Average Error: 13.8 → 10.5
Time: 1.5m
Precision: 64
\[1 - \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
↓
\[\left(\sqrt[3]{\left(\sqrt{1 + \left(\frac{5125037576950889}{18014398509481984} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{2}} + \frac{6544414927309881}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{4}}\right)} + \sqrt{\frac{4780145094533421}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{5}} + \left(\frac{6401478394306903}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{3}} + \frac{2295300911148351}{9007199254740992} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1}\right)}\right) \cdot \frac{{\left(\sqrt{1 + \left(\frac{5125037576950889}{18014398509481984} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{2}} + \frac{6544414927309881}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{4}}\right)}\right)}^{3} - {\left(\sqrt{\frac{4780145094533421}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{5}} + \left(\frac{6401478394306903}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{3}} + \frac{2295300911148351}{9007199254740992} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1}\right)}\right)}^{3}}{\left(\left(1 + \left(\frac{5125037576950889}{18014398509481984} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{2}} + \frac{6544414927309881}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{4}}\right)\right) + \left(\frac{4780145094533421}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{5}} + \left(\frac{6401478394306903}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{3}} + \frac{2295300911148351}{9007199254740992} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1}\right)\right)\right) + \sqrt{1 + \left(\frac{5125037576950889}{18014398509481984} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{2}} + \frac{6544414927309881}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{4}}\right)} \cdot \sqrt{\frac{4780145094533421}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{5}} + \left(\frac{6401478394306903}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{3}} + \frac{2295300911148351}{9007199254740992} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1}\right)}}} \cdot \sqrt[3]{\left(1 + \left(\frac{5125037576950889}{18014398509481984} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{2}} + \frac{6544414927309881}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{4}}\right)\right) - \left(\frac{4780145094533421}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{5}} + \left(\frac{6401478394306903}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{3}} + \frac{2295300911148351}{9007199254740992} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1}\right)\right)}\right) \cdot \sqrt[3]{\left(1 + \left(\frac{5125037576950889}{18014398509481984} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{2}} + \frac{6544414927309881}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{4}}\right)\right) - \left(\frac{4780145094533421}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{5}} + \left(\frac{6401478394306903}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{3}} + \frac{2295300911148351}{9007199254740992} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1}\right)\right)}\]
1 - \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}
↓
\left(\sqrt[3]{\left(\sqrt{1 + \left(\frac{5125037576950889}{18014398509481984} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{2}} + \frac{6544414927309881}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{4}}\right)} + \sqrt{\frac{4780145094533421}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{5}} + \left(\frac{6401478394306903}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{3}} + \frac{2295300911148351}{9007199254740992} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1}\right)}\right) \cdot \frac{{\left(\sqrt{1 + \left(\frac{5125037576950889}{18014398509481984} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{2}} + \frac{6544414927309881}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{4}}\right)}\right)}^{3} - {\left(\sqrt{\frac{4780145094533421}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{5}} + \left(\frac{6401478394306903}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{3}} + \frac{2295300911148351}{9007199254740992} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1}\right)}\right)}^{3}}{\left(\left(1 + \left(\frac{5125037576950889}{18014398509481984} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{2}} + \frac{6544414927309881}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{4}}\right)\right) + \left(\frac{4780145094533421}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{5}} + \left(\frac{6401478394306903}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{3}} + \frac{2295300911148351}{9007199254740992} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1}\right)\right)\right) + \sqrt{1 + \left(\frac{5125037576950889}{18014398509481984} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{2}} + \frac{6544414927309881}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{4}}\right)} \cdot \sqrt{\frac{4780145094533421}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{5}} + \left(\frac{6401478394306903}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{3}} + \frac{2295300911148351}{9007199254740992} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1}\right)}}} \cdot \sqrt[3]{\left(1 + \left(\frac{5125037576950889}{18014398509481984} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{2}} + \frac{6544414927309881}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{4}}\right)\right) - \left(\frac{4780145094533421}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{5}} + \left(\frac{6401478394306903}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{3}} + \frac{2295300911148351}{9007199254740992} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1}\right)\right)}\right) \cdot \sqrt[3]{\left(1 + \left(\frac{5125037576950889}{18014398509481984} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{2}} + \frac{6544414927309881}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{4}}\right)\right) - \left(\frac{4780145094533421}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{5}} + \left(\frac{6401478394306903}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{3}} + \frac{2295300911148351}{9007199254740992} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1}\right)\right)}
double f(double x) {
        double r219989 = 1.0;
        double r219990 = 0.3275911;
        double r219991 = x;
        double r219992 = fabs(r219991);
        double r219993 = r219990 * r219992;
        double r219994 = r219989 + r219993;
        double r219995 = r219989 / r219994;
        double r219996 = 0.254829592;
        double r219997 = -0.284496736;
        double r219998 = 1.421413741;
        double r219999 = -1.453152027;
        double r220000 = 1.061405429;
        double r220001 = r219995 * r220000;
        double r220002 = r219999 + r220001;
        double r220003 = r219995 * r220002;
        double r220004 = r219998 + r220003;
        double r220005 = r219995 * r220004;
        double r220006 = r219997 + r220005;
        double r220007 = r219995 * r220006;
        double r220008 = r219996 + r220007;
        double r220009 = r219995 * r220008;
        double r220010 = r219992 * r219992;
        double r220011 = -r220010;
        double r220012 = exp(r220011);
        double r220013 = r220009 * r220012;
        double r220014 = r219989 - r220013;
        return r220014;
}
↓
double f(double x) {
        double r220015 = 1.0;
        double r220016 = 5125037576950889.0;
        double r220017 = 18014398509481984.0;
        double r220018 = r220016 / r220017;
        double r220019 = x;
        double r220020 = fabs(r220019);
        double r220021 = 2.0;
        double r220022 = pow(r220020, r220021);
        double r220023 = -r220022;
        double r220024 = exp(r220023);
        double r220025 = 1475339155889891.0;
        double r220026 = 4503599627370496.0;
        double r220027 = r220025 / r220026;
        double r220028 = r220027 * r220020;
        double r220029 = r220028 + r220015;
        double r220030 = pow(r220029, r220021);
        double r220031 = r220024 / r220030;
        double r220032 = r220018 * r220031;
        double r220033 = 6544414927309881.0;
        double r220034 = r220033 / r220026;
        double r220035 = 4.0;
        double r220036 = pow(r220029, r220035);
        double r220037 = r220024 / r220036;
        double r220038 = r220034 * r220037;
        double r220039 = r220032 + r220038;
        double r220040 = r220015 + r220039;
        double r220041 = sqrt(r220040);
        double r220042 = 4780145094533421.0;
        double r220043 = r220042 / r220026;
        double r220044 = 5.0;
        double r220045 = pow(r220029, r220044);
        double r220046 = r220024 / r220045;
        double r220047 = r220043 * r220046;
        double r220048 = 6401478394306903.0;
        double r220049 = r220048 / r220026;
        double r220050 = 3.0;
        double r220051 = pow(r220029, r220050);
        double r220052 = r220024 / r220051;
        double r220053 = r220049 * r220052;
        double r220054 = 2295300911148351.0;
        double r220055 = 9007199254740992.0;
        double r220056 = r220054 / r220055;
        double r220057 = r220024 / r220029;
        double r220058 = r220056 * r220057;
        double r220059 = r220053 + r220058;
        double r220060 = r220047 + r220059;
        double r220061 = sqrt(r220060);
        double r220062 = r220041 + r220061;
        double r220063 = pow(r220041, r220050);
        double r220064 = pow(r220061, r220050);
        double r220065 = r220063 - r220064;
        double r220066 = r220040 + r220060;
        double r220067 = r220041 * r220061;
        double r220068 = r220066 + r220067;
        double r220069 = r220065 / r220068;
        double r220070 = r220062 * r220069;
        double r220071 = cbrt(r220070);
        double r220072 = r220040 - r220060;
        double r220073 = cbrt(r220072);
        double r220074 = r220071 * r220073;
        double r220075 = r220074 * r220073;
        return r220075;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 13.8

    \[1 - \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]

  2. Taylor expanded around 0 13.8

    \[\leadsto \color{blue}{\left(1 + \left(0.2844967359999999723108032867457950487733 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{2}} + 1.453152027000000012790792425221297889948 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{4}}\right)\right) - \left(1.061405428999999900341322245367337018251 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{5}} + \left(1.421413741000000063863240029604639858007 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{3}} + 0.2548295919999999936678136691625695675611 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right)\right)}\]

  3. Simplified13.8

    \[\leadsto \color{blue}{\left(1 + \left(\frac{5125037576950889}{18014398509481984} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{2}} + \frac{6544414927309881}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{4}}\right)\right) - \left(\frac{4780145094533421}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{5}} + \left(\frac{6401478394306903}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{3}} + \frac{2295300911148351}{9007199254740992} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1}\right)\right)}\]
  4. Using strategy rm

  5. Applied add-cube-cbrt13.8

    \[\leadsto \color{blue}{\left(\sqrt[3]{\left(1 + \left(\frac{5125037576950889}{18014398509481984} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{2}} + \frac{6544414927309881}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{4}}\right)\right) - \left(\frac{4780145094533421}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{5}} + \left(\frac{6401478394306903}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{3}} + \frac{2295300911148351}{9007199254740992} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1}\right)\right)} \cdot \sqrt[3]{\left(1 + \left(\frac{5125037576950889}{18014398509481984} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{2}} + \frac{6544414927309881}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{4}}\right)\right) - \left(\frac{4780145094533421}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{5}} + \left(\frac{6401478394306903}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{3}} + \frac{2295300911148351}{9007199254740992} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1}\right)\right)}\right) \cdot \sqrt[3]{\left(1 + \left(\frac{5125037576950889}{18014398509481984} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{2}} + \frac{6544414927309881}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{4}}\right)\right) - \left(\frac{4780145094533421}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{5}} + \left(\frac{6401478394306903}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{3}} + \frac{2295300911148351}{9007199254740992} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1}\right)\right)}}\]
  6. Using strategy rm

  7. Applied add-sqr-sqrt13.8

    \[\leadsto \left(\sqrt[3]{\left(1 + \left(\frac{5125037576950889}{18014398509481984} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{2}} + \frac{6544414927309881}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{4}}\right)\right) - \color{blue}{\sqrt{\frac{4780145094533421}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{5}} + \left(\frac{6401478394306903}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{3}} + \frac{2295300911148351}{9007199254740992} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1}\right)} \cdot \sqrt{\frac{4780145094533421}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{5}} + \left(\frac{6401478394306903}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{3}} + \frac{2295300911148351}{9007199254740992} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1}\right)}}} \cdot \sqrt[3]{\left(1 + \left(\frac{5125037576950889}{18014398509481984} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{2}} + \frac{6544414927309881}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{4}}\right)\right) - \left(\frac{4780145094533421}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{5}} + \left(\frac{6401478394306903}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{3}} + \frac{2295300911148351}{9007199254740992} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1}\right)\right)}\right) \cdot \sqrt[3]{\left(1 + \left(\frac{5125037576950889}{18014398509481984} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{2}} + \frac{6544414927309881}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{4}}\right)\right) - \left(\frac{4780145094533421}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{5}} + \left(\frac{6401478394306903}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{3}} + \frac{2295300911148351}{9007199254740992} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1}\right)\right)}\]

  8. Applied add-sqr-sqrt14.2

    \[\leadsto \left(\sqrt[3]{\color{blue}{\sqrt{1 + \left(\frac{5125037576950889}{18014398509481984} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{2}} + \frac{6544414927309881}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{4}}\right)} \cdot \sqrt{1 + \left(\frac{5125037576950889}{18014398509481984} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{2}} + \frac{6544414927309881}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{4}}\right)}} - \sqrt{\frac{4780145094533421}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{5}} + \left(\frac{6401478394306903}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{3}} + \frac{2295300911148351}{9007199254740992} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1}\right)} \cdot \sqrt{\frac{4780145094533421}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{5}} + \left(\frac{6401478394306903}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{3}} + \frac{2295300911148351}{9007199254740992} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1}\right)}} \cdot \sqrt[3]{\left(1 + \left(\frac{5125037576950889}{18014398509481984} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{2}} + \frac{6544414927309881}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{4}}\right)\right) - \left(\frac{4780145094533421}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{5}} + \left(\frac{6401478394306903}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{3}} + \frac{2295300911148351}{9007199254740992} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1}\right)\right)}\right) \cdot \sqrt[3]{\left(1 + \left(\frac{5125037576950889}{18014398509481984} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{2}} + \frac{6544414927309881}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{4}}\right)\right) - \left(\frac{4780145094533421}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{5}} + \left(\frac{6401478394306903}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{3}} + \frac{2295300911148351}{9007199254740992} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1}\right)\right)}\]

  9. Applied difference-of-squares12.8

    \[\leadsto \left(\sqrt[3]{\color{blue}{\left(\sqrt{1 + \left(\frac{5125037576950889}{18014398509481984} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{2}} + \frac{6544414927309881}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{4}}\right)} + \sqrt{\frac{4780145094533421}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{5}} + \left(\frac{6401478394306903}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{3}} + \frac{2295300911148351}{9007199254740992} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1}\right)}\right) \cdot \left(\sqrt{1 + \left(\frac{5125037576950889}{18014398509481984} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{2}} + \frac{6544414927309881}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{4}}\right)} - \sqrt{\frac{4780145094533421}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{5}} + \left(\frac{6401478394306903}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{3}} + \frac{2295300911148351}{9007199254740992} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1}\right)}\right)}} \cdot \sqrt[3]{\left(1 + \left(\frac{5125037576950889}{18014398509481984} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{2}} + \frac{6544414927309881}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{4}}\right)\right) - \left(\frac{4780145094533421}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{5}} + \left(\frac{6401478394306903}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{3}} + \frac{2295300911148351}{9007199254740992} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1}\right)\right)}\right) \cdot \sqrt[3]{\left(1 + \left(\frac{5125037576950889}{18014398509481984} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{2}} + \frac{6544414927309881}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{4}}\right)\right) - \left(\frac{4780145094533421}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{5}} + \left(\frac{6401478394306903}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{3}} + \frac{2295300911148351}{9007199254740992} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1}\right)\right)}\]
  10. Using strategy rm

  11. Applied flip3--10.5

    \[\leadsto \left(\sqrt[3]{\left(\sqrt{1 + \left(\frac{5125037576950889}{18014398509481984} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{2}} + \frac{6544414927309881}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{4}}\right)} + \sqrt{\frac{4780145094533421}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{5}} + \left(\frac{6401478394306903}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{3}} + \frac{2295300911148351}{9007199254740992} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1}\right)}\right) \cdot \color{blue}{\frac{{\left(\sqrt{1 + \left(\frac{5125037576950889}{18014398509481984} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{2}} + \frac{6544414927309881}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{4}}\right)}\right)}^{3} - {\left(\sqrt{\frac{4780145094533421}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{5}} + \left(\frac{6401478394306903}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{3}} + \frac{2295300911148351}{9007199254740992} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1}\right)}\right)}^{3}}{\sqrt{1 + \left(\frac{5125037576950889}{18014398509481984} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{2}} + \frac{6544414927309881}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{4}}\right)} \cdot \sqrt{1 + \left(\frac{5125037576950889}{18014398509481984} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{2}} + \frac{6544414927309881}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{4}}\right)} + \left(\sqrt{\frac{4780145094533421}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{5}} + \left(\frac{6401478394306903}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{3}} + \frac{2295300911148351}{9007199254740992} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1}\right)} \cdot \sqrt{\frac{4780145094533421}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{5}} + \left(\frac{6401478394306903}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{3}} + \frac{2295300911148351}{9007199254740992} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1}\right)} + \sqrt{1 + \left(\frac{5125037576950889}{18014398509481984} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{2}} + \frac{6544414927309881}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{4}}\right)} \cdot \sqrt{\frac{4780145094533421}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{5}} + \left(\frac{6401478394306903}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{3}} + \frac{2295300911148351}{9007199254740992} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1}\right)}\right)}}} \cdot \sqrt[3]{\left(1 + \left(\frac{5125037576950889}{18014398509481984} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{2}} + \frac{6544414927309881}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{4}}\right)\right) - \left(\frac{4780145094533421}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{5}} + \left(\frac{6401478394306903}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{3}} + \frac{2295300911148351}{9007199254740992} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1}\right)\right)}\right) \cdot \sqrt[3]{\left(1 + \left(\frac{5125037576950889}{18014398509481984} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{2}} + \frac{6544414927309881}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{4}}\right)\right) - \left(\frac{4780145094533421}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{5}} + \left(\frac{6401478394306903}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{3}} + \frac{2295300911148351}{9007199254740992} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1}\right)\right)}\]

  12. Simplified10.5

    \[\leadsto \left(\sqrt[3]{\left(\sqrt{1 + \left(\frac{5125037576950889}{18014398509481984} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{2}} + \frac{6544414927309881}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{4}}\right)} + \sqrt{\frac{4780145094533421}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{5}} + \left(\frac{6401478394306903}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{3}} + \frac{2295300911148351}{9007199254740992} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1}\right)}\right) \cdot \frac{{\left(\sqrt{1 + \left(\frac{5125037576950889}{18014398509481984} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{2}} + \frac{6544414927309881}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{4}}\right)}\right)}^{3} - {\left(\sqrt{\frac{4780145094533421}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{5}} + \left(\frac{6401478394306903}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{3}} + \frac{2295300911148351}{9007199254740992} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1}\right)}\right)}^{3}}{\color{blue}{\left(\left(1 + \left(\frac{5125037576950889}{18014398509481984} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{2}} + \frac{6544414927309881}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{4}}\right)\right) + \left(\frac{4780145094533421}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{5}} + \left(\frac{6401478394306903}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{3}} + \frac{2295300911148351}{9007199254740992} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1}\right)\right)\right) + \sqrt{1 + \left(\frac{5125037576950889}{18014398509481984} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{2}} + \frac{6544414927309881}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{4}}\right)} \cdot \sqrt{\frac{4780145094533421}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{5}} + \left(\frac{6401478394306903}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{3}} + \frac{2295300911148351}{9007199254740992} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1}\right)}}}} \cdot \sqrt[3]{\left(1 + \left(\frac{5125037576950889}{18014398509481984} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{2}} + \frac{6544414927309881}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{4}}\right)\right) - \left(\frac{4780145094533421}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{5}} + \left(\frac{6401478394306903}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{3}} + \frac{2295300911148351}{9007199254740992} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1}\right)\right)}\right) \cdot \sqrt[3]{\left(1 + \left(\frac{5125037576950889}{18014398509481984} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{2}} + \frac{6544414927309881}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{4}}\right)\right) - \left(\frac{4780145094533421}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{5}} + \left(\frac{6401478394306903}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{3}} + \frac{2295300911148351}{9007199254740992} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1}\right)\right)}\]

  13. Final simplification10.5

    \[\leadsto \left(\sqrt[3]{\left(\sqrt{1 + \left(\frac{5125037576950889}{18014398509481984} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{2}} + \frac{6544414927309881}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{4}}\right)} + \sqrt{\frac{4780145094533421}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{5}} + \left(\frac{6401478394306903}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{3}} + \frac{2295300911148351}{9007199254740992} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1}\right)}\right) \cdot \frac{{\left(\sqrt{1 + \left(\frac{5125037576950889}{18014398509481984} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{2}} + \frac{6544414927309881}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{4}}\right)}\right)}^{3} - {\left(\sqrt{\frac{4780145094533421}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{5}} + \left(\frac{6401478394306903}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{3}} + \frac{2295300911148351}{9007199254740992} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1}\right)}\right)}^{3}}{\left(\left(1 + \left(\frac{5125037576950889}{18014398509481984} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{2}} + \frac{6544414927309881}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{4}}\right)\right) + \left(\frac{4780145094533421}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{5}} + \left(\frac{6401478394306903}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{3}} + \frac{2295300911148351}{9007199254740992} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1}\right)\right)\right) + \sqrt{1 + \left(\frac{5125037576950889}{18014398509481984} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{2}} + \frac{6544414927309881}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{4}}\right)} \cdot \sqrt{\frac{4780145094533421}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{5}} + \left(\frac{6401478394306903}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{3}} + \frac{2295300911148351}{9007199254740992} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1}\right)}}} \cdot \sqrt[3]{\left(1 + \left(\frac{5125037576950889}{18014398509481984} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{2}} + \frac{6544414927309881}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{4}}\right)\right) - \left(\frac{4780145094533421}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{5}} + \left(\frac{6401478394306903}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{3}} + \frac{2295300911148351}{9007199254740992} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1}\right)\right)}\right) \cdot \sqrt[3]{\left(1 + \left(\frac{5125037576950889}{18014398509481984} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{2}} + \frac{6544414927309881}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{4}}\right)\right) - \left(\frac{4780145094533421}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{5}} + \left(\frac{6401478394306903}{4503599627370496} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1\right)}^{3}} + \frac{2295300911148351}{9007199254740992} \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{\frac{1475339155889891}{4503599627370496} \cdot \left|x\right| + 1}\right)\right)}\]

Reproduce

herbie shell --seed 2019303 
(FPCore (x)
  :name "Jmat.Real.erf"
  :precision binary64
  (- 1 (* (* (/ 1 (+ 1 (* 0.32759110000000002 (fabs x)))) (+ 0.25482959199999999 (* (/ 1 (+ 1 (* 0.32759110000000002 (fabs x)))) (+ -0.284496735999999972 (* (/ 1 (+ 1 (* 0.32759110000000002 (fabs x)))) (+ 1.42141374100000006 (* (/ 1 (+ 1 (* 0.32759110000000002 (fabs x)))) (+ -1.45315202700000001 (* (/ 1 (+ 1 (* 0.32759110000000002 (fabs x)))) 1.0614054289999999))))))))) (exp (- (* (fabs x) (fabs x)))))))