Average Error: 0.3 → 0.3
Time: 26.1s
Precision: 64
\[\frac{x}{y \cdot 3.0}\]
↓
\[\frac{\frac{x}{y}}{3.0}\]
\frac{x}{y \cdot 3.0}
↓
\frac{\frac{x}{y}}{3.0}
double f(double x, double y) {
        double r37268307 = x;
        double r37268308 = y;
        double r37268309 = 3.0;
        double r37268310 = r37268308 * r37268309;
        double r37268311 = r37268307 / r37268310;
        return r37268311;
}
↓
double f(double x, double y) {
        double r37268312 = x;
        double r37268313 = y;
        double r37268314 = r37268312 / r37268313;
        double r37268315 = 3.0;
        double r37268316 = r37268314 / r37268315;
        return r37268316;
}

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
\[\frac{\frac{x}{y}}{3.0}\]

Derivation

  1. Initial program 0.3

    \[\frac{x}{y \cdot 3.0}\]
  2. Using strategy rm

  3. Applied associate-/r*0.3

    \[\leadsto \color{blue}{\frac{\frac{x}{y}}{3.0}}\]

  4. Final simplification0.3

    \[\leadsto \frac{\frac{x}{y}}{3.0}\]

Reproduce

herbie shell --seed 2019165 
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, C"

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

  (/ x (* y 3.0)))