Average Error: 13.7 → 13.0
Time: 3.9m
Precision: 64
\[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
↓
\[\sqrt[3]{\left(\log \left(e^{1 - \sqrt{\frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}}{e^{\left|x\right| \cdot \left|x\right|}}}}\right) \cdot \log \left(e^{1 - \sqrt{\frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}}{e^{\left|x\right| \cdot \left|x\right|}}}}\right)\right) \cdot \left(1 - \sqrt{\frac{\frac{\left(\frac{1.061405429}{\left(\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)\right) \cdot \left(\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)\right)} + \left(0.254829592 + \frac{1.421413741}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)}\right)\right) - \left(\frac{0.284496736}{1 + \left|x\right| \cdot 0.3275911} + \frac{1.453152027}{\left(\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)}\right)}{e^{\left|x\right| \cdot \left|x\right|}}}{1 + \left|x\right| \cdot 0.3275911}}\right)} \cdot \left(\sqrt{\frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}}{e^{\left|x\right| \cdot \left|x\right|}}} + 1\right)\]
double f(double x) {
        double r21346755 = 1.0;
        double r21346756 = 0.3275911;
        double r21346757 = x;
        double r21346758 = fabs(r21346757);
        double r21346759 = r21346756 * r21346758;
        double r21346760 = r21346755 + r21346759;
        double r21346761 = r21346755 / r21346760;
        double r21346762 = 0.254829592;
        double r21346763 = -0.284496736;
        double r21346764 = 1.421413741;
        double r21346765 = -1.453152027;
        double r21346766 = 1.061405429;
        double r21346767 = r21346761 * r21346766;
        double r21346768 = r21346765 + r21346767;
        double r21346769 = r21346761 * r21346768;
        double r21346770 = r21346764 + r21346769;
        double r21346771 = r21346761 * r21346770;
        double r21346772 = r21346763 + r21346771;
        double r21346773 = r21346761 * r21346772;
        double r21346774 = r21346762 + r21346773;
        double r21346775 = r21346761 * r21346774;
        double r21346776 = r21346758 * r21346758;
        double r21346777 = -r21346776;
        double r21346778 = exp(r21346777);
        double r21346779 = r21346775 * r21346778;
        double r21346780 = r21346755 - r21346779;
        return r21346780;
}
↓
double f(double x) {
        double r21346781 = 1.0;
        double r21346782 = 0.254829592;
        double r21346783 = -0.284496736;
        double r21346784 = 1.421413741;
        double r21346785 = 1.061405429;
        double r21346786 = x;
        double r21346787 = fabs(r21346786);
        double r21346788 = 0.3275911;
        double r21346789 = r21346787 * r21346788;
        double r21346790 = r21346781 + r21346789;
        double r21346791 = r21346785 / r21346790;
        double r21346792 = -1.453152027;
        double r21346793 = r21346791 + r21346792;
        double r21346794 = r21346793 / r21346790;
        double r21346795 = r21346784 + r21346794;
        double r21346796 = r21346795 / r21346790;
        double r21346797 = r21346783 + r21346796;
        double r21346798 = r21346797 / r21346790;
        double r21346799 = r21346782 + r21346798;
        double r21346800 = r21346799 / r21346790;
        double r21346801 = r21346787 * r21346787;
        double r21346802 = exp(r21346801);
        double r21346803 = r21346800 / r21346802;
        double r21346804 = sqrt(r21346803);
        double r21346805 = r21346781 - r21346804;
        double r21346806 = exp(r21346805);
        double r21346807 = log(r21346806);
        double r21346808 = r21346807 * r21346807;
        double r21346809 = r21346790 * r21346790;
        double r21346810 = r21346809 * r21346809;
        double r21346811 = r21346785 / r21346810;
        double r21346812 = r21346784 / r21346809;
        double r21346813 = r21346782 + r21346812;
        double r21346814 = r21346811 + r21346813;
        double r21346815 = 0.284496736;
        double r21346816 = r21346815 / r21346790;
        double r21346817 = 1.453152027;
        double r21346818 = r21346809 * r21346790;
        double r21346819 = r21346817 / r21346818;
        double r21346820 = r21346816 + r21346819;
        double r21346821 = r21346814 - r21346820;
        double r21346822 = r21346821 / r21346802;
        double r21346823 = r21346822 / r21346790;
        double r21346824 = sqrt(r21346823);
        double r21346825 = r21346781 - r21346824;
        double r21346826 = r21346808 * r21346825;
        double r21346827 = cbrt(r21346826);
        double r21346828 = r21346804 + r21346781;
        double r21346829 = r21346827 * r21346828;
        return r21346829;
}


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|}
↓
\sqrt[3]{\left(\log \left(e^{1 - \sqrt{\frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}}{e^{\left|x\right| \cdot \left|x\right|}}}}\right) \cdot \log \left(e^{1 - \sqrt{\frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}}{e^{\left|x\right| \cdot \left|x\right|}}}}\right)\right) \cdot \left(1 - \sqrt{\frac{\frac{\left(\frac{1.061405429}{\left(\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)\right) \cdot \left(\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)\right)} + \left(0.254829592 + \frac{1.421413741}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)}\right)\right) - \left(\frac{0.284496736}{1 + \left|x\right| \cdot 0.3275911} + \frac{1.453152027}{\left(\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)}\right)}{e^{\left|x\right| \cdot \left|x\right|}}}{1 + \left|x\right| \cdot 0.3275911}}\right)} \cdot \left(\sqrt{\frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}}{e^{\left|x\right| \cdot \left|x\right|}}} + 1\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. Simplified13.7

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

  4. Applied add-sqr-sqrt13.7

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

  5. Applied *-un-lft-identity13.7

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

  6. Applied difference-of-squares13.7

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

  8. Applied add-log-exp13.7

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

  10. Applied add-cbrt-cube13.7

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

  11. Taylor expanded around inf 13.0

    \[\leadsto \left(1 + \sqrt{\frac{\frac{\frac{-0.284496736 + \frac{\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911} + 0.254829592}{1 + \left|x\right| \cdot 0.3275911}}{e^{\left|x\right| \cdot \left|x\right|}}}\right) \cdot \sqrt[3]{\left(\log \left(e^{1 - \sqrt{\frac{\frac{\frac{-0.284496736 + \frac{\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911} + 0.254829592}{1 + \left|x\right| \cdot 0.3275911}}{e^{\left|x\right| \cdot \left|x\right|}}}}\right) \cdot \log \left(e^{1 - \sqrt{\frac{\frac{\frac{-0.284496736 + \frac{\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911} + 0.254829592}{1 + \left|x\right| \cdot 0.3275911}}{e^{\left|x\right| \cdot \left|x\right|}}}}\right)\right) \cdot \color{blue}{\left(1 - \sqrt{\frac{\left(1.061405429 \cdot \frac{1}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{4}} + \left(1.421413741 \cdot \frac{1}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}} + 0.254829592\right)\right) - \left(0.284496736 \cdot \frac{1}{0.3275911 \cdot \left|x\right| + 1} + 1.453152027 \cdot \frac{1}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3}}\right)}{e^{{\left(\left|x\right|\right)}^{2}} \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)}}\right)}}\]

  12. Simplified13.0

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

  13. Final simplification13.0

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

Reproduce

herbie shell --seed 2019102 
(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)))))))