Average Error: 0.3 → 0.2
Time: 1.4s
Precision: 64
\[\frac{x}{y \cdot 3}\]
↓
\[\frac{\frac{x}{3}}{y}\]
\frac{x}{y \cdot 3}
↓
\frac{\frac{x}{3}}{y}
double f(double x, double y) {
        double r686079 = x;
        double r686080 = y;
        double r686081 = 3.0;
        double r686082 = r686080 * r686081;
        double r686083 = r686079 / r686082;
        return r686083;
}
↓
double f(double x, double y) {
        double r686084 = x;
        double r686085 = 3.0;
        double r686086 = r686084 / r686085;
        double r686087 = y;
        double r686088 = r686086 / r686087;
        return r686088;
}

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. Using strategy rm

  5. Applied div-inv0.3

    \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{1}{3}}\]
  6. Using strategy rm

  7. Applied associate-*l/0.3

    \[\leadsto \color{blue}{\frac{x \cdot \frac{1}{3}}{y}}\]

  8. Simplified0.2

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

  9. Final simplification0.2

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

Reproduce

herbie shell --seed 2020039 +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)))