Average Error: 14.2 → 14.2
Time: 24.4s
Precision: 64
\[1 - \left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
↓
\[\mathsf{fma}\left(\frac{\sqrt{1}}{\sqrt{1 + 0.32759110000000002 \cdot \left|x\right|}}, \sqrt{0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right)\right)} \cdot \sqrt{e^{-\left|x\right| \cdot \left|x\right|}}, \sqrt{1}\right) \cdot e^{\log \left(\sqrt{1} - \left(\frac{\sqrt{1}}{\sqrt{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \sqrt{0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right)\right)}\right) \cdot \sqrt{e^{-\left|x\right| \cdot \left|x\right|}}\right)}\]
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|}
↓
\mathsf{fma}\left(\frac{\sqrt{1}}{\sqrt{1 + 0.32759110000000002 \cdot \left|x\right|}}, \sqrt{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)} \cdot \sqrt{e^{-\left|x\right| \cdot \left|x\right|}}, \sqrt{1}\right) \cdot e^{\log \left(\sqrt{1} - \left(\frac{\sqrt{1}}{\sqrt{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \sqrt{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) \cdot \sqrt{e^{-\left|x\right| \cdot \left|x\right|}}\right)}
double code(double x) {
	return ((double) (1.0 - ((double) (((double) (((double) (1.0 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x)))))))) * ((double) (0.254829592 + ((double) (((double) (1.0 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x)))))))) * ((double) (-0.284496736 + ((double) (((double) (1.0 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x)))))))) * ((double) (1.421413741 + ((double) (((double) (1.0 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x)))))))) * ((double) (-1.453152027 + ((double) (((double) (1.0 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x)))))))) * 1.061405429)))))))))))))))))) * ((double) exp(((double) -(((double) (((double) fabs(x)) * ((double) fabs(x))))))))))));
}
↓
double code(double x) {
	return ((double) (((double) fma(((double) (((double) sqrt(1.0)) / ((double) sqrt(((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x)))))))))), ((double) (((double) sqrt(((double) (0.254829592 + ((double) (((double) (1.0 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x)))))))) * ((double) (-0.284496736 + ((double) (((double) (1.0 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x)))))))) * ((double) (1.421413741 + ((double) (((double) (1.0 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x)))))))) * ((double) (-1.453152027 + ((double) (((double) (1.0 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x)))))))) * 1.061405429)))))))))))))))))) * ((double) sqrt(((double) exp(((double) -(((double) (((double) fabs(x)) * ((double) fabs(x)))))))))))), ((double) sqrt(1.0)))) * ((double) exp(((double) log(((double) (((double) sqrt(1.0)) - ((double) (((double) (((double) (((double) sqrt(1.0)) / ((double) sqrt(((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x)))))))))) * ((double) sqrt(((double) (0.254829592 + ((double) (((double) (1.0 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x)))))))) * ((double) (-0.284496736 + ((double) (((double) (1.0 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x)))))))) * ((double) (1.421413741 + ((double) (((double) (1.0 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x)))))))) * ((double) (-1.453152027 + ((double) (((double) (1.0 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x)))))))) * 1.061405429)))))))))))))))))))) * ((double) sqrt(((double) exp(((double) -(((double) (((double) fabs(x)) * ((double) fabs(x))))))))))))))))))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.2

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

  3. Applied add-sqr-sqrt14.2

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

  4. Applied add-sqr-sqrt14.2

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

  5. Applied add-sqr-sqrt14.2

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

  6. Applied add-sqr-sqrt14.2

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

  7. Applied times-frac14.2

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

  8. Applied unswap-sqr14.2

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

  9. Applied unswap-sqr14.2

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

  10. Applied add-sqr-sqrt14.2

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

  11. Applied difference-of-squares14.2

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

  12. Simplified14.2

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

  14. Applied add-exp-log14.2

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

  15. Final simplification14.2

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

Reproduce

herbie shell --seed 2020113 +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)))))))