Average Error: 0.2 → 0.3
Time: 1.5s
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 r1008896 = x;
        double r1008897 = y;
        double r1008898 = 3.0;
        double r1008899 = r1008897 * r1008898;
        double r1008900 = r1008896 / r1008899;
        return r1008900;
}
↓
double f(double x, double y) {
        double r1008901 = x;
        double r1008902 = y;
        double r1008903 = r1008901 / r1008902;
        double r1008904 = 3.0;
        double r1008905 = r1008903 / r1008904;
        return r1008905;
}

Error

Bits error versus x

Bits error versus y

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Results

Enter valid numbers for all inputs

Target

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

Derivation

  1. Initial program 0.2

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

  3. Applied associate-/r*0.3

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

  4. Final simplification0.3

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

Reproduce

herbie shell --seed 2019353 
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, C"
  :precision binary64

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

  (/ x (* y 3)))