Average Error: 13.8 → 13.8
Time: 10.8s
Precision: 64
\[1 - \left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
↓
\[\frac{{1}^{3} + {\left(\left(-\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \sqrt[3]{{\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}\right)}^{3}} \cdot 1.0614054289999999\right)\right)\right)\right)\right) \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}}{\left(\left(-\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \sqrt[3]{{\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}\right)}^{3}} \cdot 1.0614054289999999\right)\right)\right)\right)\right) \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}\right) \cdot \left(\left(-\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \sqrt[3]{{\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}\right)}^{3}} \cdot 1.0614054289999999\right)\right)\right)\right)\right) \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}} - 1\right) + 1 \cdot 1}\]
1 - \left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}
↓
\frac{{1}^{3} + {\left(\left(-\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \sqrt[3]{{\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}\right)}^{3}} \cdot 1.0614054289999999\right)\right)\right)\right)\right) \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}}{\left(\left(-\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \sqrt[3]{{\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}\right)}^{3}} \cdot 1.0614054289999999\right)\right)\right)\right)\right) \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}\right) \cdot \left(\left(-\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \sqrt[3]{{\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}\right)}^{3}} \cdot 1.0614054289999999\right)\right)\right)\right)\right) \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}}} - 1\right) + 1 \cdot 1}
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(1.0, 3.0) + pow((-((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 / (1.0 + (0.3275911 * fabs(x)))), 3.0)) * 1.061405429))))))))) * (1.0 / exp(pow(fabs(x), 2.0)))), 3.0)) / (((-((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 / (1.0 + (0.3275911 * fabs(x)))), 3.0)) * 1.061405429))))))))) * (1.0 / exp(pow(fabs(x), 2.0)))) * ((-((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 / (1.0 + (0.3275911 * fabs(x)))), 3.0)) * 1.061405429))))))))) * (1.0 / exp(pow(fabs(x), 2.0)))) - 1.0)) + (1.0 * 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 13.8

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

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

  8. Applied add-exp-log13.8

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

  10. Applied sub-neg13.8

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

  11. Simplified13.8

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

  13. Applied flip3-+13.8

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

  14. Applied log-div13.8

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

  15. Applied exp-diff13.8

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

  16. Simplified13.8

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

  17. Simplified13.8

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

  18. Final simplification13.8

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

Reproduce

herbie shell --seed 2020105 
(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)))))))