Average Error: 5.3 → 0.1
Time: 25.0s
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 r259892 = x;
        double r259893 = y;
        double r259894 = r259893 * r259893;
        double r259895 = r259892 / r259894;
        double r259896 = 3.0;
        double r259897 = r259895 - r259896;
        return r259897;
}
↓
double f(double x, double y) {
        double r259898 = x;
        double r259899 = y;
        double r259900 = r259898 / r259899;
        double r259901 = r259900 / r259899;
        double r259902 = 3.0;
        double r259903 = r259901 - r259902;
        return r259903;
}

Error

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Bits error versus y

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Results

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Target

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

Derivation

  1. Initial program 5.3

    \[\frac{x}{y \cdot y} - 3\]
  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 2019323 
(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))