Average Error: 5.2 → 0.1
Time: 9.3s
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 r218598 = x;
        double r218599 = y;
        double r218600 = r218599 * r218599;
        double r218601 = r218598 / r218600;
        double r218602 = 3.0;
        double r218603 = r218601 - r218602;
        return r218603;
}
↓
double f(double x, double y) {
        double r218604 = x;
        double r218605 = y;
        double r218606 = r218604 / r218605;
        double r218607 = r218606 / r218605;
        double r218608 = 3.0;
        double r218609 = r218607 - r218608;
        return r218609;
}

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 
(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))