Average Error: 13.8 → 12.8
Time: 29.3s
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]{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{0.2844967359999999723108032867457950487733}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{2}} + \frac{1.453152027000000012790792425221297889948}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{4}}, 1\right) - \mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{5}} + \frac{0.2548295919999999936678136691625695675611}{\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)}, \frac{1.421413741000000063863240029604639858007}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3}}\right)} \cdot \sqrt[3]{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{0.2844967359999999723108032867457950487733}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{2}} + \frac{1.453152027000000012790792425221297889948}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{4}}, 1\right) - \mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{5}} + \frac{0.2548295919999999936678136691625695675611}{\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)}, \frac{1.421413741000000063863240029604639858007}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3}}\right)}\right) \cdot \left(\sqrt[3]{\sqrt{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{0.2844967359999999723108032867457950487733}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{2}} + \frac{1.453152027000000012790792425221297889948}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{4}}, 1\right)} + \sqrt{e^{-{\left(\left|x\right|\right)}^{2}} \cdot \left(\frac{1.421413741000000063863240029604639858007}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3}} + \left(\frac{0.2548295919999999936678136691625695675611}{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)} + \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{5}}\right)\right)}} \cdot \sqrt[3]{\sqrt{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{0.2844967359999999723108032867457950487733}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{2}} + \frac{1.453152027000000012790792425221297889948}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{4}}, 1\right)} - \sqrt{e^{-{\left(\left|x\right|\right)}^{2}} \cdot \left(\frac{1.421413741000000063863240029604639858007}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3}} + \left(\frac{0.2548295919999999936678136691625695675611}{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)} + \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{5}}\right)\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]{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{0.2844967359999999723108032867457950487733}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{2}} + \frac{1.453152027000000012790792425221297889948}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{4}}, 1\right) - \mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{5}} + \frac{0.2548295919999999936678136691625695675611}{\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)}, \frac{1.421413741000000063863240029604639858007}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3}}\right)} \cdot \sqrt[3]{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{0.2844967359999999723108032867457950487733}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{2}} + \frac{1.453152027000000012790792425221297889948}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{4}}, 1\right) - \mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{5}} + \frac{0.2548295919999999936678136691625695675611}{\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)}, \frac{1.421413741000000063863240029604639858007}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3}}\right)}\right) \cdot \left(\sqrt[3]{\sqrt{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{0.2844967359999999723108032867457950487733}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{2}} + \frac{1.453152027000000012790792425221297889948}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{4}}, 1\right)} + \sqrt{e^{-{\left(\left|x\right|\right)}^{2}} \cdot \left(\frac{1.421413741000000063863240029604639858007}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3}} + \left(\frac{0.2548295919999999936678136691625695675611}{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)} + \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{5}}\right)\right)}} \cdot \sqrt[3]{\sqrt{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{0.2844967359999999723108032867457950487733}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{2}} + \frac{1.453152027000000012790792425221297889948}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{4}}, 1\right)} - \sqrt{e^{-{\left(\left|x\right|\right)}^{2}} \cdot \left(\frac{1.421413741000000063863240029604639858007}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3}} + \left(\frac{0.2548295919999999936678136691625695675611}{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)} + \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{5}}\right)\right)}}\right)
double f(double x) {
        double r131803 = 1.0;
        double r131804 = 0.3275911;
        double r131805 = x;
        double r131806 = fabs(r131805);
        double r131807 = r131804 * r131806;
        double r131808 = r131803 + r131807;
        double r131809 = r131803 / r131808;
        double r131810 = 0.254829592;
        double r131811 = -0.284496736;
        double r131812 = 1.421413741;
        double r131813 = -1.453152027;
        double r131814 = 1.061405429;
        double r131815 = r131809 * r131814;
        double r131816 = r131813 + r131815;
        double r131817 = r131809 * r131816;
        double r131818 = r131812 + r131817;
        double r131819 = r131809 * r131818;
        double r131820 = r131811 + r131819;
        double r131821 = r131809 * r131820;
        double r131822 = r131810 + r131821;
        double r131823 = r131809 * r131822;
        double r131824 = r131806 * r131806;
        double r131825 = -r131824;
        double r131826 = exp(r131825);
        double r131827 = r131823 * r131826;
        double r131828 = r131803 - r131827;
        return r131828;
}
↓
double f(double x) {
        double r131829 = x;
        double r131830 = fabs(r131829);
        double r131831 = 2.0;
        double r131832 = pow(r131830, r131831);
        double r131833 = -r131832;
        double r131834 = exp(r131833);
        double r131835 = 0.284496736;
        double r131836 = 0.3275911;
        double r131837 = 1.0;
        double r131838 = fma(r131830, r131836, r131837);
        double r131839 = pow(r131838, r131831);
        double r131840 = r131835 / r131839;
        double r131841 = 1.453152027;
        double r131842 = 4.0;
        double r131843 = pow(r131838, r131842);
        double r131844 = r131841 / r131843;
        double r131845 = r131840 + r131844;
        double r131846 = fma(r131834, r131845, r131837);
        double r131847 = 1.061405429;
        double r131848 = 5.0;
        double r131849 = pow(r131838, r131848);
        double r131850 = r131847 / r131849;
        double r131851 = 0.254829592;
        double r131852 = fma(r131836, r131830, r131837);
        double r131853 = r131851 / r131852;
        double r131854 = r131850 + r131853;
        double r131855 = 1.421413741;
        double r131856 = exp(r131832);
        double r131857 = 3.0;
        double r131858 = pow(r131838, r131857);
        double r131859 = r131856 * r131858;
        double r131860 = r131855 / r131859;
        double r131861 = fma(r131834, r131854, r131860);
        double r131862 = r131846 - r131861;
        double r131863 = cbrt(r131862);
        double r131864 = r131863 * r131863;
        double r131865 = sqrt(r131846);
        double r131866 = r131855 / r131858;
        double r131867 = r131851 / r131838;
        double r131868 = r131867 + r131850;
        double r131869 = r131866 + r131868;
        double r131870 = r131834 * r131869;
        double r131871 = sqrt(r131870);
        double r131872 = r131865 + r131871;
        double r131873 = cbrt(r131872);
        double r131874 = r131865 - r131871;
        double r131875 = cbrt(r131874);
        double r131876 = r131873 * r131875;
        double r131877 = r131864 * r131876;
        return r131877;
}

Error

Bits error versus x

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. Simplified13.8

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

  3. Taylor expanded around 0 13.8

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

  4. Simplified13.8

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

  6. Applied add-cube-cbrt13.8

    \[\leadsto \color{blue}{\left(\sqrt[3]{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{0.2844967359999999723108032867457950487733}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{2}} + \frac{1.453152027000000012790792425221297889948}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{4}}, 1\right) - \mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{5}} + \frac{0.2548295919999999936678136691625695675611}{\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)}, \frac{1.421413741000000063863240029604639858007}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3}}\right)} \cdot \sqrt[3]{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{0.2844967359999999723108032867457950487733}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{2}} + \frac{1.453152027000000012790792425221297889948}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{4}}, 1\right) - \mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{5}} + \frac{0.2548295919999999936678136691625695675611}{\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)}, \frac{1.421413741000000063863240029604639858007}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3}}\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{0.2844967359999999723108032867457950487733}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{2}} + \frac{1.453152027000000012790792425221297889948}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{4}}, 1\right) - \mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{5}} + \frac{0.2548295919999999936678136691625695675611}{\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)}, \frac{1.421413741000000063863240029604639858007}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3}}\right)}}\]
  7. Using strategy rm

  8. Applied add-sqr-sqrt13.8

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

  9. Applied add-sqr-sqrt14.2

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

  10. Applied difference-of-squares12.8

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

  11. Applied cbrt-prod12.8

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

  12. Simplified12.8

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

  13. Simplified12.8

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

  14. Final simplification12.8

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

Reproduce

herbie shell --seed 2019303 +o rules:numerics
(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)))))))