Average Error: 13.7 → 13.7
Time: 2.1m
Precision: 64
\[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
↓
\[e^{\log \left(\log \left(e^{1 - (e^{\log_* (1 + \sqrt[3]{\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} \cdot \frac{(\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*\right) + 0.254829592)_* \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*\right) + 0.254829592)_* \cdot (\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*\right) + 0.254829592)_*\right)}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_* \cdot (0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}})} - 1)^* \cdot e^{-\left|x\right| \cdot \left|x\right|}}\right)\right)}\]
double f(double x) {
        double r35204934 = 1.0;
        double r35204935 = 0.3275911;
        double r35204936 = x;
        double r35204937 = fabs(r35204936);
        double r35204938 = r35204935 * r35204937;
        double r35204939 = r35204934 + r35204938;
        double r35204940 = r35204934 / r35204939;
        double r35204941 = 0.254829592;
        double r35204942 = -0.284496736;
        double r35204943 = 1.421413741;
        double r35204944 = -1.453152027;
        double r35204945 = 1.061405429;
        double r35204946 = r35204940 * r35204945;
        double r35204947 = r35204944 + r35204946;
        double r35204948 = r35204940 * r35204947;
        double r35204949 = r35204943 + r35204948;
        double r35204950 = r35204940 * r35204949;
        double r35204951 = r35204942 + r35204950;
        double r35204952 = r35204940 * r35204951;
        double r35204953 = r35204941 + r35204952;
        double r35204954 = r35204940 * r35204953;
        double r35204955 = r35204937 * r35204937;
        double r35204956 = -r35204955;
        double r35204957 = exp(r35204956);
        double r35204958 = r35204954 * r35204957;
        double r35204959 = r35204934 - r35204958;
        return r35204959;
}
↓
double f(double x) {
        double r35204960 = 1.0;
        double r35204961 = 0.3275911;
        double r35204962 = x;
        double r35204963 = fabs(r35204962);
        double r35204964 = fma(r35204961, r35204963, r35204960);
        double r35204965 = r35204960 / r35204964;
        double r35204966 = 1.061405429;
        double r35204967 = r35204966 / r35204964;
        double r35204968 = -1.453152027;
        double r35204969 = r35204967 + r35204968;
        double r35204970 = 1.421413741;
        double r35204971 = fma(r35204965, r35204969, r35204970);
        double r35204972 = -0.284496736;
        double r35204973 = fma(r35204965, r35204971, r35204972);
        double r35204974 = 0.254829592;
        double r35204975 = fma(r35204965, r35204973, r35204974);
        double r35204976 = r35204975 * r35204975;
        double r35204977 = r35204975 * r35204976;
        double r35204978 = r35204964 * r35204964;
        double r35204979 = r35204977 / r35204978;
        double r35204980 = r35204965 * r35204979;
        double r35204981 = cbrt(r35204980);
        double r35204982 = log1p(r35204981);
        double r35204983 = expm1(r35204982);
        double r35204984 = r35204963 * r35204963;
        double r35204985 = -r35204984;
        double r35204986 = exp(r35204985);
        double r35204987 = r35204983 * r35204986;
        double r35204988 = r35204960 - r35204987;
        double r35204989 = exp(r35204988);
        double r35204990 = log(r35204989);
        double r35204991 = log(r35204990);
        double r35204992 = exp(r35204991);
        return r35204992;
}


1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}
↓
e^{\log \left(\log \left(e^{1 - (e^{\log_* (1 + \sqrt[3]{\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} \cdot \frac{(\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*\right) + 0.254829592)_* \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*\right) + 0.254829592)_* \cdot (\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*\right) + 0.254829592)_*\right)}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_* \cdot (0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}})} - 1)^* \cdot e^{-\left|x\right| \cdot \left|x\right|}}\right)\right)}

Error

Bits error versus x

Derivation

  1. Initial program 13.7

    \[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
  2. Using strategy rm

  3. Applied add-cbrt-cube13.7

    \[\leadsto 1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \color{blue}{\sqrt[3]{\left(\left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right) \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)}}\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]

  4. Applied add-cbrt-cube13.7

    \[\leadsto 1 - \left(\frac{1}{\color{blue}{\sqrt[3]{\left(\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot \left(1 + 0.3275911 \cdot \left|x\right|\right)\right) \cdot \left(1 + 0.3275911 \cdot \left|x\right|\right)}}} \cdot \sqrt[3]{\left(\left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right) \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)}\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]

  5. Applied add-cbrt-cube13.7

    \[\leadsto 1 - \left(\frac{\color{blue}{\sqrt[3]{\left(1 \cdot 1\right) \cdot 1}}}{\sqrt[3]{\left(\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot \left(1 + 0.3275911 \cdot \left|x\right|\right)\right) \cdot \left(1 + 0.3275911 \cdot \left|x\right|\right)}} \cdot \sqrt[3]{\left(\left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right) \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)}\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]

  6. Applied cbrt-undiv13.7

    \[\leadsto 1 - \left(\color{blue}{\sqrt[3]{\frac{\left(1 \cdot 1\right) \cdot 1}{\left(\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot \left(1 + 0.3275911 \cdot \left|x\right|\right)\right) \cdot \left(1 + 0.3275911 \cdot \left|x\right|\right)}}} \cdot \sqrt[3]{\left(\left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right) \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)}\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]

  7. Applied cbrt-unprod13.7

    \[\leadsto 1 - \color{blue}{\sqrt[3]{\frac{\left(1 \cdot 1\right) \cdot 1}{\left(\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot \left(1 + 0.3275911 \cdot \left|x\right|\right)\right) \cdot \left(1 + 0.3275911 \cdot \left|x\right|\right)} \cdot \left(\left(\left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right) \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right)}} \cdot e^{-\left|x\right| \cdot \left|x\right|}\]

  8. Simplified13.7

    \[\leadsto 1 - \sqrt[3]{\color{blue}{\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} \cdot \frac{(\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*\right) + 0.254829592)_* \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*\right) + 0.254829592)_* \cdot (\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*\right) + 0.254829592)_*\right)}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_* \cdot (0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}}} \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
  9. Using strategy rm

  10. Applied expm1-log1p-u13.7

    \[\leadsto 1 - \color{blue}{(e^{\log_* (1 + \sqrt[3]{\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} \cdot \frac{(\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*\right) + 0.254829592)_* \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*\right) + 0.254829592)_* \cdot (\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*\right) + 0.254829592)_*\right)}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_* \cdot (0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}})} - 1)^*} \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
  11. Using strategy rm

  12. Applied add-log-exp13.7

    \[\leadsto \color{blue}{\log \left(e^{1 - (e^{\log_* (1 + \sqrt[3]{\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} \cdot \frac{(\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*\right) + 0.254829592)_* \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*\right) + 0.254829592)_* \cdot (\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*\right) + 0.254829592)_*\right)}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_* \cdot (0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}})} - 1)^* \cdot e^{-\left|x\right| \cdot \left|x\right|}}\right)}\]
  13. Using strategy rm

  14. Applied add-exp-log13.7

    \[\leadsto \color{blue}{e^{\log \left(\log \left(e^{1 - (e^{\log_* (1 + \sqrt[3]{\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} \cdot \frac{(\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*\right) + 0.254829592)_* \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*\right) + 0.254829592)_* \cdot (\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*\right) + 0.254829592)_*\right)}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_* \cdot (0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}})} - 1)^* \cdot e^{-\left|x\right| \cdot \left|x\right|}}\right)\right)}}\]

  15. Final simplification13.7

    \[\leadsto e^{\log \left(\log \left(e^{1 - (e^{\log_* (1 + \sqrt[3]{\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} \cdot \frac{(\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*\right) + 0.254829592)_* \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*\right) + 0.254829592)_* \cdot (\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*\right) + 0.254829592)_*\right)}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_* \cdot (0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}})} - 1)^* \cdot e^{-\left|x\right| \cdot \left|x\right|}}\right)\right)}\]

Reproduce

herbie shell --seed 2019102 +o rules:numerics
(FPCore (x)
  :name "Jmat.Real.erf"
  (- 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)))))))