Average Error: 13.9 → 2.3
Time: 14.2s
Precision: 64
\[1 - \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
↓
\[\sqrt{1 + \left(-e^{-{\left(\left|x\right|\right)}^{2}} \cdot \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\right) \cdot \left(\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 \cdot 1 - \left(0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right) \cdot \left(0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right)} \cdot \left(\left(1 - 0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right) \cdot 1.061405428999999900341322245367337018251\right)\right)\right)\right) + 0.2548295919999999936678136691625695675611\right)} \cdot \sqrt{1 - \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(\left(0.2548295919999999936678136691625695675611 + -0.2844967359999999723108032867457950487733 \cdot \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\right) + \left(\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 \cdot 1 - \left(0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right) \cdot \left(0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right)} \cdot \left(\left(1 - 0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right) \cdot 1.061405428999999900341322245367337018251\right)\right)\right)\right) \cdot \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\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|}
↓
\sqrt{1 + \left(-e^{-{\left(\left|x\right|\right)}^{2}} \cdot \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\right) \cdot \left(\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 \cdot 1 - \left(0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right) \cdot \left(0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right)} \cdot \left(\left(1 - 0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right) \cdot 1.061405428999999900341322245367337018251\right)\right)\right)\right) + 0.2548295919999999936678136691625695675611\right)} \cdot \sqrt{1 - \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(\left(0.2548295919999999936678136691625695675611 + -0.2844967359999999723108032867457950487733 \cdot \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\right) + \left(\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 \cdot 1 - \left(0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right) \cdot \left(0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right)} \cdot \left(\left(1 - 0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right) \cdot 1.061405428999999900341322245367337018251\right)\right)\right)\right) \cdot \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}}
double f(double x) {
        double r237876 = 1.0;
        double r237877 = 0.3275911;
        double r237878 = x;
        double r237879 = fabs(r237878);
        double r237880 = r237877 * r237879;
        double r237881 = r237876 + r237880;
        double r237882 = r237876 / r237881;
        double r237883 = 0.254829592;
        double r237884 = -0.284496736;
        double r237885 = 1.421413741;
        double r237886 = -1.453152027;
        double r237887 = 1.061405429;
        double r237888 = r237882 * r237887;
        double r237889 = r237886 + r237888;
        double r237890 = r237882 * r237889;
        double r237891 = r237885 + r237890;
        double r237892 = r237882 * r237891;
        double r237893 = r237884 + r237892;
        double r237894 = r237882 * r237893;
        double r237895 = r237883 + r237894;
        double r237896 = r237882 * r237895;
        double r237897 = r237879 * r237879;
        double r237898 = -r237897;
        double r237899 = exp(r237898);
        double r237900 = r237896 * r237899;
        double r237901 = r237876 - r237900;
        return r237901;
}
↓
double f(double x) {
        double r237902 = 1.0;
        double r237903 = x;
        double r237904 = fabs(r237903);
        double r237905 = 2.0;
        double r237906 = pow(r237904, r237905);
        double r237907 = -r237906;
        double r237908 = exp(r237907);
        double r237909 = 0.3275911;
        double r237910 = r237909 * r237904;
        double r237911 = r237902 + r237910;
        double r237912 = r237902 / r237911;
        double r237913 = r237908 * r237912;
        double r237914 = -r237913;
        double r237915 = -0.284496736;
        double r237916 = 1.421413741;
        double r237917 = -1.453152027;
        double r237918 = r237902 * r237902;
        double r237919 = r237910 * r237910;
        double r237920 = r237918 - r237919;
        double r237921 = r237902 / r237920;
        double r237922 = r237902 - r237910;
        double r237923 = 1.061405429;
        double r237924 = r237922 * r237923;
        double r237925 = r237921 * r237924;
        double r237926 = r237917 + r237925;
        double r237927 = r237912 * r237926;
        double r237928 = r237916 + r237927;
        double r237929 = r237912 * r237928;
        double r237930 = r237915 + r237929;
        double r237931 = r237912 * r237930;
        double r237932 = 0.254829592;
        double r237933 = r237931 + r237932;
        double r237934 = r237914 * r237933;
        double r237935 = r237902 + r237934;
        double r237936 = sqrt(r237935);
        double r237937 = r237915 * r237912;
        double r237938 = r237932 + r237937;
        double r237939 = r237929 * r237912;
        double r237940 = r237938 + r237939;
        double r237941 = r237912 * r237940;
        double r237942 = r237904 * r237904;
        double r237943 = -r237942;
        double r237944 = exp(r237943);
        double r237945 = r237941 * r237944;
        double r237946 = r237902 - r237945;
        double r237947 = sqrt(r237946);
        double r237948 = r237936 * r237947;
        return r237948;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 13.9

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

  3. Applied flip-+13.9

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

  4. Applied associate-/r/13.9

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

  5. Applied associate-*l*13.9

    \[\leadsto 1 - \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \color{blue}{\frac{1}{1 \cdot 1 - \left(0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right) \cdot \left(0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right)} \cdot \left(\left(1 - 0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right) \cdot 1.061405428999999900341322245367337018251\right)}\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
  6. Using strategy rm

  7. Applied distribute-rgt-in13.9

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

  8. Applied associate-+r+13.9

    \[\leadsto 1 - \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \color{blue}{\left(\left(0.2548295919999999936678136691625695675611 + -0.2844967359999999723108032867457950487733 \cdot \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\right) + \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 \cdot 1 - \left(0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right) \cdot \left(0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right)} \cdot \left(\left(1 - 0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right) \cdot 1.061405428999999900341322245367337018251\right)\right)\right)\right) \cdot \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\right)}\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
  9. Using strategy rm

  10. Applied add-sqr-sqrt13.9

    \[\leadsto \color{blue}{\sqrt{1 - \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(\left(0.2548295919999999936678136691625695675611 + -0.2844967359999999723108032867457950487733 \cdot \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\right) + \left(\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 \cdot 1 - \left(0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right) \cdot \left(0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right)} \cdot \left(\left(1 - 0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right) \cdot 1.061405428999999900341322245367337018251\right)\right)\right)\right) \cdot \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}} \cdot \sqrt{1 - \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(\left(0.2548295919999999936678136691625695675611 + -0.2844967359999999723108032867457950487733 \cdot \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\right) + \left(\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 \cdot 1 - \left(0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right) \cdot \left(0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right)} \cdot \left(\left(1 - 0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right) \cdot 1.061405428999999900341322245367337018251\right)\right)\right)\right) \cdot \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}}}\]
  11. Using strategy rm

  12. Applied sub-neg13.9

    \[\leadsto \sqrt{\color{blue}{1 + \left(-\left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(\left(0.2548295919999999936678136691625695675611 + -0.2844967359999999723108032867457950487733 \cdot \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\right) + \left(\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 \cdot 1 - \left(0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right) \cdot \left(0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right)} \cdot \left(\left(1 - 0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right) \cdot 1.061405428999999900341322245367337018251\right)\right)\right)\right) \cdot \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}} \cdot \sqrt{1 - \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(\left(0.2548295919999999936678136691625695675611 + -0.2844967359999999723108032867457950487733 \cdot \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\right) + \left(\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 \cdot 1 - \left(0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right) \cdot \left(0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right)} \cdot \left(\left(1 - 0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right) \cdot 1.061405428999999900341322245367337018251\right)\right)\right)\right) \cdot \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}}\]

  13. Simplified2.3

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

  14. Final simplification2.3

    \[\leadsto \sqrt{1 + \left(-e^{-{\left(\left|x\right|\right)}^{2}} \cdot \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\right) \cdot \left(\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 \cdot 1 - \left(0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right) \cdot \left(0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right)} \cdot \left(\left(1 - 0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right) \cdot 1.061405428999999900341322245367337018251\right)\right)\right)\right) + 0.2548295919999999936678136691625695675611\right)} \cdot \sqrt{1 - \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(\left(0.2548295919999999936678136691625695675611 + -0.2844967359999999723108032867457950487733 \cdot \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\right) + \left(\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 \cdot 1 - \left(0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right) \cdot \left(0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right)} \cdot \left(\left(1 - 0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right) \cdot 1.061405428999999900341322245367337018251\right)\right)\right)\right) \cdot \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}}\]

Reproduce

herbie shell --seed 2019318 
(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)))))))