Average Error: 5.2 → 0.1
Time: 13.3s
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 r245322 = x;
        double r245323 = y;
        double r245324 = r245323 * r245323;
        double r245325 = r245322 / r245324;
        double r245326 = 3.0;
        double r245327 = r245325 - r245326;
        return r245327;
}
↓
double f(double x, double y) {
        double r245328 = x;
        double r245329 = y;
        double r245330 = r245328 / r245329;
        double r245331 = r245330 / r245329;
        double r245332 = 3.0;
        double r245333 = r245331 - r245332;
        return r245333;
}

Error

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Results

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Target

Original5.2
Target0.1
Herbie0.1
\[\frac{\frac{x}{y}}{y} - 3\]

Derivation

  1. Initial program 5.2

    \[\frac{x}{y \cdot y} - 3\]
  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 2019350 
(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))