Average Error: 0.3 → 0.3
Time: 1.5s
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 r763280 = x;
        double r763281 = y;
        double r763282 = 3.0;
        double r763283 = r763281 * r763282;
        double r763284 = r763280 / r763283;
        return r763284;
}
↓
double f(double x, double y) {
        double r763285 = x;
        double r763286 = 1.0;
        double r763287 = y;
        double r763288 = r763286 / r763287;
        double r763289 = 3.0;
        double r763290 = r763288 / r763289;
        double r763291 = r763285 * r763290;
        return r763291;
}

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 *-un-lft-identity0.2

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

  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 2019354 
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, C"
  :precision binary64

  :herbie-target
  (/ (/ x y) 3)

  (/ x (* y 3)))