Average Error: 5.3 → 0.1
Time: 1.4m
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 r6282814 = x;
        double r6282815 = y;
        double r6282816 = r6282815 * r6282815;
        double r6282817 = r6282814 / r6282816;
        double r6282818 = 3.0;
        double r6282819 = r6282817 - r6282818;
        return r6282819;
}
↓
double f(double x, double y) {
        double r6282820 = x;
        double r6282821 = y;
        double r6282822 = r6282820 / r6282821;
        double r6282823 = r6282822 / r6282821;
        double r6282824 = 3.0;
        double r6282825 = r6282823 - r6282824;
        return r6282825;
}

Error

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Bits error versus y

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Results

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Target

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

Derivation

  1. Initial program 5.3

    \[\frac{x}{y \cdot y} - 3\]
  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 2019200 +o rules:numerics
(FPCore (x y)
  :name "Statistics.Sample:$skurtosis from math-functions-0.1.5.2"

  :herbie-target
  (- (/ (/ x y) y) 3.0)

  (- (/ x (* y y)) 3.0))