Average Error: 5.1 → 0.1
Time: 14.4s
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 r178819 = x;
        double r178820 = y;
        double r178821 = r178820 * r178820;
        double r178822 = r178819 / r178821;
        double r178823 = 3.0;
        double r178824 = r178822 - r178823;
        return r178824;
}
↓
double f(double x, double y) {
        double r178825 = x;
        double r178826 = y;
        double r178827 = r178825 / r178826;
        double r178828 = r178827 / r178826;
        double r178829 = 3.0;
        double r178830 = r178828 - r178829;
        return r178830;
}

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 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))