Average Error: 5.3 → 0.1
Time: 1.7s
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 r263478 = x;
        double r263479 = y;
        double r263480 = r263479 * r263479;
        double r263481 = r263478 / r263480;
        double r263482 = 3.0;
        double r263483 = r263481 - r263482;
        return r263483;
}
↓
double f(double x, double y) {
        double r263484 = x;
        double r263485 = y;
        double r263486 = r263484 / r263485;
        double r263487 = r263486 / r263485;
        double r263488 = 3.0;
        double r263489 = r263487 - r263488;
        return r263489;
}

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 2020049 
(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))