Average Error: 0.3 → 0.2
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 r702495 = x;
        double r702496 = y;
        double r702497 = 3.0;
        double r702498 = r702496 * r702497;
        double r702499 = r702495 / r702498;
        return r702499;
}
↓
double f(double x, double y) {
        double r702500 = x;
        double r702501 = y;
        double r702502 = r702500 / r702501;
        double r702503 = 3.0;
        double r702504 = r702502 / r702503;
        return r702504;
}

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

Derivation

  1. Initial program 0.3

    \[\frac{x}{y \cdot 3}\]
  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 2020049 
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, C"
  :precision binary64

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

  (/ x (* y 3)))