Average Error: 5.4 → 0.1
Time: 4.6s
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 r332820 = x;
        double r332821 = y;
        double r332822 = r332821 * r332821;
        double r332823 = r332820 / r332822;
        double r332824 = 3.0;
        double r332825 = r332823 - r332824;
        return r332825;
}
↓
double f(double x, double y) {
        double r332826 = x;
        double r332827 = y;
        double r332828 = r332826 / r332827;
        double r332829 = r332828 / r332827;
        double r332830 = 3.0;
        double r332831 = r332829 - r332830;
        return r332831;
}

Error

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Bits error versus y

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Results

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Target

Original5.4
Target0.1
Herbie0.1
\[\frac{\frac{x}{y}}{y} - 3\]

Derivation

  1. Initial program 5.4

    \[\frac{x}{y \cdot y} - 3\]
  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 2019362 +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))