Average Error: 0.3 → 0.3
Time: 9.6s
Precision: 64
\[\frac{x}{y \cdot 3}\]
↓
\[\frac{x}{3} \cdot \frac{1}{y}\]
\frac{x}{y \cdot 3}
↓
\frac{x}{3} \cdot \frac{1}{y}
double f(double x, double y) {
        double r625913 = x;
        double r625914 = y;
        double r625915 = 3.0;
        double r625916 = r625914 * r625915;
        double r625917 = r625913 / r625916;
        return r625917;
}
↓
double f(double x, double y) {
        double r625918 = x;
        double r625919 = 3.0;
        double r625920 = r625918 / r625919;
        double r625921 = 1.0;
        double r625922 = y;
        double r625923 = r625921 / r625922;
        double r625924 = r625920 * r625923;
        return r625924;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

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

Derivation

  1. Initial program 0.3

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

  2. Simplified0.3

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

  4. Applied associate-/r*0.2

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

  6. Applied div-inv0.3

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

  7. Final simplification0.3

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

Reproduce

herbie shell --seed 2019196 
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, C"

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

  (/ x (* y 3.0)))