Average Error: 0.2 → 0.2
Time: 20.9s
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 r451933 = x;
        double r451934 = y;
        double r451935 = 3.0;
        double r451936 = r451934 * r451935;
        double r451937 = r451933 / r451936;
        return r451937;
}
↓
double f(double x, double y) {
        double r451938 = x;
        double r451939 = y;
        double r451940 = r451938 / r451939;
        double r451941 = 3.0;
        double r451942 = r451940 / r451941;
        return r451942;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

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

Derivation

  1. Initial program 0.2

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

  3. Applied associate-/r*0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019323 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, C"
  :precision binary64

  :herbie-target
  (/ (/ x y) 3)

  (/ x (* y 3)))