Average Error: 0.3 → 0.3
Time: 21.8s
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 r32121151 = x;
        double r32121152 = y;
        double r32121153 = 3.0;
        double r32121154 = r32121152 * r32121153;
        double r32121155 = r32121151 / r32121154;
        return r32121155;
}
↓
double f(double x, double y) {
        double r32121156 = x;
        double r32121157 = y;
        double r32121158 = r32121156 / r32121157;
        double r32121159 = 3.0;
        double r32121160 = r32121158 / r32121159;
        return r32121160;
}

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 2019200 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, C"

  :herbie-target
  (/ (/ x y) 3.0)

  (/ x (* y 3.0)))