Average Error: 5.0 → 0.1
Time: 20.3s
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 r188566 = x;
        double r188567 = y;
        double r188568 = r188567 * r188567;
        double r188569 = r188566 / r188568;
        double r188570 = 3.0;
        double r188571 = r188569 - r188570;
        return r188571;
}
↓
double f(double x, double y) {
        double r188572 = x;
        double r188573 = y;
        double r188574 = r188572 / r188573;
        double r188575 = r188574 / r188573;
        double r188576 = 3.0;
        double r188577 = r188575 - r188576;
        return r188577;
}

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 2019199 +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))