Average Error: 0.0 → 0.1
Time: 23.8s
Precision: 64
\[x \cdot e^{y \cdot y}\]
↓
\[\left(x \cdot \left(\left|\sqrt[3]{e^{y \cdot y}}\right| \cdot \sqrt{\left(\sqrt[3]{\sqrt[3]{e^{y \cdot y}}} \cdot \sqrt[3]{\sqrt[3]{e^{y \cdot y}}}\right) \cdot \sqrt[3]{\sqrt[3]{e^{y \cdot y}}}}\right)\right) \cdot \sqrt{e^{y \cdot y}}\]
x \cdot e^{y \cdot y}
↓
\left(x \cdot \left(\left|\sqrt[3]{e^{y \cdot y}}\right| \cdot \sqrt{\left(\sqrt[3]{\sqrt[3]{e^{y \cdot y}}} \cdot \sqrt[3]{\sqrt[3]{e^{y \cdot y}}}\right) \cdot \sqrt[3]{\sqrt[3]{e^{y \cdot y}}}}\right)\right) \cdot \sqrt{e^{y \cdot y}}
double f(double x, double y) {
        double r507858 = x;
        double r507859 = y;
        double r507860 = r507859 * r507859;
        double r507861 = exp(r507860);
        double r507862 = r507858 * r507861;
        return r507862;
}
↓
double f(double x, double y) {
        double r507863 = x;
        double r507864 = y;
        double r507865 = r507864 * r507864;
        double r507866 = exp(r507865);
        double r507867 = cbrt(r507866);
        double r507868 = fabs(r507867);
        double r507869 = cbrt(r507867);
        double r507870 = r507869 * r507869;
        double r507871 = r507870 * r507869;
        double r507872 = sqrt(r507871);
        double r507873 = r507868 * r507872;
        double r507874 = r507863 * r507873;
        double r507875 = sqrt(r507866);
        double r507876 = r507874 * r507875;
        return r507876;
}

Error

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Results

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Target

Original0.0
Target0.0
Herbie0.1
\[x \cdot {\left(e^{y}\right)}^{y}\]

Derivation

  1. Initial program 0.0

    \[x \cdot e^{y \cdot y}\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt0.0

    \[\leadsto x \cdot \color{blue}{\left(\sqrt{e^{y \cdot y}} \cdot \sqrt{e^{y \cdot y}}\right)}\]

  4. Applied associate-*r*0.0

    \[\leadsto \color{blue}{\left(x \cdot \sqrt{e^{y \cdot y}}\right) \cdot \sqrt{e^{y \cdot y}}}\]
  5. Using strategy rm

  6. Applied add-cube-cbrt0.1

    \[\leadsto \left(x \cdot \sqrt{\color{blue}{\left(\sqrt[3]{e^{y \cdot y}} \cdot \sqrt[3]{e^{y \cdot y}}\right) \cdot \sqrt[3]{e^{y \cdot y}}}}\right) \cdot \sqrt{e^{y \cdot y}}\]

  7. Applied sqrt-prod0.1

    \[\leadsto \left(x \cdot \color{blue}{\left(\sqrt{\sqrt[3]{e^{y \cdot y}} \cdot \sqrt[3]{e^{y \cdot y}}} \cdot \sqrt{\sqrt[3]{e^{y \cdot y}}}\right)}\right) \cdot \sqrt{e^{y \cdot y}}\]

  8. Simplified0.1

    \[\leadsto \left(x \cdot \left(\color{blue}{\left|\sqrt[3]{e^{y \cdot y}}\right|} \cdot \sqrt{\sqrt[3]{e^{y \cdot y}}}\right)\right) \cdot \sqrt{e^{y \cdot y}}\]
  9. Using strategy rm

  10. Applied add-cube-cbrt0.1

    \[\leadsto \left(x \cdot \left(\left|\sqrt[3]{e^{y \cdot y}}\right| \cdot \sqrt{\color{blue}{\left(\sqrt[3]{\sqrt[3]{e^{y \cdot y}}} \cdot \sqrt[3]{\sqrt[3]{e^{y \cdot y}}}\right) \cdot \sqrt[3]{\sqrt[3]{e^{y \cdot y}}}}}\right)\right) \cdot \sqrt{e^{y \cdot y}}\]

  11. Final simplification0.1

    \[\leadsto \left(x \cdot \left(\left|\sqrt[3]{e^{y \cdot y}}\right| \cdot \sqrt{\left(\sqrt[3]{\sqrt[3]{e^{y \cdot y}}} \cdot \sqrt[3]{\sqrt[3]{e^{y \cdot y}}}\right) \cdot \sqrt[3]{\sqrt[3]{e^{y \cdot y}}}}\right)\right) \cdot \sqrt{e^{y \cdot y}}\]

Reproduce

herbie shell --seed 2019326 
(FPCore (x y)
  :name "Data.Number.Erf:$dmerfcx from erf-2.0.0.0"
  :precision binary64

  :herbie-target
  (* x (pow (exp y) y))

  (* x (exp (* y y))))