Average Error: 5.3 → 0.1
Time: 22.1s
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 r211876 = x;
        double r211877 = y;
        double r211878 = r211877 * r211877;
        double r211879 = r211876 / r211878;
        double r211880 = 3.0;
        double r211881 = r211879 - r211880;
        return r211881;
}
↓
double f(double x, double y) {
        double r211882 = x;
        double r211883 = y;
        double r211884 = r211882 / r211883;
        double r211885 = r211884 / r211883;
        double r211886 = 3.0;
        double r211887 = r211885 - r211886;
        return r211887;
}

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 2019326 
(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))