Average Error: 0.3 → 0.3
Time: 16.7s
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 r472008 = x;
        double r472009 = y;
        double r472010 = 3.0;
        double r472011 = r472009 * r472010;
        double r472012 = r472008 / r472011;
        return r472012;
}
↓
double f(double x, double y) {
        double r472013 = x;
        double r472014 = y;
        double r472015 = r472013 / r472014;
        double r472016 = 3.0;
        double r472017 = r472015 / r472016;
        return r472017;
}

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 2019304 +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)))