Average Error: 13.9 → 13.1
Time: 15.7s
Precision: 64
\[1 - \left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
↓
\[\sqrt[3]{\log \left(e^{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}, \frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1\right)}\right)} \cdot \left(\sqrt[3]{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}, \frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1\right)} \cdot \sqrt[3]{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}, \frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1\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|}
↓
\sqrt[3]{\log \left(e^{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}, \frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1\right)}\right)} \cdot \left(\sqrt[3]{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}, \frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1\right)} \cdot \sqrt[3]{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}, \frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1\right)}\right)
double f(double x) {
        double r213138 = 1.0;
        double r213139 = 0.3275911;
        double r213140 = x;
        double r213141 = fabs(r213140);
        double r213142 = r213139 * r213141;
        double r213143 = r213138 + r213142;
        double r213144 = r213138 / r213143;
        double r213145 = 0.254829592;
        double r213146 = -0.284496736;
        double r213147 = 1.421413741;
        double r213148 = -1.453152027;
        double r213149 = 1.061405429;
        double r213150 = r213144 * r213149;
        double r213151 = r213148 + r213150;
        double r213152 = r213144 * r213151;
        double r213153 = r213147 + r213152;
        double r213154 = r213144 * r213153;
        double r213155 = r213146 + r213154;
        double r213156 = r213144 * r213155;
        double r213157 = r213145 + r213156;
        double r213158 = r213144 * r213157;
        double r213159 = r213141 * r213141;
        double r213160 = -r213159;
        double r213161 = exp(r213160);
        double r213162 = r213158 * r213161;
        double r213163 = r213138 - r213162;
        return r213163;
}
↓
double f(double x) {
        double r213164 = 1.0;
        double r213165 = x;
        double r213166 = fabs(r213165);
        double r213167 = 0.3275911;
        double r213168 = fma(r213166, r213167, r213164);
        double r213169 = r213164 / r213168;
        double r213170 = 1.061405429;
        double r213171 = -1.453152027;
        double r213172 = fma(r213169, r213170, r213171);
        double r213173 = 1.421413741;
        double r213174 = fma(r213169, r213172, r213173);
        double r213175 = -0.284496736;
        double r213176 = fma(r213169, r213174, r213175);
        double r213177 = 0.254829592;
        double r213178 = fma(r213169, r213176, r213177);
        double r213179 = 2.0;
        double r213180 = pow(r213166, r213179);
        double r213181 = exp(r213180);
        double r213182 = r213178 / r213181;
        double r213183 = -r213164;
        double r213184 = r213183 / r213168;
        double r213185 = fma(r213182, r213184, r213164);
        double r213186 = exp(r213185);
        double r213187 = log(r213186);
        double r213188 = cbrt(r213187);
        double r213189 = cbrt(r213185);
        double r213190 = r213189 * r213189;
        double r213191 = r213188 * r213190;
        return r213191;
}

Error

Bits error versus x

Derivation

  1. Initial program 13.9

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

  2. Simplified13.9

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

  4. Applied add-log-exp13.9

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

  5. Simplified13.9

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

  7. Applied add-cube-cbrt13.9

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

  9. Applied add-cube-cbrt13.9

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

  10. Applied exp-prod13.9

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

  11. Applied log-pow13.9

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

  12. Simplified13.9

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

  14. Applied add-log-exp13.1

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

  15. Simplified13.1

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

  16. Final simplification13.1

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

Reproduce

herbie shell --seed 2020046 +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)))))))