Average Error: 0.3 → 0.3
Time: 19.4s
Precision: 64
\[\frac{x}{y \cdot 3}\]
↓
\[\frac{\frac{x}{y}}{3}\]
\frac{x}{y \cdot 3}
↓
\frac{\frac{x}{y}}{3}
double f(double x, double y) {
        double r69518 = x;
        double r69519 = y;
        double r69520 = 3.0;
        double r69521 = r69519 * r69520;
        double r69522 = r69518 / r69521;
        return r69522;
}
↓
double f(double x, double y) {
        double r69523 = x;
        double r69524 = y;
        double r69525 = r69523 / r69524;
        double r69526 = 3.0;
        double r69527 = r69525 / r69526;
        return r69527;
}

Error

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Bits error versus y

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Results

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Target

Original0.3
Target0.3
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*0.3

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

  10. Applied associate-*r/0.3

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

  11. Simplified0.3

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

  12. Final simplification0.3

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

Reproduce

herbie shell --seed 2019310 +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)))