Average Error: 13.4 → 11.8
Time: 28.8s
Precision: 64
\[1 - \left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
\[\begin{array}{l} \mathbf{if}\;x \le -1.2684304358020804 \cdot 10^{-16} \lor \neg \left(x \le 7.17410032066940479 \cdot 10^{-14}\right):\\ \;\;\;\;\mathsf{fma}\left(1, \mathsf{fma}\left(0.284496735999999972, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}, -\sqrt{\mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right)} \cdot \sqrt{\mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right)}\right) + \mathsf{fma}\left(1.45315202700000001, \frac{\frac{1}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{4}}}{e^{{\left(\left|x\right|\right)}^{2}}}, \mathsf{fma}\left(-1, \mathsf{fma}\left(\frac{1.0614054289999999}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{5}}, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}, \frac{\frac{0.25482959199999999}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right), \mathsf{fma}\left(\frac{1.0614054289999999}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{5}}, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}, \frac{\frac{0.25482959199999999}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right), \left(\mathsf{fma}\left(0.284496735999999972, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}\right) + \mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right), \left(\mathsf{fma}\left(0.284496735999999972, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}\right) \cdot \left(\mathsf{fma}\left(0.284496735999999972, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}\right)\right), \frac{1.45315202700000001}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{4}}, \left({\left(\mathsf{fma}\left(0.284496735999999972, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3} - {\left(\mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right)\right)}^{3}\right) \cdot e^{{\left(\left|x\right|\right)}^{2}}\right)}{e^{{\left(\left|x\right|\right)}^{2}} \cdot \left(\mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right) \cdot \left(\mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right) + \left(\mathsf{fma}\left(0.284496735999999972, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}\right)\right) + \left(\mathsf{fma}\left(0.284496735999999972, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}\right) \cdot \left(\mathsf{fma}\left(0.284496735999999972, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}\right)\right)}\\ \end{array}\]
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|}
\begin{array}{l}
\mathbf{if}\;x \le -1.2684304358020804 \cdot 10^{-16} \lor \neg \left(x \le 7.17410032066940479 \cdot 10^{-14}\right):\\
\;\;\;\;\mathsf{fma}\left(1, \mathsf{fma}\left(0.284496735999999972, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}, -\sqrt{\mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right)} \cdot \sqrt{\mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right)}\right) + \mathsf{fma}\left(1.45315202700000001, \frac{\frac{1}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{4}}}{e^{{\left(\left|x\right|\right)}^{2}}}, \mathsf{fma}\left(-1, \mathsf{fma}\left(\frac{1.0614054289999999}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{5}}, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}, \frac{\frac{0.25482959199999999}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right), \mathsf{fma}\left(\frac{1.0614054289999999}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{5}}, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}, \frac{\frac{0.25482959199999999}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right)\right)\right)\\

\mathbf{else}:\\
\;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right), \left(\mathsf{fma}\left(0.284496735999999972, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}\right) + \mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right), \left(\mathsf{fma}\left(0.284496735999999972, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}\right) \cdot \left(\mathsf{fma}\left(0.284496735999999972, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}\right)\right), \frac{1.45315202700000001}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{4}}, \left({\left(\mathsf{fma}\left(0.284496735999999972, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3} - {\left(\mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right)\right)}^{3}\right) \cdot e^{{\left(\left|x\right|\right)}^{2}}\right)}{e^{{\left(\left|x\right|\right)}^{2}} \cdot \left(\mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right) \cdot \left(\mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right) + \left(\mathsf{fma}\left(0.284496735999999972, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}\right)\right) + \left(\mathsf{fma}\left(0.284496735999999972, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}\right) \cdot \left(\mathsf{fma}\left(0.284496735999999972, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}\right)\right)}\\

\end{array}
double f(double x) {
        double r644 = 1.0;
        double r645 = 0.3275911;
        double r646 = x;
        double r647 = fabs(r646);
        double r648 = r645 * r647;
        double r649 = r644 + r648;
        double r650 = r644 / r649;
        double r651 = 0.254829592;
        double r652 = -0.284496736;
        double r653 = 1.421413741;
        double r654 = -1.453152027;
        double r655 = 1.061405429;
        double r656 = r650 * r655;
        double r657 = r654 + r656;
        double r658 = r650 * r657;
        double r659 = r653 + r658;
        double r660 = r650 * r659;
        double r661 = r652 + r660;
        double r662 = r650 * r661;
        double r663 = r651 + r662;
        double r664 = r650 * r663;
        double r665 = r647 * r647;
        double r666 = -r665;
        double r667 = exp(r666);
        double r668 = r664 * r667;
        double r669 = r644 - r668;
        return r669;
}

double f(double x) {
        double r670 = x;
        double r671 = -1.2684304358020804e-16;
        bool r672 = r670 <= r671;
        double r673 = 7.174100320669405e-14;
        bool r674 = r670 <= r673;
        double r675 = !r674;
        bool r676 = r672 || r675;
        double r677 = 1.0;
        double r678 = 0.284496736;
        double r679 = fabs(r670);
        double r680 = 2.0;
        double r681 = pow(r679, r680);
        double r682 = exp(r681);
        double r683 = 0.3275911;
        double r684 = r683 * r679;
        double r685 = 1.0;
        double r686 = r684 + r685;
        double r687 = pow(r686, r680);
        double r688 = r682 * r687;
        double r689 = r677 / r688;
        double r690 = fma(r678, r689, r685);
        double r691 = 1.421413741;
        double r692 = fma(r683, r679, r685);
        double r693 = 3.0;
        double r694 = pow(r692, r693);
        double r695 = r691 / r694;
        double r696 = r677 / r682;
        double r697 = r695 * r696;
        double r698 = r690 - r697;
        double r699 = 1.061405429;
        double r700 = 5.0;
        double r701 = pow(r686, r700);
        double r702 = r682 * r701;
        double r703 = r677 / r702;
        double r704 = r696 / r692;
        double r705 = 0.254829592;
        double r706 = r704 * r705;
        double r707 = fma(r699, r703, r706);
        double r708 = sqrt(r707);
        double r709 = r708 * r708;
        double r710 = -r709;
        double r711 = fma(r677, r698, r710);
        double r712 = 1.453152027;
        double r713 = 4.0;
        double r714 = pow(r692, r713);
        double r715 = r677 / r714;
        double r716 = r715 / r682;
        double r717 = -r677;
        double r718 = pow(r692, r700);
        double r719 = r699 / r718;
        double r720 = r705 / r682;
        double r721 = r720 / r692;
        double r722 = fma(r719, r696, r721);
        double r723 = fma(r717, r722, r722);
        double r724 = fma(r712, r716, r723);
        double r725 = r711 + r724;
        double r726 = r698 + r707;
        double r727 = r698 * r698;
        double r728 = fma(r707, r726, r727);
        double r729 = r712 / r714;
        double r730 = pow(r698, r693);
        double r731 = pow(r707, r693);
        double r732 = r730 - r731;
        double r733 = r732 * r682;
        double r734 = fma(r728, r729, r733);
        double r735 = r707 + r698;
        double r736 = r707 * r735;
        double r737 = r736 + r727;
        double r738 = r682 * r737;
        double r739 = r734 / r738;
        double r740 = r676 ? r725 : r739;
        return r740;
}

Error

Bits error versus x

Derivation

  1. Split input into 2 regimes
  2. if x < -1.2684304358020804e-16 or 7.174100320669405e-14 < x

    1. Initial program 0.8

      \[1 - \left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
    2. Simplified0.8

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), -0.284496735999999972\right), 0.25482959199999999\right)}{e^{\left|x\right| \cdot \left|x\right|}}, \frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1\right)}\]
    3. Taylor expanded around 0 0.8

      \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{\left(1.0614054289999999 \cdot \frac{1}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{4}} + \left(1.42141374100000006 \cdot \frac{1}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}} + 0.25482959199999999\right)\right) - \left(1.45315202700000001 \cdot \frac{1}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{3}} + 0.284496735999999972 \cdot \frac{1}{0.32759110000000002 \cdot \left|x\right| + 1}\right)}}{e^{\left|x\right| \cdot \left|x\right|}}, \frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1\right)\]
    4. Simplified0.8

      \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{\mathsf{fma}\left(1.42141374100000006, \frac{1}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 0.25482959199999999\right) - \left(\mathsf{fma}\left(0.284496735999999972, \frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \frac{1 \cdot 1.45315202700000001}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}}\right) - \frac{1 \cdot 1.0614054289999999}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{4}}\right)}}{e^{\left|x\right| \cdot \left|x\right|}}, \frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1\right)\]
    5. Taylor expanded around 0 0.9

      \[\leadsto \color{blue}{\left(1 + \left(1.45315202700000001 \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{4}} + 0.284496735999999972 \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}\right)\right) - \left(1.42141374100000006 \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{3}} + \left(1.0614054289999999 \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}} + 0.25482959199999999 \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot \left(0.32759110000000002 \cdot \left|x\right| + 1\right)}\right)\right)}\]
    6. Simplified0.8

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(0.284496735999999972, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}\right) - \mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right)\right) + \frac{\frac{1.45315202700000001}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{4}}}{e^{{\left(\left|x\right|\right)}^{2}}}}\]
    7. Using strategy rm
    8. Applied add-sqr-sqrt0.8

      \[\leadsto \left(\left(\mathsf{fma}\left(0.284496735999999972, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}\right) - \color{blue}{\sqrt{\mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right)} \cdot \sqrt{\mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right)}}\right) + \frac{\frac{1.45315202700000001}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{4}}}{e^{{\left(\left|x\right|\right)}^{2}}}\]
    9. Applied *-un-lft-identity0.8

      \[\leadsto \left(\color{blue}{1 \cdot \left(\mathsf{fma}\left(0.284496735999999972, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}\right)} - \sqrt{\mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right)} \cdot \sqrt{\mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right)}\right) + \frac{\frac{1.45315202700000001}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{4}}}{e^{{\left(\left|x\right|\right)}^{2}}}\]
    10. Applied prod-diff0.8

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(1, \mathsf{fma}\left(0.284496735999999972, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}, -\sqrt{\mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right)} \cdot \sqrt{\mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right)}\right) + \mathsf{fma}\left(-\sqrt{\mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right)}, \sqrt{\mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right)}, \sqrt{\mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right)} \cdot \sqrt{\mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right)}\right)\right)} + \frac{\frac{1.45315202700000001}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{4}}}{e^{{\left(\left|x\right|\right)}^{2}}}\]
    11. Applied associate-+l+0.8

      \[\leadsto \color{blue}{\mathsf{fma}\left(1, \mathsf{fma}\left(0.284496735999999972, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}, -\sqrt{\mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right)} \cdot \sqrt{\mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right)}\right) + \left(\mathsf{fma}\left(-\sqrt{\mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right)}, \sqrt{\mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right)}, \sqrt{\mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right)} \cdot \sqrt{\mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right)}\right) + \frac{\frac{1.45315202700000001}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{4}}}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}\]
    12. Simplified0.9

      \[\leadsto \mathsf{fma}\left(1, \mathsf{fma}\left(0.284496735999999972, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}, -\sqrt{\mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right)} \cdot \sqrt{\mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right)}\right) + \color{blue}{\mathsf{fma}\left(1.45315202700000001, \frac{\frac{1}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{4}}}{e^{{\left(\left|x\right|\right)}^{2}}}, \mathsf{fma}\left(-1, \mathsf{fma}\left(\frac{1.0614054289999999}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{5}}, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}, \frac{\frac{0.25482959199999999}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right), \mathsf{fma}\left(\frac{1.0614054289999999}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{5}}, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}, \frac{\frac{0.25482959199999999}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right)\right)\right)}\]

    if -1.2684304358020804e-16 < x < 7.174100320669405e-14

    1. Initial program 28.0

      \[1 - \left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
    2. Simplified28.0

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, \mathsf{fma}\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), -0.284496735999999972\right), 0.25482959199999999\right)}{e^{\left|x\right| \cdot \left|x\right|}}, \frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1\right)}\]
    3. Taylor expanded around 0 29.6

      \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{\left(1.0614054289999999 \cdot \frac{1}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{4}} + \left(1.42141374100000006 \cdot \frac{1}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}} + 0.25482959199999999\right)\right) - \left(1.45315202700000001 \cdot \frac{1}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{3}} + 0.284496735999999972 \cdot \frac{1}{0.32759110000000002 \cdot \left|x\right| + 1}\right)}}{e^{\left|x\right| \cdot \left|x\right|}}, \frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1\right)\]
    4. Simplified28.0

      \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{\mathsf{fma}\left(1.42141374100000006, \frac{1}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 0.25482959199999999\right) - \left(\mathsf{fma}\left(0.284496735999999972, \frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \frac{1 \cdot 1.45315202700000001}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}}\right) - \frac{1 \cdot 1.0614054289999999}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{4}}\right)}}{e^{\left|x\right| \cdot \left|x\right|}}, \frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1\right)\]
    5. Taylor expanded around 0 28.0

      \[\leadsto \color{blue}{\left(1 + \left(1.45315202700000001 \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{4}} + 0.284496735999999972 \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}\right)\right) - \left(1.42141374100000006 \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{3}} + \left(1.0614054289999999 \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}} + 0.25482959199999999 \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot \left(0.32759110000000002 \cdot \left|x\right| + 1\right)}\right)\right)}\]
    6. Simplified28.0

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(0.284496735999999972, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}\right) - \mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right)\right) + \frac{\frac{1.45315202700000001}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{4}}}{e^{{\left(\left|x\right|\right)}^{2}}}}\]
    7. Using strategy rm
    8. Applied flip3--30.3

      \[\leadsto \color{blue}{\frac{{\left(\mathsf{fma}\left(0.284496735999999972, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3} - {\left(\mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right)\right)}^{3}}{\left(\mathsf{fma}\left(0.284496735999999972, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}\right) \cdot \left(\mathsf{fma}\left(0.284496735999999972, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}\right) + \left(\mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right) \cdot \mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right) + \left(\mathsf{fma}\left(0.284496735999999972, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}\right) \cdot \mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right)\right)}} + \frac{\frac{1.45315202700000001}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{4}}}{e^{{\left(\left|x\right|\right)}^{2}}}\]
    9. Applied frac-add30.4

      \[\leadsto \color{blue}{\frac{\left({\left(\mathsf{fma}\left(0.284496735999999972, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3} - {\left(\mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right)\right)}^{3}\right) \cdot e^{{\left(\left|x\right|\right)}^{2}} + \left(\left(\mathsf{fma}\left(0.284496735999999972, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}\right) \cdot \left(\mathsf{fma}\left(0.284496735999999972, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}\right) + \left(\mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right) \cdot \mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right) + \left(\mathsf{fma}\left(0.284496735999999972, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}\right) \cdot \mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right)\right)\right) \cdot \frac{1.45315202700000001}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{4}}}{\left(\left(\mathsf{fma}\left(0.284496735999999972, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}\right) \cdot \left(\mathsf{fma}\left(0.284496735999999972, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}\right) + \left(\mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right) \cdot \mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right) + \left(\mathsf{fma}\left(0.284496735999999972, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}\right) \cdot \mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right)\right)\right) \cdot e^{{\left(\left|x\right|\right)}^{2}}}}\]
    10. Simplified24.4

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right), \left(\mathsf{fma}\left(0.284496735999999972, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}\right) + \mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right), \left(\mathsf{fma}\left(0.284496735999999972, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}\right) \cdot \left(\mathsf{fma}\left(0.284496735999999972, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}\right)\right), \frac{1.45315202700000001}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{4}}, \left({\left(\mathsf{fma}\left(0.284496735999999972, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3} - {\left(\mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right)\right)}^{3}\right) \cdot e^{{\left(\left|x\right|\right)}^{2}}\right)}}{\left(\left(\mathsf{fma}\left(0.284496735999999972, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}\right) \cdot \left(\mathsf{fma}\left(0.284496735999999972, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}\right) + \left(\mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right) \cdot \mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right) + \left(\mathsf{fma}\left(0.284496735999999972, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}\right) \cdot \mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right)\right)\right) \cdot e^{{\left(\left|x\right|\right)}^{2}}}\]
    11. Simplified24.4

      \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right), \left(\mathsf{fma}\left(0.284496735999999972, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}\right) + \mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right), \left(\mathsf{fma}\left(0.284496735999999972, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}\right) \cdot \left(\mathsf{fma}\left(0.284496735999999972, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}\right)\right), \frac{1.45315202700000001}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{4}}, \left({\left(\mathsf{fma}\left(0.284496735999999972, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3} - {\left(\mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right)\right)}^{3}\right) \cdot e^{{\left(\left|x\right|\right)}^{2}}\right)}{\color{blue}{e^{{\left(\left|x\right|\right)}^{2}} \cdot \left(\mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right) \cdot \left(\mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right) + \left(\mathsf{fma}\left(0.284496735999999972, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}\right)\right) + \left(\mathsf{fma}\left(0.284496735999999972, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}\right) \cdot \left(\mathsf{fma}\left(0.284496735999999972, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}\right)\right)}}\]
  3. Recombined 2 regimes into one program.
  4. Final simplification11.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.2684304358020804 \cdot 10^{-16} \lor \neg \left(x \le 7.17410032066940479 \cdot 10^{-14}\right):\\ \;\;\;\;\mathsf{fma}\left(1, \mathsf{fma}\left(0.284496735999999972, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}, -\sqrt{\mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right)} \cdot \sqrt{\mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right)}\right) + \mathsf{fma}\left(1.45315202700000001, \frac{\frac{1}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{4}}}{e^{{\left(\left|x\right|\right)}^{2}}}, \mathsf{fma}\left(-1, \mathsf{fma}\left(\frac{1.0614054289999999}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{5}}, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}, \frac{\frac{0.25482959199999999}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right), \mathsf{fma}\left(\frac{1.0614054289999999}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{5}}, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}, \frac{\frac{0.25482959199999999}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right), \left(\mathsf{fma}\left(0.284496735999999972, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}\right) + \mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right), \left(\mathsf{fma}\left(0.284496735999999972, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}\right) \cdot \left(\mathsf{fma}\left(0.284496735999999972, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}\right)\right), \frac{1.45315202700000001}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{4}}, \left({\left(\mathsf{fma}\left(0.284496735999999972, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3} - {\left(\mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right)\right)}^{3}\right) \cdot e^{{\left(\left|x\right|\right)}^{2}}\right)}{e^{{\left(\left|x\right|\right)}^{2}} \cdot \left(\mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right) \cdot \left(\mathsf{fma}\left(1.0614054289999999, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, \frac{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} \cdot 0.25482959199999999\right) + \left(\mathsf{fma}\left(0.284496735999999972, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}\right)\right) + \left(\mathsf{fma}\left(0.284496735999999972, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}\right) \cdot \left(\mathsf{fma}\left(0.284496735999999972, \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right) - \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}} \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}\right)\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2020025 +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)))))))