Average Error: 0.3 → 0.2
Time: 5.5s
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 r15389272 = x;
        double r15389273 = y;
        double r15389274 = 3.0;
        double r15389275 = r15389273 * r15389274;
        double r15389276 = r15389272 / r15389275;
        return r15389276;
}
↓
double f(double x, double y) {
        double r15389277 = x;
        double r15389278 = y;
        double r15389279 = r15389277 / r15389278;
        double r15389280 = 3.0;
        double r15389281 = r15389279 / r15389280;
        return r15389281;
}

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

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

  (/ x (* y 3.0)))