Average Error: 0.3 → 0.2
Time: 6.9s
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 r14518347 = x;
        double r14518348 = y;
        double r14518349 = 3.0;
        double r14518350 = r14518348 * r14518349;
        double r14518351 = r14518347 / r14518350;
        return r14518351;
}
↓
double f(double x, double y) {
        double r14518352 = x;
        double r14518353 = y;
        double r14518354 = r14518352 / r14518353;
        double r14518355 = 3.0;
        double r14518356 = r14518354 / r14518355;
        return r14518356;
}

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

Derivation

  1. Initial program 0.3

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

  3. Applied associate-/r*0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019156 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, C"

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

  (/ x (* y 3.0)))