Average Error: 5.1 → 0.1
Time: 6.2s
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 r223747 = x;
        double r223748 = y;
        double r223749 = r223748 * r223748;
        double r223750 = r223747 / r223749;
        double r223751 = 3.0;
        double r223752 = r223750 - r223751;
        return r223752;
}
↓
double f(double x, double y) {
        double r223753 = x;
        double r223754 = y;
        double r223755 = r223753 / r223754;
        double r223756 = r223755 / r223754;
        double r223757 = 3.0;
        double r223758 = r223756 - r223757;
        return r223758;
}

Error

Bits error versus x

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 2019291 
(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))