Average Error: 5.0 → 0.1
Time: 12.8s
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 r311814 = x;
        double r311815 = y;
        double r311816 = r311815 * r311815;
        double r311817 = r311814 / r311816;
        double r311818 = 3.0;
        double r311819 = r311817 - r311818;
        return r311819;
}
↓
double f(double x, double y) {
        double r311820 = x;
        double r311821 = y;
        double r311822 = r311820 / r311821;
        double r311823 = r311822 / r311821;
        double r311824 = 3.0;
        double r311825 = r311823 - r311824;
        return r311825;
}

Error

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Bits error versus y

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Results

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Target

Original5.0
Target0.1
Herbie0.1
\[\frac{\frac{x}{y}}{y} - 3\]

Derivation

  1. Initial program 5.0

    \[\frac{x}{y \cdot y} - 3\]
  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 2020043 +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))