Average Error: 5.4 → 0.1
Time: 4.5s
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 r405873 = x;
        double r405874 = y;
        double r405875 = r405874 * r405874;
        double r405876 = r405873 / r405875;
        double r405877 = 3.0;
        double r405878 = r405876 - r405877;
        return r405878;
}
↓
double f(double x, double y) {
        double r405879 = x;
        double r405880 = y;
        double r405881 = r405879 / r405880;
        double r405882 = r405881 / r405880;
        double r405883 = 3.0;
        double r405884 = r405882 - r405883;
        return r405884;
}

Error

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Bits error versus y

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Results

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Target

Original5.4
Target0.1
Herbie0.1
\[\frac{\frac{x}{y}}{y} - 3\]

Derivation

  1. Initial program 5.4

    \[\frac{x}{y \cdot y} - 3\]
  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 2019362 
(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))