Average Error: 5.3 → 0.1
Time: 24.8s
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 r192925 = x;
        double r192926 = y;
        double r192927 = r192926 * r192926;
        double r192928 = r192925 / r192927;
        double r192929 = 3.0;
        double r192930 = r192928 - r192929;
        return r192930;
}
↓
double f(double x, double y) {
        double r192931 = x;
        double r192932 = y;
        double r192933 = r192931 / r192932;
        double r192934 = r192933 / r192932;
        double r192935 = 3.0;
        double r192936 = r192934 - r192935;
        return r192936;
}

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 2019323 +o rules:numerics
(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))