Average Error: 4.6 → 0.1
Time: 11.5s
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 r182584 = x;
        double r182585 = y;
        double r182586 = r182585 * r182585;
        double r182587 = r182584 / r182586;
        double r182588 = 3.0;
        double r182589 = r182587 - r182588;
        return r182589;
}
↓
double f(double x, double y) {
        double r182590 = x;
        double r182591 = y;
        double r182592 = r182590 / r182591;
        double r182593 = r182592 / r182591;
        double r182594 = 3.0;
        double r182595 = r182593 - r182594;
        return r182595;
}

Error

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Bits error versus y

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Results

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Target

Original4.6
Target0.1
Herbie0.1
\[\frac{\frac{x}{y}}{y} - 3\]

Derivation

  1. Initial program 4.6

    \[\frac{x}{y \cdot y} - 3\]
  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 2019174 +o rules:numerics
(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))