.Inferenc...     2 .\compiler\typeinfer.jl        355 type_annotate!(::Core.Compiler.Inferenc...     1 .\compiler\typeinfer.jl        384 type_annotate!(::Core.Compiler.Inferenc...  2141 .\compiler\typeinfer.jl         15 typeinf(::Core.Compiler.InferenceState)
     5 .\compiler\typeinfer.jl         24 typeinf(::Core.Compiler.InferenceState)
 22925 .\compiler\typeinfer.jl         35 typeinf(::Core.Compiler.InferenceState)
     1 .\compiler\typeinfer.jl         36 typeinf(::Core.Compiler.InferenceState)
     5 .\compiler\typeinfer.jl         61 typeinf(::Core.Compiler.InferenceState)
     1 .\compiler\typeinfer.jl         72 typeinf(::Core.Compiler.InferenceState)
     8 .\compiler\typeinfer.jl        456 typeinf_edge(::Method, ::Any, ::Core.Si...     1 .\compiler\typeinfer.jl        459 typeinf_edge(::Method, ::Any, ::Core.Si...     1 .\compiler\typeinfer.jl        468 typeinf_edge(::Method, ::Any, ::Core.Si...   167 .\compiler\typeinfer.jl        483 typeinf_edge(::Method, ::Any, ::Core.Si...  1468 .\compiler\typeinfer.jl        492 typeinf_edge(::Method, ::Any, ::Core.Si...     1 .\compiler\typeinfer.jl        565 typeinf_ext(::Core.MethodInstance, ::Co... 23272 .\compiler\typeinfer.jl        567 typeinf_ext(::Core.MethodInstance, ::Co... 23273 .\compiler\typeinfer.jl        604 typeinf_ext(::Core.MethodInstance, ::UI...     1 .\compiler\typeinfer.jl        212 widen_all_consts!(::Core.CodeInfo)
     2 .\compiler\typelattice.jl       12 Type
     2 .\compiler\typelattice.jl      144 widenconst(::Core.Compiler.Const)
     2 .\compiler\typelattice.jl      148 widenconst(::Core.Compiler.Const)
     1 .\compiler\typelattice.jl      105 ⊑(::Any, ::Any)
     1 .\compiler\typelattice.jl      106 ⊑(::Any, ::Any)
     1 .\compiler\typelattice.jl      110 ⊑(::Any, ::Any)
     1 .\compiler\typelattice.jl      111 ⊑
     3 .\compiler\typelimits.jl       281 tmerge(::Any, ::Any)
    15 .\compiler\typeutils.jl         40 argtypes_to_type
     7 .\compiler\utilities.jl         39 anymap(::typeof(Core.Compiler.widencons...     5 .\compiler\utilities.jl        167 argextype
     5 .\compiler\utilities.jl        187 argextype(::Any, ::Core.CodeInfo, ::Cor...     1 .\compiler\utilities.jl        193 argextype(::Any, ::Core.Compiler.IRCode...     8 .\compiler\utilities.jl        125 code_for_method
     4 .\compiler\utilities.jl        138 code_for_method
     8 .\compiler\utilities.jl        142 code_for_method
     1 .\compiler\utilities.jl        202 find_ssavalue_uses(::Array{Any,1}, ::In...   173 .\compiler\utilities.jl         91 get_staged(::Core.MethodInstance)
     1 .\compiler\utilities.jl         67 is_self_quoting
     1 .\compiler\utilities.jl         48 istopfunction
     1 .\compiler\utilities.jl         72 quoted
   173 .\compiler\utilities.jl        112 retrieve_code_info(::Core.MethodInstance)
     3 .\compiler\utilities.jl        116 retrieve_code_info(::Core.MethodInstance)
     3 .\essentials.jl                429 setindex!
    20 .\expr.jl                       36 copy(::Expr)
    49 .\expr.jl                       37 copy(::Expr)
   119 .\expr.jl                       60 copy_exprargs(::Array{Any,1})
    69 .\expr.jl                       43 copy_exprs(::Expr)
     2 .\generator.jl                  32 Type
  1369 .\int.jl                        53 +
  1925 .\int.jl                        52 -
     1 .\int.jl                       443 <<
     1 .\int.jl                       450 <<
    14 .\int.jl                       441 >>
    14 .\int.jl                       448 >>
     2 .\int.jl                        53 iterate
     3 .\int.jl                       384 trailing_zeros
     1 .\iterators.jl                 434 _collect(::Core.Compiler.UnitRange{Int6...     3 .\iterators.jl                 138 iterate
     3 .\iterators.jl                 141 iterate(::Core.Compiler.Iterators.Enume... 23205 .\loading.jl                  1002 include_string(::Module, ::String, ::St...     2 .\operators.jl                 502 +
     1 .\operators.jl                  83 ==
     1 .\operators.jl                 949 in
     1 .\operators.jl                 950 in
     1 .\pair.jl                       12 Type
     1 .\range.jl                     576 iterate
   146 .\reflection.jl                717 _methods_by_ftype
     1 .\reflection.jl                227 isconst
     1 .\sort.jl                      687 #sort#8(::Core.Compiler.Iterators.Pairs... 23205 .\task.jl                       85 (::getfield(Atom, Symbol("##108#113")){...     3 .\tuple.jl                      24 getindex
     4 .\tuple.jl                      60 indexed_iterate
     2 .\tuple.jl                      41 iterate
 23205 ...es\Atom\jodeb\src\eval.jl    90 #109
 23205 ...es\Atom\jodeb\src\eval.jl    91 (::getfield(Atom, Symbol("##110#115")){... 23205 ...es\Atom\jodeb\src\eval.jl    89 macro expansion
 23205 ...es\Atom\jodeb\src\eval.jl    46 withpath
 23205 ...es\Atom\jodeb\src\repl.jl    76 hideprompt(::getfield(Atom, Symbol("##1... 23205 ...deTools\8CjYJ\src\eval.jl    30 include_string(::Module, ::String, ::St... 23205 ...eTools\8CjYJ\src\utils.jl    30 withpath(::getfield(Atom, Symbol("##110...     8 ...iff\kTOVi\src\apiutils.jl    51 #s31#67(::Any, ::Any, ::Any, ::Any)
    47 ...dDiff\kTOVi\src\config.jl   184 ForwardDiff.JacobianConfig(::getfield(M... 23008 ...iff\kTOVi\src\jacobian.jl   212 chunk_mode_jacobian(::getfield(Main, Sy... 46182 ...iff\kTOVi\src\jacobian.jl    32 jacobian(::Function, ::Array{Float64,1}... 23044 ...iff\kTOVi\src\jacobian.jl    36 jacobian(::Function, ::Array{Float64,1}...     9 ...iff\kTOVi\src\partials.jl    10 #s12#9(::Any, ::Any, ::Any, ::Any, ::Ty...    18 ...iff\kTOVi\src\partials.jl   174 #s19#17(::Any, ::Any, ::Any, ::Any)
    10 ...iff\kTOVi\src\partials.jl   198 #s19#29(::Any, ::Any, ::Any, ::Any)
    10 ...iff\kTOVi\src\partials.jl   202 #s19#32(::Any, ::Any, ::Any, ::Any)
    10 ...iff\kTOVi\src\partials.jl   206 #s19#35(::Any, ::Any, ::Any, ::Any)
    11 ...iff\kTOVi\src\partials.jl   210 #s19#38(::Any, ::Any, ::Any, ::Any)
    12 ...iff\kTOVi\src\partials.jl   214 #s19#41(::Any, ::Any, ::Any)
     9 ...iff\kTOVi\src\partials.jl   218 #s19#44(::Any, ::Any, ::Any, ::Any, ::A...    71 ...iff\kTOVi\src\partials.jl   151 tupexpr(::Function, ::Int64)
     1 ...a-1.0.0\lib\julia\sys.dll    -1 getindex(::Array{Core.Compiler.BasicBlo...     1 ...a-1.0.0\lib\julia\sys.dll    -1 length(::Array{Any,1})
     7 ...a-1.0.0\lib\julia\sys.dll    -1 stupdate1!(::Array{Any,1}, ::Core.Compi...     1 ...a-1.0.0\lib\julia\sys.dll    -1 switchtupleunion(::Any)
 23205 ....0\Profile\src\Profile.jl    25 top-level scope
 23008 ...\Computer\Desktop\test.jl   276 (::getfield(Main, Symbol("##13#14")))(:...

It looks like it shows up. Is that the step in type inference taking all of the time?

@timholy
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timholy commented Aug 25, 2018 •
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Most likely. Maybe double-check in tree mode with Profile.print(noisefloor=2) and make sure there isn't anything on the same order of magnitude below it. (In flat mode it's a little harder to tell who's really responsible.)

Also go to n = 10^7 (that's still only 80MB, no big deal on modern systems) to capture the whole trace.

@ChrisRackauckas
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┌ Warning: The profile data buffer is full; profiling probably terminated
│ before your program finished. To profile for longer runs, call
│ `Profile.init()` with a larger buffer and/or larger delay.
└ @ Profile C:\cygwin\home\Administrator\buildbot\worker\package_win64\build\usr\share\julia\stdlib\v1.0\Profile\src\Profile.jl:312
1     .\compiler/ssair\driver.jl:120; run_passes(::Core.CodeInfo, ::Int64,...
23205 .\task.jl:85; (::getfield(Atom, Symbol("##108#113"...
 23205 ...\Atom\jodeb\src\eval.jl:89; macro expansion
  23205 ...Atom\jodeb\src\repl.jl:76; hideprompt(::getfield(Atom, Symbol(...
   23205 ...Atom\jodeb\src\eval.jl:90; #109
    23205 ...tom\jodeb\src\eval.jl:46; withpath
     23205 ...ls\8CjYJ\src\utils.jl:30; withpath(::getfield(Atom, Symbol(...
      23205 ...tom\jodeb\src\eval.jl:91; (::getfield(Atom, Symbol("##110#1...
       23205 ...ls\8CjYJ\src\eval.jl:30; include_string(::Module, ::Strin...
        23205 .\loading.jl:1002; include_string(::Module, ::Str...
         23205 ...file\src\Profile.jl:25; top-level scope
          23138 ...OVi\src\jacobian.jl:32; jacobian(::Function, ::Array{F...
           23044 ...Vi\src\jacobian.jl:32; jacobian(::Function, ::Array{...
            23044 ...Vi\src\jacobian.jl:36; jacobian(::Function, ::Array{...
             23008 ...i\src\jacobian.jl:212; chunk_mode_jacobian(::getfie...
              23008 ...r\Desktop\test.jl:276; (::getfield(Main, Symbol("#...
               23008 ...iler\typeinfer.jl:604; typeinf_ext(::Core.MethodIn...
                23007 ...ler\typeinfer.jl:567; typeinf_ext(::Core.MethodI...
                 22714 ...ler\typeinfer.jl:35; typeinf(::Core.Compiler.In...
                  22714 ...ler\optimize.jl:162; optimize(::Core.Compiler....
                   22463 ...ssair\driver.jl:120; run_passes(::Core.CodeIn...
                    21635 ...sair\domtree.jl:86; construct_domtree(::Core...
                     1798 .\array.jl:731; getindex
                     3708 .\bitset.jl:300; in
                      3286 .\bitset.jl:67; _bits_getindex
                       1364 .\int.jl:53; +
                       1922 .\int.jl:52; -
                      273  .\bitset.jl:68; _bits_getindex
                    548   ...sair\domtree.jl:87; construct_domtree(::Core...
                     523 .\array.jl:707; iterate

Looks like domtree.

Also go to n = 10^7 (that's still only 80MB, no big deal on modern systems) to capture the whole trace.

Anything but the default segfaults on Windows with the standard binary. That's probably issue worthy.

@timholy
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timholy commented Aug 25, 2018

Yes indeed.

Anything but the default segfaults on Windows with the standard binary. That's probably issue worthy.

Whoa! Definitely, thanks in advance for reporting that. I don't have easy access to a Windows machine so am not the right one to fix it (@vtjnash?), but I would be surprised if this is more than a couple-liner to fix.

@ChrisRackauckas ChrisRackauckas mentioned this issue Aug 25, 2018
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I haven't done a report since I'm not sure of an MWE. Any simple example doesn't seem to do it. But any time I've reported compiler issues that needed profiles, if I change n it segfaults even when it should be fairly easy to fit into memory. 🤷‍♂️

Closing this as a duplicate of #25927

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@ViralBShah @dlfivefifty @timholy @ChrisRackauckas @tknopp @jrevels