Average Error: 4.9 → 0.1
Time: 2.8s
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 r367749 = x;
        double r367750 = y;
        double r367751 = r367750 * r367750;
        double r367752 = r367749 / r367751;
        double r367753 = 3.0;
        double r367754 = r367752 - r367753;
        return r367754;
}
↓
double f(double x, double y) {
        double r367755 = x;
        double r367756 = y;
        double r367757 = r367755 / r367756;
        double r367758 = r367757 / r367756;
        double r367759 = 3.0;
        double r367760 = r367758 - r367759;
        return r367760;
}

Error

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Bits error versus y

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Results

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Target

Original4.9
Target0.1
Herbie0.1
\[\frac{\frac{x}{y}}{y} - 3\]

Derivation

  1. Initial program 4.9

    \[\frac{x}{y \cdot y} - 3\]
  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 2020020 +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))