Average Error: 13.5 → 12.7
Time: 10.0s
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(\mathsf{fma}\left(\frac{\sqrt[3]{{\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)}, \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), -0.284496735999999972\right), 0.25482959199999999\right)\right)}^{3}}}{e^{\left|x\right| \cdot \left|x\right|}}, \frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1\right)\right)} \cdot \sqrt[3]{\log \left(\mathsf{fma}\left(\frac{\sqrt[3]{{\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)}, \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), -0.284496735999999972\right), 0.25482959199999999\right)\right)}^{3}}}{e^{\left|x\right| \cdot \left|x\right|}}, \frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1\right)\right)}}\right)}^{\left(\sqrt[3]{\log \left(\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}} \cdot \left(\frac{1.45315202700000001}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{4}} + \frac{0.284496735999999972}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}\right) - \left(\left(\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}} \cdot \left(\frac{0.25482959199999999}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} + \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}}\right) + \frac{\frac{1.0614054289999999}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{5}}}{e^{{\left(\left|x\right|\right)}^{2}}}\right) - 1\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(\mathsf{fma}\left(\frac{\sqrt[3]{{\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)}, \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), -0.284496735999999972\right), 0.25482959199999999\right)\right)}^{3}}}{e^{\left|x\right| \cdot \left|x\right|}}, \frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1\right)\right)} \cdot \sqrt[3]{\log \left(\mathsf{fma}\left(\frac{\sqrt[3]{{\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)}, \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), -0.284496735999999972\right), 0.25482959199999999\right)\right)}^{3}}}{e^{\left|x\right| \cdot \left|x\right|}}, \frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1\right)\right)}}\right)}^{\left(\sqrt[3]{\log \left(\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}} \cdot \left(\frac{1.45315202700000001}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{4}} + \frac{0.284496735999999972}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}\right) - \left(\left(\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}} \cdot \left(\frac{0.25482959199999999}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)} + \frac{1.42141374100000006}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{3}}\right) + \frac{\frac{1.0614054289999999}{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{5}}}{e^{{\left(\left|x\right|\right)}^{2}}}\right) - 1\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(fma((cbrt(pow(fma((1.0 / fma(fabs(x), 0.3275911, 1.0)), fma((1.0 / fma(fabs(x), 0.3275911, 1.0)), fma((1.0 / fma(fabs(x), 0.3275911, 1.0)), fma((1.0 / fma(fabs(x), 0.3275911, 1.0)), 1.061405429, -1.453152027), 1.421413741), -0.284496736), 0.254829592), 3.0)) / exp((fabs(x) * fabs(x)))), (-1.0 / fma(fabs(x), 0.3275911, 1.0)), 1.0))) * cbrt(log(fma((cbrt(pow(fma((1.0 / fma(fabs(x), 0.3275911, 1.0)), fma((1.0 / fma(fabs(x), 0.3275911, 1.0)), fma((1.0 / fma(fabs(x), 0.3275911, 1.0)), fma((1.0 / fma(fabs(x), 0.3275911, 1.0)), 1.061405429, -1.453152027), 1.421413741), -0.284496736), 0.254829592), 3.0)) / exp((fabs(x) * fabs(x)))), (-1.0 / fma(fabs(x), 0.3275911, 1.0)), 1.0))))), cbrt(log((((1.0 / exp(pow(fabs(x), 2.0))) * ((1.453152027 / pow(fma(0.3275911, fabs(x), 1.0), 4.0)) + (0.284496736 / pow(fma(0.3275911, fabs(x), 1.0), 2.0)))) - ((((1.0 / exp(pow(fabs(x), 2.0))) * ((0.254829592 / fma(0.3275911, fabs(x), 1.0)) + (1.421413741 / pow(fma(0.3275911, fabs(x), 1.0), 3.0)))) + ((1.061405429 / pow(fma(0.3275911, fabs(x), 1.0), 5.0)) / exp(pow(fabs(x), 2.0)))) - 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 13.5

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

  2. Simplified13.5

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

  4. Applied add-cbrt-cube13.5

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

  5. Simplified13.5

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

  7. Applied add-exp-log13.5

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

  9. Applied add-cube-cbrt13.5

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

  10. Applied exp-prod13.5

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

  11. Taylor expanded around 0 13.5

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

  12. Simplified12.7

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

  13. Final simplification12.7

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

Reproduce

herbie shell --seed 2020102 +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)))))))