Average Error: 5.1 → 0.1
Time: 2.0s
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 r285586 = x;
        double r285587 = y;
        double r285588 = r285587 * r285587;
        double r285589 = r285586 / r285588;
        double r285590 = 3.0;
        double r285591 = r285589 - r285590;
        return r285591;
}
↓
double f(double x, double y) {
        double r285592 = x;
        double r285593 = y;
        double r285594 = r285592 / r285593;
        double r285595 = r285594 / r285593;
        double r285596 = 3.0;
        double r285597 = r285595 - r285596;
        return r285597;
}

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 2020036 +o rules:numerics
(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))