Average Error: 13.6 → 12.7
Time: 19.3s
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{\frac{{\left({1}^{3}\right)}^{3} - {\left(\sqrt{{\left(\left(\frac{1}{1 \cdot 1 - \left(0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(0.32759110000000002 \cdot \left|x\right|\right)} \cdot \mathsf{fma}\left(1 - 0.32759110000000002 \cdot \left|x\right|, \mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right), 0.25482959199999999 \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}} \cdot \sqrt{{\left(\left(\frac{1}{1 \cdot 1 - \left(0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(0.32759110000000002 \cdot \left|x\right|\right)} \cdot \mathsf{fma}\left(1 - 0.32759110000000002 \cdot \left|x\right|, \mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right), 0.25482959199999999 \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}}\right)}^{3}}{\mathsf{fma}\left({\left(\left(\frac{1}{1 \cdot 1 - \left(0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(0.32759110000000002 \cdot \left|x\right|\right)} \cdot \mathsf{fma}\left(1 - 0.32759110000000002 \cdot \left|x\right|, \mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right), 0.25482959199999999 \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}, {\left(\left(\frac{1}{1 \cdot 1 - \left(0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(0.32759110000000002 \cdot \left|x\right|\right)} \cdot \mathsf{fma}\left(1 - 0.32759110000000002 \cdot \left|x\right|, \mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right), 0.25482959199999999 \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3} + {1}^{3}, {1}^{6}\right)}}{\frac{\frac{\left(\left(1 - 0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(\mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right) + 0.25482959199999999\right)\right) \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right) \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)}}{e^{{\left(\left|x\right|\right)}^{2}}} \cdot \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right) \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)}, \frac{\left(\left(1 - 0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(\mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right) + 0.25482959199999999\right)\right) \cdot 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{\frac{{\left({1}^{3}\right)}^{3} - {\left(\sqrt{{\left(\left(\frac{1}{1 \cdot 1 - \left(0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(0.32759110000000002 \cdot \left|x\right|\right)} \cdot \mathsf{fma}\left(1 - 0.32759110000000002 \cdot \left|x\right|, \mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right), 0.25482959199999999 \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}} \cdot \sqrt{{\left(\left(\frac{1}{1 \cdot 1 - \left(0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(0.32759110000000002 \cdot \left|x\right|\right)} \cdot \mathsf{fma}\left(1 - 0.32759110000000002 \cdot \left|x\right|, \mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right), 0.25482959199999999 \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}}\right)}^{3}}{\mathsf{fma}\left({\left(\left(\frac{1}{1 \cdot 1 - \left(0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(0.32759110000000002 \cdot \left|x\right|\right)} \cdot \mathsf{fma}\left(1 - 0.32759110000000002 \cdot \left|x\right|, \mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right), 0.25482959199999999 \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}, {\left(\left(\frac{1}{1 \cdot 1 - \left(0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(0.32759110000000002 \cdot \left|x\right|\right)} \cdot \mathsf{fma}\left(1 - 0.32759110000000002 \cdot \left|x\right|, \mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right), 0.25482959199999999 \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3} + {1}^{3}, {1}^{6}\right)}}{\frac{\frac{\left(\left(1 - 0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(\mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right) + 0.25482959199999999\right)\right) \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right) \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)}}{e^{{\left(\left|x\right|\right)}^{2}}} \cdot \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right) \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)}, \frac{\left(\left(1 - 0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(\mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right) + 0.25482959199999999\right)\right) \cdot 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(pow(1.0, 3.0), 3.0) - pow((sqrt(pow((((1.0 / ((1.0 * 1.0) - ((0.3275911 * fabs(x)) * (0.3275911 * fabs(x))))) * fma((1.0 - (0.3275911 * fabs(x))), fma((1.0 / (pow(fma(0.3275911, fabs(x), 1.0), 2.0) / 1.0)), fma((1.0 / fma(0.3275911, fabs(x), 1.0)), fma((1.0 / fma(0.3275911, fabs(x), 1.0)), 1.061405429, -1.453152027), 1.421413741), ((-0.284496736 * 1.0) / fma(0.3275911, fabs(x), 1.0))), (0.254829592 * (1.0 - (0.3275911 * fabs(x)))))) * exp(-(fabs(x) * fabs(x)))), 3.0)) * sqrt(pow((((1.0 / ((1.0 * 1.0) - ((0.3275911 * fabs(x)) * (0.3275911 * fabs(x))))) * fma((1.0 - (0.3275911 * fabs(x))), fma((1.0 / (pow(fma(0.3275911, fabs(x), 1.0), 2.0) / 1.0)), fma((1.0 / fma(0.3275911, fabs(x), 1.0)), fma((1.0 / fma(0.3275911, fabs(x), 1.0)), 1.061405429, -1.453152027), 1.421413741), ((-0.284496736 * 1.0) / fma(0.3275911, fabs(x), 1.0))), (0.254829592 * (1.0 - (0.3275911 * fabs(x)))))) * exp(-(fabs(x) * fabs(x)))), 3.0))), 3.0)) / fma(pow((((1.0 / ((1.0 * 1.0) - ((0.3275911 * fabs(x)) * (0.3275911 * fabs(x))))) * fma((1.0 - (0.3275911 * fabs(x))), fma((1.0 / (pow(fma(0.3275911, fabs(x), 1.0), 2.0) / 1.0)), fma((1.0 / fma(0.3275911, fabs(x), 1.0)), fma((1.0 / fma(0.3275911, fabs(x), 1.0)), 1.061405429, -1.453152027), 1.421413741), ((-0.284496736 * 1.0) / fma(0.3275911, fabs(x), 1.0))), (0.254829592 * (1.0 - (0.3275911 * fabs(x)))))) * exp(-(fabs(x) * fabs(x)))), 3.0), (pow((((1.0 / ((1.0 * 1.0) - ((0.3275911 * fabs(x)) * (0.3275911 * fabs(x))))) * fma((1.0 - (0.3275911 * fabs(x))), fma((1.0 / (pow(fma(0.3275911, fabs(x), 1.0), 2.0) / 1.0)), fma((1.0 / fma(0.3275911, fabs(x), 1.0)), fma((1.0 / fma(0.3275911, fabs(x), 1.0)), 1.061405429, -1.453152027), 1.421413741), ((-0.284496736 * 1.0) / fma(0.3275911, fabs(x), 1.0))), (0.254829592 * (1.0 - (0.3275911 * fabs(x)))))) * exp(-(fabs(x) * fabs(x)))), 3.0) + pow(1.0, 3.0)), pow(1.0, 6.0))) / (((((((1.0 - (0.3275911 * fabs(x))) * (fma((1.0 / (pow(fma(0.3275911, fabs(x), 1.0), 2.0) / 1.0)), fma((1.0 / fma(0.3275911, fabs(x), 1.0)), fma((1.0 / fma(0.3275911, fabs(x), 1.0)), 1.061405429, -1.453152027), 1.421413741), ((-0.284496736 * 1.0) / fma(0.3275911, fabs(x), 1.0))) + 0.254829592)) * 1.0) / (fma(0.3275911, fabs(x), 1.0) * (1.0 - (0.3275911 * fabs(x))))) / exp(pow(fabs(x), 2.0))) * fma((1.0 / (fma(0.3275911, fabs(x), 1.0) * (1.0 - (0.3275911 * fabs(x))))), ((((1.0 - (0.3275911 * fabs(x))) * (fma((1.0 / (pow(fma(0.3275911, fabs(x), 1.0), 2.0) / 1.0)), fma((1.0 / fma(0.3275911, fabs(x), 1.0)), fma((1.0 / fma(0.3275911, fabs(x), 1.0)), 1.061405429, -1.453152027), 1.421413741), ((-0.284496736 * 1.0) / fma(0.3275911, fabs(x), 1.0))) + 0.254829592)) * 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 13.6

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

  3. Applied flip-+13.6

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

  4. Applied associate-/r/13.6

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

  5. Applied associate-*l*13.6

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

  6. Simplified13.6

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

  8. Applied flip3--13.6

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

  9. Simplified13.6

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

  11. Applied add-sqr-sqrt12.8

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

  13. Applied flip3--12.7

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

  14. Simplified12.7

    \[\leadsto \frac{\frac{{\left({1}^{3}\right)}^{3} - {\left(\sqrt{{\left(\left(\frac{1}{1 \cdot 1 - \left(0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(0.32759110000000002 \cdot \left|x\right|\right)} \cdot \mathsf{fma}\left(1 - 0.32759110000000002 \cdot \left|x\right|, \mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right), 0.25482959199999999 \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}} \cdot \sqrt{{\left(\left(\frac{1}{1 \cdot 1 - \left(0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(0.32759110000000002 \cdot \left|x\right|\right)} \cdot \mathsf{fma}\left(1 - 0.32759110000000002 \cdot \left|x\right|, \mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right), 0.25482959199999999 \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}}\right)}^{3}}{\color{blue}{\mathsf{fma}\left({\left(\left(\frac{1}{1 \cdot 1 - \left(0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(0.32759110000000002 \cdot \left|x\right|\right)} \cdot \mathsf{fma}\left(1 - 0.32759110000000002 \cdot \left|x\right|, \mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right), 0.25482959199999999 \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}, {\left(\left(\frac{1}{1 \cdot 1 - \left(0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(0.32759110000000002 \cdot \left|x\right|\right)} \cdot \mathsf{fma}\left(1 - 0.32759110000000002 \cdot \left|x\right|, \mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right), 0.25482959199999999 \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3} + {1}^{3}, {1}^{6}\right)}}}{\frac{\frac{\left(\left(1 - 0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(\mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right) + 0.25482959199999999\right)\right) \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right) \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)}}{e^{{\left(\left|x\right|\right)}^{2}}} \cdot \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right) \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)}, \frac{\left(\left(1 - 0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(\mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right) + 0.25482959199999999\right)\right) \cdot 1}{e^{{\left(\left|x\right|\right)}^{2}}}, 1\right) + 1 \cdot 1}\]

  15. Final simplification12.7

    \[\leadsto \frac{\frac{{\left({1}^{3}\right)}^{3} - {\left(\sqrt{{\left(\left(\frac{1}{1 \cdot 1 - \left(0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(0.32759110000000002 \cdot \left|x\right|\right)} \cdot \mathsf{fma}\left(1 - 0.32759110000000002 \cdot \left|x\right|, \mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right), 0.25482959199999999 \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}} \cdot \sqrt{{\left(\left(\frac{1}{1 \cdot 1 - \left(0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(0.32759110000000002 \cdot \left|x\right|\right)} \cdot \mathsf{fma}\left(1 - 0.32759110000000002 \cdot \left|x\right|, \mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right), 0.25482959199999999 \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}}\right)}^{3}}{\mathsf{fma}\left({\left(\left(\frac{1}{1 \cdot 1 - \left(0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(0.32759110000000002 \cdot \left|x\right|\right)} \cdot \mathsf{fma}\left(1 - 0.32759110000000002 \cdot \left|x\right|, \mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right), 0.25482959199999999 \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}, {\left(\left(\frac{1}{1 \cdot 1 - \left(0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(0.32759110000000002 \cdot \left|x\right|\right)} \cdot \mathsf{fma}\left(1 - 0.32759110000000002 \cdot \left|x\right|, \mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right), 0.25482959199999999 \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3} + {1}^{3}, {1}^{6}\right)}}{\frac{\frac{\left(\left(1 - 0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(\mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right) + 0.25482959199999999\right)\right) \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right) \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)}}{e^{{\left(\left|x\right|\right)}^{2}}} \cdot \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right) \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)}, \frac{\left(\left(1 - 0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(\mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right) + 0.25482959199999999\right)\right) \cdot 1}{e^{{\left(\left|x\right|\right)}^{2}}}, 1\right) + 1 \cdot 1}\]

Reproduce

herbie shell --seed 2020049 +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)))))))