Average Error: 0.2 → 0.3
Time: 19.4s
Precision: 64
\[\frac{x}{y \cdot 3}\]
↓
\[x \cdot \frac{\frac{1}{y}}{3}\]
\frac{x}{y \cdot 3}
↓
x \cdot \frac{\frac{1}{y}}{3}
double f(double x, double y) {
        double r89744499 = x;
        double r89744500 = y;
        double r89744501 = 3.0;
        double r89744502 = r89744500 * r89744501;
        double r89744503 = r89744499 / r89744502;
        return r89744503;
}
↓
double f(double x, double y) {
        double r89744504 = x;
        double r89744505 = 1.0;
        double r89744506 = y;
        double r89744507 = r89744505 / r89744506;
        double r89744508 = 3.0;
        double r89744509 = r89744507 / r89744508;
        double r89744510 = r89744504 * r89744509;
        return r89744510;
}

Error

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Bits error versus y

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Results

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Target

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

Derivation

  1. Initial program 0.2

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

  3. Applied associate-/r*0.3

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

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

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

  6. Applied div-inv0.3

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

  7. Applied times-frac0.3

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

  8. Simplified0.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2019173 +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)))