Average Error: 5.3 → 0.1
Time: 1.8s
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 r218823 = x;
        double r218824 = y;
        double r218825 = r218824 * r218824;
        double r218826 = r218823 / r218825;
        double r218827 = 3.0;
        double r218828 = r218826 - r218827;
        return r218828;
}
↓
double f(double x, double y) {
        double r218829 = x;
        double r218830 = y;
        double r218831 = r218829 / r218830;
        double r218832 = r218831 / r218830;
        double r218833 = 3.0;
        double r218834 = r218832 - r218833;
        return r218834;
}

Error

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Bits error versus y

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Results

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Target

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

Derivation

  1. Initial program 5.3

    \[\frac{x}{y \cdot y} - 3\]
  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 2020062 
(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))