Average Error: 5.1 → 0.1
Time: 2.5s
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 r264999 = x;
        double r265000 = y;
        double r265001 = r265000 * r265000;
        double r265002 = r264999 / r265001;
        double r265003 = 3.0;
        double r265004 = r265002 - r265003;
        return r265004;
}
↓
double f(double x, double y) {
        double r265005 = x;
        double r265006 = y;
        double r265007 = r265005 / r265006;
        double r265008 = r265007 / r265006;
        double r265009 = 3.0;
        double r265010 = r265008 - r265009;
        return r265010;
}

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 2020024 
(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))