Average Error: 13.8 → 13.1
Time: 11.5s
Precision: 64
\[1 - \left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
↓
\[{\left(e^{\sqrt[3]{\log \left(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 + \sqrt[3]{{\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right)}^{3}} \cdot 1.0614054289999999\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)} \cdot \sqrt[3]{\log \left(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 + \sqrt[3]{{\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right)}^{3}} \cdot 1.0614054289999999\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}}\right)}^{\left(\sqrt[3]{\log \left(\mathsf{fma}\left(1.45315202700000001, \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{4}}, \mathsf{fma}\left(0.284496735999999972, \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right)\right) - \mathsf{fma}\left(\frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, 1.0614054289999999, \mathsf{fma}\left(\frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{3}}, 1.42141374100000006, \frac{0.25482959199999999 \cdot e^{-{\left(\left|x\right|\right)}^{2}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right)\right)\right)}\right)}\]
1 - \left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \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(e^{\sqrt[3]{\log \left(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 + \sqrt[3]{{\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right)}^{3}} \cdot 1.0614054289999999\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)} \cdot \sqrt[3]{\log \left(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 + \sqrt[3]{{\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right)}^{3}} \cdot 1.0614054289999999\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}}\right)}^{\left(\sqrt[3]{\log \left(\mathsf{fma}\left(1.45315202700000001, \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{4}}, \mathsf{fma}\left(0.284496735999999972, \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}, 1\right)\right) - \mathsf{fma}\left(\frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{5}}, 1.0614054289999999, \mathsf{fma}\left(\frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{3}}, 1.42141374100000006, \frac{0.25482959199999999 \cdot e^{-{\left(\left|x\right|\right)}^{2}}}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right)\right)\right)}\right)}
double code(double x) {
	return (1.0 - (((1.0 / (1.0 + (0.3275911 * fabs(x)))) * (0.254829592 + ((1.0 / (1.0 + (0.3275911 * fabs(x)))) * (-0.284496736 + ((1.0 / (1.0 + (0.3275911 * fabs(x)))) * (1.421413741 + ((1.0 / (1.0 + (0.3275911 * fabs(x)))) * (-1.453152027 + ((1.0 / (1.0 + (0.3275911 * fabs(x)))) * 1.061405429))))))))) * exp(-(fabs(x) * fabs(x)))));
}
↓
double code(double x) {
	return pow(exp((cbrt(log((1.0 - (((1.0 / (1.0 + (0.3275911 * fabs(x)))) * (0.254829592 + ((1.0 / (1.0 + (0.3275911 * fabs(x)))) * (-0.284496736 + ((1.0 / (1.0 + (0.3275911 * fabs(x)))) * (1.421413741 + ((1.0 / (1.0 + (0.3275911 * fabs(x)))) * (-1.453152027 + (cbrt(pow((1.0 / fma(0.3275911, fabs(x), 1.0)), 3.0)) * 1.061405429))))))))) * exp(-(fabs(x) * fabs(x))))))) * cbrt(log((1.0 - (((1.0 / (1.0 + (0.3275911 * fabs(x)))) * (0.254829592 + ((1.0 / (1.0 + (0.3275911 * fabs(x)))) * (-0.284496736 + ((1.0 / (1.0 + (0.3275911 * fabs(x)))) * (1.421413741 + ((1.0 / (1.0 + (0.3275911 * fabs(x)))) * (-1.453152027 + (cbrt(pow((1.0 / fma(0.3275911, fabs(x), 1.0)), 3.0)) * 1.061405429))))))))) * exp(-(fabs(x) * fabs(x))))))))), cbrt(log((fma(1.453152027, (exp(-pow(fabs(x), 2.0)) / pow(((0.3275911 * fabs(x)) + 1.0), 4.0)), fma(0.284496736, (exp(-pow(fabs(x), 2.0)) / pow(((0.3275911 * fabs(x)) + 1.0), 2.0)), 1.0)) - fma((exp(-pow(fabs(x), 2.0)) / pow(((0.3275911 * fabs(x)) + 1.0), 5.0)), 1.061405429, fma((exp(-pow(fabs(x), 2.0)) / pow(((0.3275911 * fabs(x)) + 1.0), 3.0)), 1.421413741, ((0.254829592 * exp(-pow(fabs(x), 2.0))) / fma(0.3275911, fabs(x), 1.0))))))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 13.8

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

  3. Applied add-cbrt-cube13.8

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

  4. Applied add-cbrt-cube13.8

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

  5. Applied cbrt-undiv13.8

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

  6. Simplified13.8

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

  8. Applied add-exp-log13.8

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

  10. Applied add-cube-cbrt13.8

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

  11. Applied exp-prod13.8

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

  12. Taylor expanded around 0 13.1

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

  13. Simplified13.1

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

  14. Final simplification13.1

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

Reproduce

herbie shell --seed 2020105 +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)))))))