Average Error: 5.0 → 0.1
Time: 3.7s
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 r261744 = x;
        double r261745 = y;
        double r261746 = r261745 * r261745;
        double r261747 = r261744 / r261746;
        double r261748 = 3.0;
        double r261749 = r261747 - r261748;
        return r261749;
}
↓
double f(double x, double y) {
        double r261750 = x;
        double r261751 = y;
        double r261752 = r261750 / r261751;
        double r261753 = r261752 / r261751;
        double r261754 = 3.0;
        double r261755 = r261753 - r261754;
        return r261755;
}

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 2020025 +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))