Average Error: 5.3 → 0.1
Time: 20.1s
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 r187334 = x;
        double r187335 = y;
        double r187336 = r187335 * r187335;
        double r187337 = r187334 / r187336;
        double r187338 = 3.0;
        double r187339 = r187337 - r187338;
        return r187339;
}
↓
double f(double x, double y) {
        double r187340 = x;
        double r187341 = y;
        double r187342 = r187340 / r187341;
        double r187343 = r187342 / r187341;
        double r187344 = 3.0;
        double r187345 = r187343 - r187344;
        return r187345;
}

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 2019326 +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))