Jmat.Real.erf

Average Error: 14.0 → 13.3

Time: 28.3s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r130010 = 1.0;
        double r130011 = 0.3275911;
        double r130012 = x;
        double r130013 = fabs(r130012);
        double r130014 = r130011 * r130013;
        double r130015 = r130010 + r130014;
        double r130016 = r130010 / r130015;
        double r130017 = 0.254829592;
        double r130018 = -0.284496736;
        double r130019 = 1.421413741;
        double r130020 = -1.453152027;
        double r130021 = 1.061405429;
        double r130022 = r130016 * r130021;
        double r130023 = r130020 + r130022;
        double r130024 = r130016 * r130023;
        double r130025 = r130019 + r130024;
        double r130026 = r130016 * r130025;
        double r130027 = r130018 + r130026;
        double r130028 = r130016 * r130027;
        double r130029 = r130017 + r130028;
        double r130030 = r130016 * r130029;
        double r130031 = r130013 * r130013;
        double r130032 = -r130031;
        double r130033 = exp(r130032);
        double r130034 = r130030 * r130033;
        double r130035 = r130010 - r130034;
        return r130035;
}

↓

double f(double x) {
        double r130036 = 1.061405429;
        double r130037 = x;
        double r130038 = fabs(r130037);
        double r130039 = 0.3275911;
        double r130040 = 1.0;
        double r130041 = fma(r130038, r130039, r130040);
        double r130042 = 4.0;
        double r130043 = pow(r130041, r130042);
        double r130044 = r130036 / r130043;
        double r130045 = 1.421413741;
        double r130046 = 2.0;
        double r130047 = pow(r130041, r130046);
        double r130048 = r130045 / r130047;
        double r130049 = 0.254829592;
        double r130050 = r130048 + r130049;
        double r130051 = 1.453152027;
        double r130052 = 3.0;
        double r130053 = pow(r130041, r130052);
        double r130054 = r130051 / r130053;
        double r130055 = r130050 - r130054;
        double r130056 = 0.284496736;
        double r130057 = fma(r130039, r130038, r130040);
        double r130058 = r130056 / r130057;
        double r130059 = r130055 - r130058;
        double r130060 = r130044 + r130059;
        double r130061 = pow(r130038, r130046);
        double r130062 = exp(r130061);
        double r130063 = r130060 / r130062;
        double r130064 = -r130063;
        double r130065 = r130040 / r130041;
        double r130066 = fma(r130064, r130065, r130040);
        double r130067 = cbrt(r130066);
        double r130068 = r130067 * r130067;
        double r130069 = cbrt(r130050);
        double r130070 = r130069 * r130069;
        double r130071 = sqrt(r130051);
        double r130072 = sqrt(r130053);
        double r130073 = r130071 / r130072;
        double r130074 = r130073 * r130073;
        double r130075 = -r130074;
        double r130076 = fma(r130070, r130069, r130075);
        double r130077 = -r130073;
        double r130078 = r130077 + r130073;
        double r130079 = r130073 * r130078;
        double r130080 = r130076 + r130079;
        double r130081 = r130080 - r130058;
        double r130082 = r130044 + r130081;
        double r130083 = r130082 / r130062;
        double r130084 = -r130083;
        double r130085 = fma(r130084, r130065, r130040);
        double r130086 = cbrt(r130085);
        double r130087 = r130068 * r130086;
        return r130087;
}

Error

Bits error versus x

Derivation

1. Initial program 14.0

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

2. Simplified 14.0

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

3. Taylor expanded around 0 14.8

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

4. Simplified 14.0

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

6. Applied fma-udef 14.0

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

7. Simplified 14.0

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

9. Applied add-cube-cbrt 14.0

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

10. Simplified 14.0

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

11. Simplified 14.0

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

13. Applied add-sqr-sqrt 14.0

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

14. Applied add-sqr-sqrt 14.0

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

15. Applied times-frac 14.0

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

16. Applied add-cube-cbrt 13.3

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

17. Applied prod-diff 13.3

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

18. Simplified 13.3

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

19. Final simplification 13.3

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

Reproduce

herbie shell --seed 2019208 +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)))))))