Average Error: 0.3 → 0.2
Time: 12.9s
Precision: 64
\[\frac{x}{y \cdot 3}\]
↓
\[\frac{\frac{x}{y}}{3}\]
\frac{x}{y \cdot 3}
↓
\frac{\frac{x}{y}}{3}
double f(double x, double y) {
        double r33918877 = x;
        double r33918878 = y;
        double r33918879 = 3.0;
        double r33918880 = r33918878 * r33918879;
        double r33918881 = r33918877 / r33918880;
        return r33918881;
}
↓
double f(double x, double y) {
        double r33918882 = x;
        double r33918883 = y;
        double r33918884 = r33918882 / r33918883;
        double r33918885 = 3.0;
        double r33918886 = r33918884 / r33918885;
        return r33918886;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

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

Derivation

  1. Initial program 0.3

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

  3. Applied associate-/r*0.2

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

  5. Applied *-un-lft-identity0.2

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

  6. Applied div-inv0.3

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

  7. Applied times-frac0.3

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

  8. Simplified0.3

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

  10. Applied associate-*r/0.3

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

  11. Simplified0.2

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

  12. Final simplification0.2

    \[\leadsto \frac{\frac{x}{y}}{3}\]

Reproduce

herbie shell --seed 2019172 
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, C"

  :herbie-target
  (/ (/ x y) 3.0)

  (/ x (* y 3.0)))