Average Error: 5.1 → 0.1
Time: 2.6s
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 r360883 = x;
        double r360884 = y;
        double r360885 = r360884 * r360884;
        double r360886 = r360883 / r360885;
        double r360887 = 3.0;
        double r360888 = r360886 - r360887;
        return r360888;
}
↓
double f(double x, double y) {
        double r360889 = x;
        double r360890 = y;
        double r360891 = r360889 / r360890;
        double r360892 = r360891 / r360890;
        double r360893 = 3.0;
        double r360894 = r360892 - r360893;
        return r360894;
}

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 2020057 
(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))