Average Error: 0.3 → 0.3
Time: 1.4s
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 r888771 = x;
        double r888772 = y;
        double r888773 = 3.0;
        double r888774 = r888772 * r888773;
        double r888775 = r888771 / r888774;
        return r888775;
}
↓
double f(double x, double y) {
        double r888776 = x;
        double r888777 = y;
        double r888778 = r888776 / r888777;
        double r888779 = 3.0;
        double r888780 = r888778 / r888779;
        return r888780;
}

Error

Bits error versus x

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. Final simplification0.3

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

Reproduce

herbie shell --seed 2020057 
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, C"
  :precision binary64

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

  (/ x (* y 3)))