Average Error: 4.9 → 0.1
Time: 12.6s
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 r244250 = x;
        double r244251 = y;
        double r244252 = r244251 * r244251;
        double r244253 = r244250 / r244252;
        double r244254 = 3.0;
        double r244255 = r244253 - r244254;
        return r244255;
}
↓
double f(double x, double y) {
        double r244256 = x;
        double r244257 = y;
        double r244258 = r244256 / r244257;
        double r244259 = r244258 / r244257;
        double r244260 = 3.0;
        double r244261 = r244259 - r244260;
        return r244261;
}

Error

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Bits error versus y

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Results

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Target

Original4.9
Target0.1
Herbie0.1
\[\frac{\frac{x}{y}}{y} - 3\]

Derivation

  1. Initial program 4.9

    \[\frac{x}{y \cdot y} - 3\]
  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 2019208 +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))