Average Error: 5.1 → 0.1
Time: 5.5s
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 r259672 = x;
        double r259673 = y;
        double r259674 = r259673 * r259673;
        double r259675 = r259672 / r259674;
        double r259676 = 3.0;
        double r259677 = r259675 - r259676;
        return r259677;
}
↓
double f(double x, double y) {
        double r259678 = x;
        double r259679 = y;
        double r259680 = r259678 / r259679;
        double r259681 = r259680 / r259679;
        double r259682 = 3.0;
        double r259683 = r259681 - r259682;
        return r259683;
}

Error

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Bits error versus y

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Results

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Target

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

Derivation

  1. Initial program 5.1

    \[\frac{x}{y \cdot y} - 3\]
  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 2019304 
(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))