Average Error: 5.0 → 0.1
Time: 18.2s
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 r11966602 = x;
        double r11966603 = y;
        double r11966604 = r11966603 * r11966603;
        double r11966605 = r11966602 / r11966604;
        double r11966606 = 3.0;
        double r11966607 = r11966605 - r11966606;
        return r11966607;
}
↓
double f(double x, double y) {
        double r11966608 = x;
        double r11966609 = y;
        double r11966610 = r11966608 / r11966609;
        double r11966611 = r11966610 / r11966609;
        double r11966612 = 3.0;
        double r11966613 = r11966611 - r11966612;
        return r11966613;
}

Error

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Bits error versus y

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Results

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Target

Original5.0
Target0.1
Herbie0.1
\[\frac{\frac{x}{y}}{y} - 3\]

Derivation

  1. Initial program 5.0

    \[\frac{x}{y \cdot y} - 3\]
  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 2019172 +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))