Average Error: 5.2 → 0.1
Time: 9.0s
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 r186690 = x;
        double r186691 = y;
        double r186692 = r186691 * r186691;
        double r186693 = r186690 / r186692;
        double r186694 = 3.0;
        double r186695 = r186693 - r186694;
        return r186695;
}
↓
double f(double x, double y) {
        double r186696 = x;
        double r186697 = y;
        double r186698 = r186696 / r186697;
        double r186699 = r186698 / r186697;
        double r186700 = 3.0;
        double r186701 = r186699 - r186700;
        return r186701;
}

Error

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Bits error versus y

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Results

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Target

Original5.2
Target0.1
Herbie0.1
\[\frac{\frac{x}{y}}{y} - 3\]

Derivation

  1. Initial program 5.2

    \[\frac{x}{y \cdot y} - 3\]
  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 2019198 +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))