Average Error: 5.2 → 0.1
Time: 26.1s
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 r225927 = x;
        double r225928 = y;
        double r225929 = r225928 * r225928;
        double r225930 = r225927 / r225929;
        double r225931 = 3.0;
        double r225932 = r225930 - r225931;
        return r225932;
}
↓
double f(double x, double y) {
        double r225933 = x;
        double r225934 = y;
        double r225935 = r225933 / r225934;
        double r225936 = r225935 / r225934;
        double r225937 = 3.0;
        double r225938 = r225936 - r225937;
        return r225938;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original5.2
Target0.1
Herbie0.1
\[\frac{\frac{x}{y}}{y} - 3\]

Derivation

  1. Initial program 5.2

    \[\frac{x}{y \cdot y} - 3\]
  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 2019303 
(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))