Average Error: 0.3 → 0.2
Time: 10.2s
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 r29822139 = x;
        double r29822140 = y;
        double r29822141 = 3.0;
        double r29822142 = r29822140 * r29822141;
        double r29822143 = r29822139 / r29822142;
        return r29822143;
}
↓
double f(double x, double y) {
        double r29822144 = x;
        double r29822145 = y;
        double r29822146 = r29822144 / r29822145;
        double r29822147 = 3.0;
        double r29822148 = r29822146 / r29822147;
        return r29822148;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original0.3
Target0.2
Herbie0.2
\[\frac{\frac{x}{y}}{3}\]

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. Final simplification0.2

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

Reproduce

herbie shell --seed 2019172 +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)))