Average Error: 13.7 → 1.9
Time: 9.8s
Precision: 64
\[1 - \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
↓
\[\sqrt{e^{\log \left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}, \mathsf{fma}\left(\sqrt[3]{{\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)}\right)}^{3}}, 1.061405428999999900341322245367337018251, -1.453152027000000012790792425221297889948\right), 1.421413741000000063863240029604639858007\right), -0.2844967359999999723108032867457950487733\right), 0.2548295919999999936678136691625695675611\right)}{e^{\left|x\right| \cdot \left|x\right|}}, \frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)}, 1\right)\right)}} \cdot \sqrt{\left(\left(\mathsf{fma}\left(0.2844967359999999723108032867457950487733, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.421413741000000063863240029604639858007}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}\right) - \mathsf{fma}\left(\frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{5}}, 1.061405428999999900341322245367337018251, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)} \cdot 0.2548295919999999936678136691625695675611\right)\right) + \frac{\frac{1.453152027000000012790792425221297889948}{{\left(\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)\right)}^{4}}}{e^{{\left(\left|x\right|\right)}^{2}}}}\]
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{e^{\log \left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}, \mathsf{fma}\left(\sqrt[3]{{\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)}\right)}^{3}}, 1.061405428999999900341322245367337018251, -1.453152027000000012790792425221297889948\right), 1.421413741000000063863240029604639858007\right), -0.2844967359999999723108032867457950487733\right), 0.2548295919999999936678136691625695675611\right)}{e^{\left|x\right| \cdot \left|x\right|}}, \frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)}, 1\right)\right)}} \cdot \sqrt{\left(\left(\mathsf{fma}\left(0.2844967359999999723108032867457950487733, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.421413741000000063863240029604639858007}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}\right) - \mathsf{fma}\left(\frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{5}}, 1.061405428999999900341322245367337018251, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)} \cdot 0.2548295919999999936678136691625695675611\right)\right) + \frac{\frac{1.453152027000000012790792425221297889948}{{\left(\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)\right)}^{4}}}{e^{{\left(\left|x\right|\right)}^{2}}}}
double f(double x) {
        double r201955 = 1.0;
        double r201956 = 0.3275911;
        double r201957 = x;
        double r201958 = fabs(r201957);
        double r201959 = r201956 * r201958;
        double r201960 = r201955 + r201959;
        double r201961 = r201955 / r201960;
        double r201962 = 0.254829592;
        double r201963 = -0.284496736;
        double r201964 = 1.421413741;
        double r201965 = -1.453152027;
        double r201966 = 1.061405429;
        double r201967 = r201961 * r201966;
        double r201968 = r201965 + r201967;
        double r201969 = r201961 * r201968;
        double r201970 = r201964 + r201969;
        double r201971 = r201961 * r201970;
        double r201972 = r201963 + r201971;
        double r201973 = r201961 * r201972;
        double r201974 = r201962 + r201973;
        double r201975 = r201961 * r201974;
        double r201976 = r201958 * r201958;
        double r201977 = -r201976;
        double r201978 = exp(r201977);
        double r201979 = r201975 * r201978;
        double r201980 = r201955 - r201979;
        return r201980;
}
↓
double f(double x) {
        double r201981 = 1.0;
        double r201982 = 0.3275911;
        double r201983 = x;
        double r201984 = fabs(r201983);
        double r201985 = r201982 * r201984;
        double r201986 = r201981 + r201985;
        double r201987 = r201981 / r201986;
        double r201988 = fma(r201984, r201982, r201981);
        double r201989 = r201981 / r201988;
        double r201990 = 3.0;
        double r201991 = pow(r201989, r201990);
        double r201992 = cbrt(r201991);
        double r201993 = 1.061405429;
        double r201994 = -1.453152027;
        double r201995 = fma(r201992, r201993, r201994);
        double r201996 = 1.421413741;
        double r201997 = fma(r201987, r201995, r201996);
        double r201998 = -0.284496736;
        double r201999 = fma(r201987, r201997, r201998);
        double r202000 = 0.254829592;
        double r202001 = fma(r201987, r201999, r202000);
        double r202002 = r201984 * r201984;
        double r202003 = exp(r202002);
        double r202004 = r202001 / r202003;
        double r202005 = -r201981;
        double r202006 = r202005 / r201988;
        double r202007 = fma(r202004, r202006, r201981);
        double r202008 = log(r202007);
        double r202009 = exp(r202008);
        double r202010 = sqrt(r202009);
        double r202011 = 0.284496736;
        double r202012 = 1.0;
        double r202013 = 2.0;
        double r202014 = pow(r201984, r202013);
        double r202015 = exp(r202014);
        double r202016 = r201985 + r201981;
        double r202017 = pow(r202016, r202013);
        double r202018 = r202015 * r202017;
        double r202019 = r202012 / r202018;
        double r202020 = fma(r202011, r202019, r201981);
        double r202021 = pow(r201988, r201990);
        double r202022 = r201996 / r202021;
        double r202023 = r202012 / r202015;
        double r202024 = r202022 * r202023;
        double r202025 = r202020 - r202024;
        double r202026 = 5.0;
        double r202027 = pow(r202016, r202026);
        double r202028 = r202015 * r202027;
        double r202029 = r202012 / r202028;
        double r202030 = fma(r201982, r201984, r201981);
        double r202031 = r202023 / r202030;
        double r202032 = r202031 * r202000;
        double r202033 = fma(r202029, r201993, r202032);
        double r202034 = r202025 - r202033;
        double r202035 = 1.453152027;
        double r202036 = 4.0;
        double r202037 = pow(r202030, r202036);
        double r202038 = r202035 / r202037;
        double r202039 = r202038 / r202015;
        double r202040 = r202034 + r202039;
        double r202041 = sqrt(r202040);
        double r202042 = r202010 * r202041;
        return r202042;
}

Error

Bits error versus x

Derivation

  1. Initial program 13.7

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

  2. Simplified13.7

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

  4. Applied add-cbrt-cube13.7

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

  5. Applied add-cbrt-cube13.7

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

  6. Applied cbrt-undiv13.7

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

  7. Simplified13.7

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

  9. Applied add-sqr-sqrt13.7

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

  10. Taylor expanded around 0 2.2

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

  11. Simplified2.2

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

  13. Applied add-exp-log1.9

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

  14. Final simplification1.9

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

Reproduce

herbie shell --seed 2019353 +o rules:numerics
(FPCore (x)
  :name "Jmat.Real.erf"
  :precision binary64
  (- 1 (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x)))))))