Average Error: 0.3 → 0.2
Time: 11.6s
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 r47839804 = x;
        double r47839805 = y;
        double r47839806 = 3.0;
        double r47839807 = r47839805 * r47839806;
        double r47839808 = r47839804 / r47839807;
        return r47839808;
}
↓
double f(double x, double y) {
        double r47839809 = x;
        double r47839810 = 3.0;
        double r47839811 = r47839809 / r47839810;
        double r47839812 = y;
        double r47839813 = r47839811 / r47839812;
        return r47839813;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

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

Derivation

  1. Initial program 0.3

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

  3. Applied *-un-lft-identity0.3

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

  4. Applied times-frac0.3

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

  6. Applied associate-*l/0.2

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

  7. Simplified0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, C"

  :herbie-target
  (/ (/ x y) 3.0)

  (/ x (* y 3.0)))