Average Error: 0.3 → 0.2
Time: 11.3s
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 r934224 = x;
        double r934225 = y;
        double r934226 = 3.0;
        double r934227 = r934225 * r934226;
        double r934228 = r934224 / r934227;
        return r934228;
}
↓
double f(double x, double y) {
        double r934229 = x;
        double r934230 = 3.0;
        double r934231 = r934229 / r934230;
        double r934232 = y;
        double r934233 = r934231 / r934232;
        return r934233;
}

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 associate-/r*0.3

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

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

  9. Applied associate-/r*0.2

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

  10. Final simplification0.2

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

Reproduce

herbie shell --seed 2019305 +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)))