Average Error: 0.3 → 0.3
Time: 8.9s
Precision: 64
\[\frac{x}{y \cdot 3}\]
↓
\[\frac{x}{y \cdot 3}\]
\frac{x}{y \cdot 3}
↓
\frac{x}{y \cdot 3}
double f(double x, double y) {
        double r651461 = x;
        double r651462 = y;
        double r651463 = 3.0;
        double r651464 = r651462 * r651463;
        double r651465 = r651461 / r651464;
        return r651465;
}
↓
double f(double x, double y) {
        double r651466 = x;
        double r651467 = y;
        double r651468 = 3.0;
        double r651469 = r651467 * r651468;
        double r651470 = r651466 / r651469;
        return r651470;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

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

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

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

  6. Applied associate-/l*0.3

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

  7. Simplified0.3

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

  8. Final simplification0.3

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

Reproduce

herbie shell --seed 2020047 +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)))