Average Error: 5.1 → 0.1
Time: 11.2s
Precision: 64
\[\frac{x}{y \cdot y} - 3\]
↓
\[\frac{\frac{x}{y}}{y} - 3\]
\frac{x}{y \cdot y} - 3
↓
\frac{\frac{x}{y}}{y} - 3
double f(double x, double y) {
        double r338251 = x;
        double r338252 = y;
        double r338253 = r338252 * r338252;
        double r338254 = r338251 / r338253;
        double r338255 = 3.0;
        double r338256 = r338254 - r338255;
        return r338256;
}
↓
double f(double x, double y) {
        double r338257 = x;
        double r338258 = y;
        double r338259 = r338257 / r338258;
        double r338260 = r338259 / r338258;
        double r338261 = 3.0;
        double r338262 = r338260 - r338261;
        return r338262;
}

Error

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Bits error versus y

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Results

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Target

Original5.1
Target0.1
Herbie0.1
\[\frac{\frac{x}{y}}{y} - 3\]

Derivation

  1. Initial program 5.1

    \[\frac{x}{y \cdot y} - 3\]
  2. Using strategy rm

  3. Applied associate-/r*0.1

    \[\leadsto \color{blue}{\frac{\frac{x}{y}}{y}} - 3\]

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2020060 +o rules:numerics
(FPCore (x y)
  :name "Statistics.Sample:$skurtosis from math-functions-0.1.5.2"
  :precision binary64

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

  (- (/ x (* y y)) 3))