Average Error: 5.0 → 0.1
Time: 2.5s
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 r310686 = x;
        double r310687 = y;
        double r310688 = r310687 * r310687;
        double r310689 = r310686 / r310688;
        double r310690 = 3.0;
        double r310691 = r310689 - r310690;
        return r310691;
}
↓
double f(double x, double y) {
        double r310692 = x;
        double r310693 = y;
        double r310694 = r310692 / r310693;
        double r310695 = r310694 / r310693;
        double r310696 = 3.0;
        double r310697 = r310695 - r310696;
        return r310697;
}

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 2020018 
(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))