Average Error: 0.2 → 0.3
Time: 1.8s
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 r817242 = x;
        double r817243 = y;
        double r817244 = 3.0;
        double r817245 = r817243 * r817244;
        double r817246 = r817242 / r817245;
        return r817246;
}
↓
double f(double x, double y) {
        double r817247 = x;
        double r817248 = y;
        double r817249 = r817247 / r817248;
        double r817250 = 3.0;
        double r817251 = r817249 / r817250;
        return r817251;
}

Error

Bits error versus x

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. Final simplification0.3

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

Reproduce

herbie shell --seed 2019353 +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)))