Jmat.Real.erf

Average Error: 13.9 → 13.0

Time: 2.9m

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r10281719 = 1.0;
        double r10281720 = 0.3275911;
        double r10281721 = x;
        double r10281722 = fabs(r10281721);
        double r10281723 = r10281720 * r10281722;
        double r10281724 = r10281719 + r10281723;
        double r10281725 = r10281719 / r10281724;
        double r10281726 = 0.254829592;
        double r10281727 = -0.284496736;
        double r10281728 = 1.421413741;
        double r10281729 = -1.453152027;
        double r10281730 = 1.061405429;
        double r10281731 = r10281725 * r10281730;
        double r10281732 = r10281729 + r10281731;
        double r10281733 = r10281725 * r10281732;
        double r10281734 = r10281728 + r10281733;
        double r10281735 = r10281725 * r10281734;
        double r10281736 = r10281727 + r10281735;
        double r10281737 = r10281725 * r10281736;
        double r10281738 = r10281726 + r10281737;
        double r10281739 = r10281725 * r10281738;
        double r10281740 = r10281722 * r10281722;
        double r10281741 = -r10281740;
        double r10281742 = exp(r10281741);
        double r10281743 = r10281739 * r10281742;
        double r10281744 = r10281719 - r10281743;
        return r10281744;
}

↓

double f(double x) {
        double r10281745 = 1.0;
        double r10281746 = 0.254829592;
        double r10281747 = -1.453152027;
        double r10281748 = 1.061405429;
        double r10281749 = 0.3275911;
        double r10281750 = x;
        double r10281751 = fabs(r10281750);
        double r10281752 = r10281749 * r10281751;
        double r10281753 = r10281745 + r10281752;
        double r10281754 = r10281748 / r10281753;
        double r10281755 = r10281747 + r10281754;
        double r10281756 = r10281755 / r10281753;
        double r10281757 = 1.421413741;
        double r10281758 = r10281756 + r10281757;
        double r10281759 = r10281758 / r10281753;
        double r10281760 = r10281759 * r10281759;
        double r10281761 = -0.284496736;
        double r10281762 = r10281761 * r10281761;
        double r10281763 = r10281760 - r10281762;
        double r10281764 = r10281759 - r10281761;
        double r10281765 = r10281764 * r10281753;
        double r10281766 = r10281763 / r10281765;
        double r10281767 = r10281746 + r10281766;
        double r10281768 = r10281751 * r10281751;
        double r10281769 = exp(r10281768);
        double r10281770 = r10281769 * r10281753;
        double r10281771 = r10281767 / r10281770;
        double r10281772 = 3.0;
        double r10281773 = pow(r10281771, r10281772);
        double r10281774 = sqrt(r10281773);
        double r10281775 = r10281774 * r10281774;
        double r10281776 = pow(r10281775, r10281772);
        double r10281777 = r10281745 - r10281776;
        double r10281778 = r10281775 * r10281775;
        double r10281779 = r10281778 + r10281775;
        double r10281780 = r10281779 + r10281745;
        double r10281781 = r10281777 / r10281780;
        double r10281782 = r10281771 * r10281771;
        double r10281783 = r10281782 + r10281771;
        double r10281784 = r10281783 + r10281745;
        double r10281785 = r10281781 / r10281784;
        return r10281785;
}

Error

Bits error versus x

Derivation

1. Initial program 13.9

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

2. Simplified 13.9

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

4. Applied flip-+ 13.9

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

5. Applied associate-/l/ 13.9

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

7. Applied flip3-- 13.9

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

9. Applied add-sqr-sqrt 13.1

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

11. Applied flip3-- 13.0

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

12. Final simplification 13.0

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

Reproduce

herbie shell --seed 2019130 
(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)))))))