Average Error: 5.3 → 0.1
Time: 7.2s
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 r209848 = x;
        double r209849 = y;
        double r209850 = r209849 * r209849;
        double r209851 = r209848 / r209850;
        double r209852 = 3.0;
        double r209853 = r209851 - r209852;
        return r209853;
}
↓
double f(double x, double y) {
        double r209854 = x;
        double r209855 = y;
        double r209856 = r209854 / r209855;
        double r209857 = r209856 / r209855;
        double r209858 = 3.0;
        double r209859 = r209857 - r209858;
        return r209859;
}

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 2019235 
(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))