Jmat.Real.erf

Average Error: 13.9 → 0.8

Time: 25.5s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r126932 = 1.0;
        double r126933 = 0.3275911;
        double r126934 = x;
        double r126935 = fabs(r126934);
        double r126936 = r126933 * r126935;
        double r126937 = r126932 + r126936;
        double r126938 = r126932 / r126937;
        double r126939 = 0.254829592;
        double r126940 = -0.284496736;
        double r126941 = 1.421413741;
        double r126942 = -1.453152027;
        double r126943 = 1.061405429;
        double r126944 = r126938 * r126943;
        double r126945 = r126942 + r126944;
        double r126946 = r126938 * r126945;
        double r126947 = r126941 + r126946;
        double r126948 = r126938 * r126947;
        double r126949 = r126940 + r126948;
        double r126950 = r126938 * r126949;
        double r126951 = r126939 + r126950;
        double r126952 = r126938 * r126951;
        double r126953 = r126935 * r126935;
        double r126954 = -r126953;
        double r126955 = exp(r126954);
        double r126956 = r126952 * r126955;
        double r126957 = r126932 - r126956;
        return r126957;
}

↓

double f(double x) {
        double r126958 = 1.0;
        double r126959 = 0.3275911;
        double r126960 = x;
        double r126961 = fabs(r126960);
        double r126962 = fma(r126959, r126961, r126958);
        double r126963 = r126958 / r126962;
        double r126964 = 1.061405429;
        double r126965 = -1.453152027;
        double r126966 = fma(r126964, r126963, r126965);
        double r126967 = r126963 * r126966;
        double r126968 = 1.421413741;
        double r126969 = r126967 + r126968;
        double r126970 = -0.284496736;
        double r126971 = fma(r126963, r126969, r126970);
        double r126972 = 0.254829592;
        double r126973 = fma(r126963, r126971, r126972);
        double r126974 = r126958 * r126973;
        double r126975 = -r126974;
        double r126976 = r126975 / r126962;
        double r126977 = exp(r126961);
        double r126978 = -2.0;
        double r126979 = r126978 * r126961;
        double r126980 = pow(r126977, r126979);
        double r126981 = r126962 / r126973;
        double r126982 = r126958 / r126981;
        double r126983 = r126980 * r126982;
        double r126984 = r126958 * r126958;
        double r126985 = fma(r126976, r126983, r126984);
        double r126986 = 2.0;
        double r126987 = pow(r126961, r126986);
        double r126988 = exp(r126987);
        double r126989 = r126963 / r126988;
        double r126990 = fma(r126989, r126973, r126958);
        double r126991 = r126985 / r126990;
        return r126991;
}

Error

Bits error versus x

Derivation

1. Initial program 13.9

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

3. Applied add-cube-cbrt 13.9

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

4. Simplified 13.9

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

5. Simplified 13.9

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

7. Applied flip-- 13.9

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

8. Simplified 0.8

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

9. Simplified 0.8

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

10. Final simplification 0.8

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

Reproduce

herbie shell --seed 2019326 +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)))))))