Jmat.Real.erf

Average Error: 14.0 → 13.2

Time: 16.4s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r355899 = 1.0;
        double r355900 = 0.3275911;
        double r355901 = x;
        double r355902 = fabs(r355901);
        double r355903 = r355900 * r355902;
        double r355904 = r355899 + r355903;
        double r355905 = r355899 / r355904;
        double r355906 = 0.254829592;
        double r355907 = -0.284496736;
        double r355908 = 1.421413741;
        double r355909 = -1.453152027;
        double r355910 = 1.061405429;
        double r355911 = r355905 * r355910;
        double r355912 = r355909 + r355911;
        double r355913 = r355905 * r355912;
        double r355914 = r355908 + r355913;
        double r355915 = r355905 * r355914;
        double r355916 = r355907 + r355915;
        double r355917 = r355905 * r355916;
        double r355918 = r355906 + r355917;
        double r355919 = r355905 * r355918;
        double r355920 = r355902 * r355902;
        double r355921 = -r355920;
        double r355922 = exp(r355921);
        double r355923 = r355919 * r355922;
        double r355924 = r355899 - r355923;
        return r355924;
}

↓

double f(double x) {
        double r355925 = 1.0;
        double r355926 = 0.3275911;
        double r355927 = x;
        double r355928 = fabs(r355927);
        double r355929 = r355926 * r355928;
        double r355930 = r355925 + r355929;
        double r355931 = r355925 / r355930;
        double r355932 = 0.254829592;
        double r355933 = -0.284496736;
        double r355934 = 1.421413741;
        double r355935 = -1.453152027;
        double r355936 = 1.061405429;
        double r355937 = r355931 * r355936;
        double r355938 = r355935 + r355937;
        double r355939 = r355931 * r355938;
        double r355940 = r355934 + r355939;
        double r355941 = r355931 * r355940;
        double r355942 = r355933 + r355941;
        double r355943 = r355931 * r355942;
        double r355944 = r355932 + r355943;
        double r355945 = 3.0;
        double r355946 = pow(r355944, r355945);
        double r355947 = cbrt(r355946);
        double r355948 = r355931 * r355947;
        double r355949 = r355928 * r355928;
        double r355950 = -r355949;
        double r355951 = exp(r355950);
        double r355952 = r355948 * r355951;
        double r355953 = r355925 - r355952;
        double r355954 = log(r355953);
        double r355955 = cbrt(r355954);
        double r355956 = -r355931;
        double r355957 = 1.0;
        double r355958 = 2.0;
        double r355959 = pow(r355928, r355958);
        double r355960 = exp(r355959);
        double r355961 = r355957 / r355960;
        double r355962 = r355944 * r355961;
        double r355963 = r355956 * r355962;
        double r355964 = r355963 + r355925;
        double r355965 = pow(r355964, r355945);
        double r355966 = cbrt(r355965);
        double r355967 = log(r355966);
        double r355968 = cbrt(r355967);
        double r355969 = r355955 * r355968;
        double r355970 = exp(r355969);
        double r355971 = pow(r355970, r355955);
        return r355971;
}

Error

Bits error versus x

Derivation

1. Initial program 14.0

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

3. Applied add-cbrt-cube 14.0

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

4. Simplified 14.0

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

6. Applied add-exp-log 14.0

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

8. Applied add-cube-cbrt 14.0

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

9. Applied exp-prod 14.0

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

11. Applied add-cbrt-cube 14.0

    \[\leadsto {\left(e^{\sqrt[3]{\log \left(1 - \left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \sqrt[3]{{\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)}^{3}}\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)} \cdot \sqrt[3]{\log \color{blue}{\left(\sqrt[3]{\left(\left(1 - \left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \sqrt[3]{{\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)}^{3}}\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right) \cdot \left(1 - \left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \sqrt[3]{{\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)}^{3}}\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)\right) \cdot \left(1 - \left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \sqrt[3]{{\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)}^{3}}\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}\right)}}}\right)}^{\left(\sqrt[3]{\log \left(1 - \left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \sqrt[3]{{\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)}^{3}}\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}\right)}\]

12. Simplified 13.2

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

13. Final simplification 13.2

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

Reproduce

herbie shell --seed 2020059 
(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)))))))