Average Error: 10.8 → 0.3
Time: 2.0s
Precision: 64
\[\frac{x}{y \cdot y}\]
↓
\[\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\frac{y}{x}} \cdot \frac{\sqrt[3]{1}}{y}\]
\frac{x}{y \cdot y}
↓
\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\frac{y}{x}} \cdot \frac{\sqrt[3]{1}}{y}
double f(double x, double y) {
        double r338834 = x;
        double r338835 = y;
        double r338836 = r338835 * r338835;
        double r338837 = r338834 / r338836;
        return r338837;
}
↓
double f(double x, double y) {
        double r338838 = 1.0;
        double r338839 = cbrt(r338838);
        double r338840 = r338839 * r338839;
        double r338841 = y;
        double r338842 = x;
        double r338843 = r338841 / r338842;
        double r338844 = r338840 / r338843;
        double r338845 = r338839 / r338841;
        double r338846 = r338844 * r338845;
        return r338846;
}

Error

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Results

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Target

Original10.8
Target0.2
Herbie0.3
\[\frac{\frac{x}{y}}{y}\]

Derivation

  1. Initial program 10.8

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

  3. Applied associate-/r*0.2

    \[\leadsto \color{blue}{\frac{\frac{x}{y}}{y}}\]
  4. Using strategy rm

  5. Applied clear-num0.6

    \[\leadsto \color{blue}{\frac{1}{\frac{y}{\frac{x}{y}}}}\]
  6. Using strategy rm

  7. Applied associate-/r/0.6

    \[\leadsto \frac{1}{\color{blue}{\frac{y}{x} \cdot y}}\]

  8. Applied add-cube-cbrt0.6

    \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{\frac{y}{x} \cdot y}\]

  9. Applied times-frac0.3

    \[\leadsto \color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\frac{y}{x}} \cdot \frac{\sqrt[3]{1}}{y}}\]

  10. Final simplification0.3

    \[\leadsto \frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\frac{y}{x}} \cdot \frac{\sqrt[3]{1}}{y}\]

Reproduce

herbie shell --seed 2019354 
(FPCore (x y)
  :name "Physics.ForceLayout:coulombForce from force-layout-0.4.0.2"
  :precision binary64

  :herbie-target
  (/ (/ x y) y)

  (/ x (* y y)))