Average Error: 5.0 → 0.1
Time: 2.0s
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 r394926 = x;
        double r394927 = y;
        double r394928 = r394927 * r394927;
        double r394929 = r394926 / r394928;
        double r394930 = 3.0;
        double r394931 = r394929 - r394930;
        return r394931;
}
↓
double f(double x, double y) {
        double r394932 = x;
        double r394933 = y;
        double r394934 = r394932 / r394933;
        double r394935 = r394934 / r394933;
        double r394936 = 3.0;
        double r394937 = r394935 - r394936;
        return r394937;
}

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 2020065 
(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))