Average Error: 0.3 → 0.2
Time: 1.3s
Precision: 64
\[\frac{x}{y \cdot 3}\]
↓
\[\frac{\frac{x}{3}}{y} \cdot \left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right)\]
\frac{x}{y \cdot 3}
↓
\frac{\frac{x}{3}}{y} \cdot \left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right)
double f(double x, double y) {
        double r851334 = x;
        double r851335 = y;
        double r851336 = 3.0;
        double r851337 = r851335 * r851336;
        double r851338 = r851334 / r851337;
        return r851338;
}
↓
double f(double x, double y) {
        double r851339 = x;
        double r851340 = 3.0;
        double r851341 = r851339 / r851340;
        double r851342 = y;
        double r851343 = r851341 / r851342;
        double r851344 = 1.0;
        double r851345 = cbrt(r851344);
        double r851346 = r851345 * r851345;
        double r851347 = r851343 * r851346;
        return r851347;
}

Error

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Results

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Target

Original0.3
Target0.3
Herbie0.2
\[\frac{\frac{x}{y}}{3}\]

Derivation

  1. Initial program 0.3

    \[\frac{x}{y \cdot 3}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity0.3

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

  4. Applied times-frac0.3

    \[\leadsto \color{blue}{\frac{1}{y} \cdot \frac{x}{3}}\]
  5. Using strategy rm

  6. Applied *-un-lft-identity0.3

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

  7. Applied add-cube-cbrt0.3

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

  8. Applied times-frac0.3

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

  9. Applied associate-*l*0.3

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

  10. Simplified0.2

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

  11. Final simplification0.2

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

Reproduce

herbie shell --seed 2020065 
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, C"
  :precision binary64

  :herbie-target
  (/ (/ x y) 3)

  (/ x (* y 3)))