Jmat.Real.erf

Average Error: 13.8 → 13.1

Time: 17.4s

Precision: 64

Math

\[1 - \left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]

↓

\[\left(\sqrt[3]{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \frac{\sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), -0.284496735999999972\right), 0.25482959199999999\right)}{e^{\left|x\right| \cdot \left|x\right|}}, \frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1\right)} \cdot \sqrt[3]{\mathsf{fma}\left(\frac{\frac{-\sqrt{1}}{\sqrt{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}}}{\frac{1}{1}}, \frac{\frac{\sqrt{1}}{\sqrt{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}}}{\frac{e^{{\left(\left|x\right|\right)}^{2}}}{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left({\left(\frac{\sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}}\right)}^{3}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}}, 1\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \frac{\sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), -0.284496735999999972\right), 0.25482959199999999\right)}{e^{\left|x\right| \cdot \left|x\right|}}, \frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1\right)}\]

C

double f(double x) {
        double r210806 = 1.0;
        double r210807 = 0.3275911;
        double r210808 = x;
        double r210809 = fabs(r210808);
        double r210810 = r210807 * r210809;
        double r210811 = r210806 + r210810;
        double r210812 = r210806 / r210811;
        double r210813 = 0.254829592;
        double r210814 = -0.284496736;
        double r210815 = 1.421413741;
        double r210816 = -1.453152027;
        double r210817 = 1.061405429;
        double r210818 = r210812 * r210817;
        double r210819 = r210816 + r210818;
        double r210820 = r210812 * r210819;
        double r210821 = r210815 + r210820;
        double r210822 = r210812 * r210821;
        double r210823 = r210814 + r210822;
        double r210824 = r210812 * r210823;
        double r210825 = r210813 + r210824;
        double r210826 = r210812 * r210825;
        double r210827 = r210809 * r210809;
        double r210828 = -r210827;
        double r210829 = exp(r210828);
        double r210830 = r210826 * r210829;
        double r210831 = r210806 - r210830;
        return r210831;
}

↓

double f(double x) {
        double r210832 = 1.0;
        double r210833 = 0.3275911;
        double r210834 = x;
        double r210835 = fabs(r210834);
        double r210836 = r210833 * r210835;
        double r210837 = r210832 + r210836;
        double r210838 = r210832 / r210837;
        double r210839 = cbrt(r210832);
        double r210840 = r210839 * r210839;
        double r210841 = cbrt(r210837);
        double r210842 = r210841 * r210841;
        double r210843 = r210840 / r210842;
        double r210844 = r210839 / r210841;
        double r210845 = r210843 * r210844;
        double r210846 = 1.061405429;
        double r210847 = -1.453152027;
        double r210848 = fma(r210838, r210846, r210847);
        double r210849 = 1.421413741;
        double r210850 = fma(r210845, r210848, r210849);
        double r210851 = -0.284496736;
        double r210852 = fma(r210838, r210850, r210851);
        double r210853 = 0.254829592;
        double r210854 = fma(r210838, r210852, r210853);
        double r210855 = r210835 * r210835;
        double r210856 = exp(r210855);
        double r210857 = r210854 / r210856;
        double r210858 = -r210832;
        double r210859 = fma(r210835, r210833, r210832);
        double r210860 = r210858 / r210859;
        double r210861 = fma(r210857, r210860, r210832);
        double r210862 = cbrt(r210861);
        double r210863 = sqrt(r210832);
        double r210864 = -r210863;
        double r210865 = sqrt(r210859);
        double r210866 = r210864 / r210865;
        double r210867 = 1.0;
        double r210868 = r210867 / r210867;
        double r210869 = r210866 / r210868;
        double r210870 = r210863 / r210865;
        double r210871 = 2.0;
        double r210872 = pow(r210835, r210871);
        double r210873 = exp(r210872);
        double r210874 = r210832 / r210859;
        double r210875 = 3.0;
        double r210876 = pow(r210844, r210875);
        double r210877 = fma(r210874, r210846, r210847);
        double r210878 = fma(r210876, r210877, r210849);
        double r210879 = fma(r210878, r210874, r210851);
        double r210880 = fma(r210874, r210879, r210853);
        double r210881 = r210873 / r210880;
        double r210882 = r210870 / r210881;
        double r210883 = fma(r210869, r210882, r210832);
        double r210884 = cbrt(r210883);
        double r210885 = r210862 * r210884;
        double r210886 = r210885 * r210862;
        return r210886;
}

Error

Bits error versus x

Derivation

1. Initial program 13.8

   \[1 - \left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]

2. Simplified 13.8

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), -0.284496735999999972\right), 0.25482959199999999\right)}{e^{\left|x\right| \cdot \left|x\right|}}, \frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1\right)}\]
3. Using strategy rm

4. Applied add-cube-cbrt 13.8

   \[\leadsto \mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{1}{\color{blue}{\left(\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}\right) \cdot \sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}}}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), -0.284496735999999972\right), 0.25482959199999999\right)}{e^{\left|x\right| \cdot \left|x\right|}}, \frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1\right)\]

5. Applied add-cube-cbrt 13.8

   \[\leadsto \mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{\left(\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}\right) \cdot \sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), -0.284496735999999972\right), 0.25482959199999999\right)}{e^{\left|x\right| \cdot \left|x\right|}}, \frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1\right)\]

6. Applied times-frac 13.8

   \[\leadsto \mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \frac{\sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}}}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), -0.284496735999999972\right), 0.25482959199999999\right)}{e^{\left|x\right| \cdot \left|x\right|}}, \frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1\right)\]
7. Using strategy rm

8. Applied add-cube-cbrt 13.8

   \[\leadsto \color{blue}{\left(\sqrt[3]{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \frac{\sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), -0.284496735999999972\right), 0.25482959199999999\right)}{e^{\left|x\right| \cdot \left|x\right|}}, \frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1\right)} \cdot \sqrt[3]{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \frac{\sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), -0.284496735999999972\right), 0.25482959199999999\right)}{e^{\left|x\right| \cdot \left|x\right|}}, \frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \frac{\sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), -0.284496735999999972\right), 0.25482959199999999\right)}{e^{\left|x\right| \cdot \left|x\right|}}, \frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1\right)}}\]
9. Using strategy rm

10. Applied fma-udef 13.8

    \[\leadsto \left(\sqrt[3]{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \frac{\sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), -0.284496735999999972\right), 0.25482959199999999\right)}{e^{\left|x\right| \cdot \left|x\right|}}, \frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1\right)} \cdot \sqrt[3]{\color{blue}{\frac{\mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \frac{\sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), -0.284496735999999972\right), 0.25482959199999999\right)}{e^{\left|x\right| \cdot \left|x\right|}} \cdot \frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)} + 1}}\right) \cdot \sqrt[3]{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \frac{\sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), -0.284496735999999972\right), 0.25482959199999999\right)}{e^{\left|x\right| \cdot \left|x\right|}}, \frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1\right)}\]

11. Simplified 13.1

    \[\leadsto \left(\sqrt[3]{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \frac{\sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), -0.284496735999999972\right), 0.25482959199999999\right)}{e^{\left|x\right| \cdot \left|x\right|}}, \frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1\right)} \cdot \sqrt[3]{\color{blue}{\frac{\frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}}{\frac{e^{{\left(\left|x\right|\right)}^{2}}}{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left({\left(\frac{\sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}}\right)}^{3}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}}} + 1}\right) \cdot \sqrt[3]{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \frac{\sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), -0.284496735999999972\right), 0.25482959199999999\right)}{e^{\left|x\right| \cdot \left|x\right|}}, \frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1\right)}\]
12. Using strategy rm

13. Applied *-un-lft-identity 13.1

    \[\leadsto \left(\sqrt[3]{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \frac{\sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), -0.284496735999999972\right), 0.25482959199999999\right)}{e^{\left|x\right| \cdot \left|x\right|}}, \frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1\right)} \cdot \sqrt[3]{\frac{\frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}}{\frac{e^{{\left(\left|x\right|\right)}^{2}}}{\color{blue}{1 \cdot \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left({\left(\frac{\sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}}\right)}^{3}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}}} + 1}\right) \cdot \sqrt[3]{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \frac{\sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), -0.284496735999999972\right), 0.25482959199999999\right)}{e^{\left|x\right| \cdot \left|x\right|}}, \frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1\right)}\]

14. Applied *-un-lft-identity 13.1

    \[\leadsto \left(\sqrt[3]{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \frac{\sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), -0.284496735999999972\right), 0.25482959199999999\right)}{e^{\left|x\right| \cdot \left|x\right|}}, \frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1\right)} \cdot \sqrt[3]{\frac{\frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}}{\frac{\color{blue}{1 \cdot e^{{\left(\left|x\right|\right)}^{2}}}}{1 \cdot \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left({\left(\frac{\sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}}\right)}^{3}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}} + 1}\right) \cdot \sqrt[3]{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \frac{\sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), -0.284496735999999972\right), 0.25482959199999999\right)}{e^{\left|x\right| \cdot \left|x\right|}}, \frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1\right)}\]

15. Applied times-frac 13.1

    \[\leadsto \left(\sqrt[3]{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \frac{\sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), -0.284496735999999972\right), 0.25482959199999999\right)}{e^{\left|x\right| \cdot \left|x\right|}}, \frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1\right)} \cdot \sqrt[3]{\frac{\frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}}{\color{blue}{\frac{1}{1} \cdot \frac{e^{{\left(\left|x\right|\right)}^{2}}}{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left({\left(\frac{\sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}}\right)}^{3}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}}} + 1}\right) \cdot \sqrt[3]{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \frac{\sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), -0.284496735999999972\right), 0.25482959199999999\right)}{e^{\left|x\right| \cdot \left|x\right|}}, \frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1\right)}\]

16. Applied add-sqr-sqrt 13.1

    \[\leadsto \left(\sqrt[3]{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \frac{\sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), -0.284496735999999972\right), 0.25482959199999999\right)}{e^{\left|x\right| \cdot \left|x\right|}}, \frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1\right)} \cdot \sqrt[3]{\frac{\frac{-1}{\color{blue}{\sqrt{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)} \cdot \sqrt{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}}}}{\frac{1}{1} \cdot \frac{e^{{\left(\left|x\right|\right)}^{2}}}{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left({\left(\frac{\sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}}\right)}^{3}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}} + 1}\right) \cdot \sqrt[3]{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \frac{\sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), -0.284496735999999972\right), 0.25482959199999999\right)}{e^{\left|x\right| \cdot \left|x\right|}}, \frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1\right)}\]

17. Applied add-sqr-sqrt 13.1

    \[\leadsto \left(\sqrt[3]{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \frac{\sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), -0.284496735999999972\right), 0.25482959199999999\right)}{e^{\left|x\right| \cdot \left|x\right|}}, \frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1\right)} \cdot \sqrt[3]{\frac{\frac{-\color{blue}{\sqrt{1} \cdot \sqrt{1}}}{\sqrt{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)} \cdot \sqrt{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}}}{\frac{1}{1} \cdot \frac{e^{{\left(\left|x\right|\right)}^{2}}}{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left({\left(\frac{\sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}}\right)}^{3}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}} + 1}\right) \cdot \sqrt[3]{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \frac{\sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), -0.284496735999999972\right), 0.25482959199999999\right)}{e^{\left|x\right| \cdot \left|x\right|}}, \frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1\right)}\]

18. Applied distribute-lft-neg-in 13.1

    \[\leadsto \left(\sqrt[3]{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \frac{\sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), -0.284496735999999972\right), 0.25482959199999999\right)}{e^{\left|x\right| \cdot \left|x\right|}}, \frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1\right)} \cdot \sqrt[3]{\frac{\frac{\color{blue}{\left(-\sqrt{1}\right) \cdot \sqrt{1}}}{\sqrt{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)} \cdot \sqrt{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}}}{\frac{1}{1} \cdot \frac{e^{{\left(\left|x\right|\right)}^{2}}}{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left({\left(\frac{\sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}}\right)}^{3}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}} + 1}\right) \cdot \sqrt[3]{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \frac{\sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), -0.284496735999999972\right), 0.25482959199999999\right)}{e^{\left|x\right| \cdot \left|x\right|}}, \frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1\right)}\]

19. Applied times-frac 13.1

    \[\leadsto \left(\sqrt[3]{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \frac{\sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), -0.284496735999999972\right), 0.25482959199999999\right)}{e^{\left|x\right| \cdot \left|x\right|}}, \frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1\right)} \cdot \sqrt[3]{\frac{\color{blue}{\frac{-\sqrt{1}}{\sqrt{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}} \cdot \frac{\sqrt{1}}{\sqrt{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}}}}{\frac{1}{1} \cdot \frac{e^{{\left(\left|x\right|\right)}^{2}}}{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left({\left(\frac{\sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}}\right)}^{3}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}} + 1}\right) \cdot \sqrt[3]{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \frac{\sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), -0.284496735999999972\right), 0.25482959199999999\right)}{e^{\left|x\right| \cdot \left|x\right|}}, \frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1\right)}\]

20. Applied times-frac 13.1

    \[\leadsto \left(\sqrt[3]{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \frac{\sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), -0.284496735999999972\right), 0.25482959199999999\right)}{e^{\left|x\right| \cdot \left|x\right|}}, \frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1\right)} \cdot \sqrt[3]{\color{blue}{\frac{\frac{-\sqrt{1}}{\sqrt{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}}}{\frac{1}{1}} \cdot \frac{\frac{\sqrt{1}}{\sqrt{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}}}{\frac{e^{{\left(\left|x\right|\right)}^{2}}}{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left({\left(\frac{\sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}}\right)}^{3}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}}} + 1}\right) \cdot \sqrt[3]{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \frac{\sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), -0.284496735999999972\right), 0.25482959199999999\right)}{e^{\left|x\right| \cdot \left|x\right|}}, \frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1\right)}\]

21. Applied fma-def 13.1

    \[\leadsto \left(\sqrt[3]{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \frac{\sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), -0.284496735999999972\right), 0.25482959199999999\right)}{e^{\left|x\right| \cdot \left|x\right|}}, \frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1\right)} \cdot \sqrt[3]{\color{blue}{\mathsf{fma}\left(\frac{\frac{-\sqrt{1}}{\sqrt{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}}}{\frac{1}{1}}, \frac{\frac{\sqrt{1}}{\sqrt{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}}}{\frac{e^{{\left(\left|x\right|\right)}^{2}}}{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left({\left(\frac{\sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}}\right)}^{3}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}}, 1\right)}}\right) \cdot \sqrt[3]{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \frac{\sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), -0.284496735999999972\right), 0.25482959199999999\right)}{e^{\left|x\right| \cdot \left|x\right|}}, \frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1\right)}\]

22. Final simplification 13.1

    \[\leadsto \left(\sqrt[3]{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \frac{\sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), -0.284496735999999972\right), 0.25482959199999999\right)}{e^{\left|x\right| \cdot \left|x\right|}}, \frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1\right)} \cdot \sqrt[3]{\mathsf{fma}\left(\frac{\frac{-\sqrt{1}}{\sqrt{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}}}{\frac{1}{1}}, \frac{\frac{\sqrt{1}}{\sqrt{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}}}{\frac{e^{{\left(\left|x\right|\right)}^{2}}}{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left({\left(\frac{\sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}}\right)}^{3}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}}, 1\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \frac{\sqrt[3]{1}}{\sqrt[3]{1 + 0.32759110000000002 \cdot \left|x\right|}}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), -0.284496735999999972\right), 0.25482959199999999\right)}{e^{\left|x\right| \cdot \left|x\right|}}, \frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1\right)}\]

Reproduce

herbie shell --seed 2020021 +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)))))))