Jmat.Real.erf

Average Error: 13.9 → 13.1

Time: 12.9s

Precision: 64

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

Math

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

↓

\[\left(\sqrt{1} + \sqrt{\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)} \cdot \frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}\right) \cdot \frac{\left(\sqrt[3]{1 - \frac{1 \cdot \frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}} \cdot \sqrt[3]{1 - \frac{1 \cdot \frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}}\right) \cdot \sqrt[3]{\left(1 - \frac{1}{\frac{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}{\frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}}\right) + \frac{1}{\frac{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}{\frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}} \cdot 0}}{\sqrt{1} + \sqrt{\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)} \cdot \frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}}\]

C

double f(double x) {
        double r193598 = 1.0;
        double r193599 = 0.3275911;
        double r193600 = x;
        double r193601 = fabs(r193600);
        double r193602 = r193599 * r193601;
        double r193603 = r193598 + r193602;
        double r193604 = r193598 / r193603;
        double r193605 = 0.254829592;
        double r193606 = -0.284496736;
        double r193607 = 1.421413741;
        double r193608 = -1.453152027;
        double r193609 = 1.061405429;
        double r193610 = r193604 * r193609;
        double r193611 = r193608 + r193610;
        double r193612 = r193604 * r193611;
        double r193613 = r193607 + r193612;
        double r193614 = r193604 * r193613;
        double r193615 = r193606 + r193614;
        double r193616 = r193604 * r193615;
        double r193617 = r193605 + r193616;
        double r193618 = r193604 * r193617;
        double r193619 = r193601 * r193601;
        double r193620 = -r193619;
        double r193621 = exp(r193620);
        double r193622 = r193618 * r193621;
        double r193623 = r193598 - r193622;
        return r193623;
}

↓

double f(double x) {
        double r193624 = 1.0;
        double r193625 = sqrt(r193624);
        double r193626 = x;
        double r193627 = fabs(r193626);
        double r193628 = 0.3275911;
        double r193629 = fma(r193627, r193628, r193624);
        double r193630 = r193624 / r193629;
        double r193631 = 1.061405429;
        double r193632 = -1.453152027;
        double r193633 = fma(r193630, r193631, r193632);
        double r193634 = 1.421413741;
        double r193635 = fma(r193630, r193633, r193634);
        double r193636 = -0.284496736;
        double r193637 = fma(r193635, r193630, r193636);
        double r193638 = 0.254829592;
        double r193639 = fma(r193630, r193637, r193638);
        double r193640 = 2.0;
        double r193641 = pow(r193627, r193640);
        double r193642 = exp(r193641);
        double r193643 = r193639 / r193642;
        double r193644 = r193630 * r193643;
        double r193645 = sqrt(r193644);
        double r193646 = r193625 + r193645;
        double r193647 = r193624 * r193643;
        double r193648 = r193647 / r193629;
        double r193649 = r193624 - r193648;
        double r193650 = cbrt(r193649);
        double r193651 = r193650 * r193650;
        double r193652 = r193629 / r193643;
        double r193653 = r193624 / r193652;
        double r193654 = r193624 - r193653;
        double r193655 = 0.0;
        double r193656 = r193653 * r193655;
        double r193657 = r193654 + r193656;
        double r193658 = cbrt(r193657);
        double r193659 = r193651 * r193658;
        double r193660 = r193659 / r193646;
        double r193661 = r193646 * r193660;
        return r193661;
}

Error

Bits error versus x

Derivation

1. Initial program 13.9

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

2. Simplified 13.9

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

4. Applied add-sqr-sqrt 13.9

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

5. Applied add-sqr-sqrt 13.9

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

6. Applied difference-of-squares 13.9

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

7. Simplified 13.9

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

8. Simplified 13.9

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

10. Applied flip-- 13.9

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

11. Simplified 13.9

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

13. Applied add-cube-cbrt 13.9

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

15. Applied add-cube-cbrt 14.5

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

16. Applied add-sqr-sqrt 14.5

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

17. Applied prod-diff 14.5

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

18. Simplified 13.1

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

19. Simplified 13.1

    \[\leadsto \left(\sqrt{1} + \sqrt{\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)} \cdot \frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}\right) \cdot \frac{\left(\sqrt[3]{1 - \frac{1 \cdot \frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}} \cdot \sqrt[3]{1 - \frac{1 \cdot \frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}}\right) \cdot \sqrt[3]{\left(1 - \frac{1}{\frac{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}{\frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}}\right) + \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}{\frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}} \cdot 0}}}{\sqrt{1} + \sqrt{\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)} \cdot \frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}}\]

20. Final simplification 13.1

    \[\leadsto \left(\sqrt{1} + \sqrt{\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)} \cdot \frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}\right) \cdot \frac{\left(\sqrt[3]{1 - \frac{1 \cdot \frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}} \cdot \sqrt[3]{1 - \frac{1 \cdot \frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}}\right) \cdot \sqrt[3]{\left(1 - \frac{1}{\frac{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}{\frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}}\right) + \frac{1}{\frac{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}{\frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}} \cdot 0}}{\sqrt{1} + \sqrt{\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)} \cdot \frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}}\]

Reproduce

herbie shell --seed 2020046 +o rules:numerics
(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)))))))