Jmat.Real.erf

Average Error: 13.8 → 10.6

Time: 30.3s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

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

↓

\[\frac{e^{\log \left(1 \cdot 1 - \frac{\left(1 \cdot 1\right) \cdot \frac{\left(0.25482959199999999 + \left(-0.284496735999999972 + \frac{1 \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999 + -1.45315202700000001\right)\right)}{0.32759110000000002 \cdot \left|x\right| + 1}\right) \cdot \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}\right) \cdot \left(\frac{1.0614054289999999}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{4}} + \left(\left(\left(\frac{1.42141374100000006}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}} + 0.25482959199999999\right) - \frac{1.45315202700000001}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{3}}\right) - \frac{0.284496735999999972}{0.32759110000000002 \cdot \left|x\right| + 1}\right)\right)}{{\left(e^{{\left(\left|x\right|\right)}^{2}}\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}\right)}}{\frac{\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{{\left(\sqrt[3]{1}\right)}^{3}}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right) + -0.284496735999999972\right) + 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}} + 1}\]

C

double f(double x) {
        double r273628 = 1.0;
        double r273629 = 0.3275911;
        double r273630 = x;
        double r273631 = fabs(r273630);
        double r273632 = r273629 * r273631;
        double r273633 = r273628 + r273632;
        double r273634 = r273628 / r273633;
        double r273635 = 0.254829592;
        double r273636 = -0.284496736;
        double r273637 = 1.421413741;
        double r273638 = -1.453152027;
        double r273639 = 1.061405429;
        double r273640 = r273634 * r273639;
        double r273641 = r273638 + r273640;
        double r273642 = r273634 * r273641;
        double r273643 = r273637 + r273642;
        double r273644 = r273634 * r273643;
        double r273645 = r273636 + r273644;
        double r273646 = r273634 * r273645;
        double r273647 = r273635 + r273646;
        double r273648 = r273634 * r273647;
        double r273649 = r273631 * r273631;
        double r273650 = -r273649;
        double r273651 = exp(r273650);
        double r273652 = r273648 * r273651;
        double r273653 = r273628 - r273652;
        return r273653;
}

↓

double f(double x) {
        double r273654 = 1.0;
        double r273655 = r273654 * r273654;
        double r273656 = 0.254829592;
        double r273657 = -0.284496736;
        double r273658 = 1.421413741;
        double r273659 = 0.3275911;
        double r273660 = x;
        double r273661 = fabs(r273660);
        double r273662 = r273659 * r273661;
        double r273663 = r273654 + r273662;
        double r273664 = r273654 / r273663;
        double r273665 = 1.061405429;
        double r273666 = r273664 * r273665;
        double r273667 = -1.453152027;
        double r273668 = r273666 + r273667;
        double r273669 = r273664 * r273668;
        double r273670 = r273658 + r273669;
        double r273671 = r273654 * r273670;
        double r273672 = r273662 + r273654;
        double r273673 = r273671 / r273672;
        double r273674 = r273657 + r273673;
        double r273675 = r273674 * r273664;
        double r273676 = r273656 + r273675;
        double r273677 = 4.0;
        double r273678 = pow(r273672, r273677);
        double r273679 = r273665 / r273678;
        double r273680 = 2.0;
        double r273681 = pow(r273672, r273680);
        double r273682 = r273658 / r273681;
        double r273683 = r273682 + r273656;
        double r273684 = 1.453152027;
        double r273685 = 3.0;
        double r273686 = pow(r273672, r273685);
        double r273687 = r273684 / r273686;
        double r273688 = r273683 - r273687;
        double r273689 = 0.284496736;
        double r273690 = r273689 / r273672;
        double r273691 = r273688 - r273690;
        double r273692 = r273679 + r273691;
        double r273693 = r273676 * r273692;
        double r273694 = pow(r273661, r273680);
        double r273695 = exp(r273694);
        double r273696 = pow(r273695, r273680);
        double r273697 = r273693 / r273696;
        double r273698 = r273655 * r273697;
        double r273699 = r273698 / r273681;
        double r273700 = r273655 - r273699;
        double r273701 = log(r273700);
        double r273702 = exp(r273701);
        double r273703 = cbrt(r273654);
        double r273704 = pow(r273703, r273685);
        double r273705 = r273704 / r273663;
        double r273706 = r273705 * r273665;
        double r273707 = r273667 + r273706;
        double r273708 = r273664 * r273707;
        double r273709 = r273658 + r273708;
        double r273710 = r273664 * r273709;
        double r273711 = r273710 + r273657;
        double r273712 = r273664 * r273711;
        double r273713 = r273712 + r273656;
        double r273714 = r273664 * r273713;
        double r273715 = r273714 / r273695;
        double r273716 = r273715 + r273654;
        double r273717 = r273702 / r273716;
        return r273717;
}

Error

Bits error versus x

Derivation

1. Initial program 13.8

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

3. Applied add-sqr-sqrt 13.8

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

4. Applied add-cube-cbrt 13.8

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

5. Applied times-frac 13.8

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

7. Applied flip-- 13.8

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

8. Simplified 13.8

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

9. Simplified 13.8

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

10. Taylor expanded around 0 14.3

    \[\leadsto \frac{1 \cdot 1 - \frac{1 \cdot 1}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{2}} \cdot \left(\frac{\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{{\left(\sqrt[3]{1}\right)}^{3}}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right) + -0.284496735999999972\right) + 0.25482959199999999}{e^{{\left(\left|x\right|\right)}^{2}}} \cdot \frac{\color{blue}{\left(1.0614054289999999 \cdot \frac{1}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{4}} + \left(1.42141374100000006 \cdot \frac{1}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}} + 0.25482959199999999\right)\right) - \left(1.45315202700000001 \cdot \frac{1}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{3}} + 0.284496735999999972 \cdot \frac{1}{0.32759110000000002 \cdot \left|x\right| + 1}\right)}}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}{\frac{\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{{\left(\sqrt[3]{1}\right)}^{3}}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right) + -0.284496735999999972\right) + 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}} + 1}\]

11. Simplified 10.6

    \[\leadsto \frac{1 \cdot 1 - \frac{1 \cdot 1}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{2}} \cdot \left(\frac{\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{{\left(\sqrt[3]{1}\right)}^{3}}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right) + -0.284496735999999972\right) + 0.25482959199999999}{e^{{\left(\left|x\right|\right)}^{2}}} \cdot \frac{\color{blue}{\frac{1.0614054289999999}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{4}} + \left(\left(\left(\frac{1.42141374100000006}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}} + 0.25482959199999999\right) - \frac{1.45315202700000001}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{3}}\right) - \frac{0.284496735999999972}{0.32759110000000002 \cdot \left|x\right| + 1}\right)}}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}{\frac{\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{{\left(\sqrt[3]{1}\right)}^{3}}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right) + -0.284496735999999972\right) + 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}} + 1}\]
12. Using strategy rm

13. Applied add-exp-log 10.6

    \[\leadsto \frac{\color{blue}{e^{\log \left(1 \cdot 1 - \frac{1 \cdot 1}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{2}} \cdot \left(\frac{\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{{\left(\sqrt[3]{1}\right)}^{3}}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right) + -0.284496735999999972\right) + 0.25482959199999999}{e^{{\left(\left|x\right|\right)}^{2}}} \cdot \frac{\frac{1.0614054289999999}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{4}} + \left(\left(\left(\frac{1.42141374100000006}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}} + 0.25482959199999999\right) - \frac{1.45315202700000001}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{3}}\right) - \frac{0.284496735999999972}{0.32759110000000002 \cdot \left|x\right| + 1}\right)}{e^{{\left(\left|x\right|\right)}^{2}}}\right)\right)}}}{\frac{\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{{\left(\sqrt[3]{1}\right)}^{3}}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right) + -0.284496735999999972\right) + 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}} + 1}\]

14. Simplified 10.6

    \[\leadsto \frac{e^{\color{blue}{\log \left(1 \cdot 1 - \frac{\left(1 \cdot 1\right) \cdot \frac{\left(0.25482959199999999 + \left(-0.284496735999999972 + \frac{1 \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999 + -1.45315202700000001\right)\right)}{0.32759110000000002 \cdot \left|x\right| + 1}\right) \cdot \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}\right) \cdot \left(\frac{1.0614054289999999}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{4}} + \left(\left(\left(\frac{1.42141374100000006}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}} + 0.25482959199999999\right) - \frac{1.45315202700000001}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{3}}\right) - \frac{0.284496735999999972}{0.32759110000000002 \cdot \left|x\right| + 1}\right)\right)}{{\left(e^{{\left(\left|x\right|\right)}^{2}}\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}\right)}}}{\frac{\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{{\left(\sqrt[3]{1}\right)}^{3}}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right) + -0.284496735999999972\right) + 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}} + 1}\]

15. Final simplification 10.6

    \[\leadsto \frac{e^{\log \left(1 \cdot 1 - \frac{\left(1 \cdot 1\right) \cdot \frac{\left(0.25482959199999999 + \left(-0.284496735999999972 + \frac{1 \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999 + -1.45315202700000001\right)\right)}{0.32759110000000002 \cdot \left|x\right| + 1}\right) \cdot \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}\right) \cdot \left(\frac{1.0614054289999999}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{4}} + \left(\left(\left(\frac{1.42141374100000006}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}} + 0.25482959199999999\right) - \frac{1.45315202700000001}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{3}}\right) - \frac{0.284496735999999972}{0.32759110000000002 \cdot \left|x\right| + 1}\right)\right)}{{\left(e^{{\left(\left|x\right|\right)}^{2}}\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}\right)}}{\frac{\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{{\left(\sqrt[3]{1}\right)}^{3}}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right) + -0.284496735999999972\right) + 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}} + 1}\]

Reproduce

herbie shell --seed 2020045 
(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)))))))