Average Error: 4.6 → 0.1
Time: 13.4s
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 r18263880 = x;
        double r18263881 = y;
        double r18263882 = r18263881 * r18263881;
        double r18263883 = r18263880 / r18263882;
        double r18263884 = 3.0;
        double r18263885 = r18263883 - r18263884;
        return r18263885;
}
↓
double f(double x, double y) {
        double r18263886 = x;
        double r18263887 = y;
        double r18263888 = r18263886 / r18263887;
        double r18263889 = r18263888 / r18263887;
        double r18263890 = 3.0;
        double r18263891 = r18263889 - r18263890;
        return r18263891;
}

Error

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Bits error versus y

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Results

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Target

Original4.6
Target0.1
Herbie0.1
\[\frac{\frac{x}{y}}{y} - 3\]

Derivation

  1. Initial program 4.6

    \[\frac{x}{y \cdot y} - 3\]
  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 2019174 +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))