Average Error: 4.6 → 0.1
Time: 15.5s
Precision: 64
\[\frac{x}{y \cdot y} - 3.0\]
↓
\[\frac{\frac{x}{y}}{y} - 3.0\]
\frac{x}{y \cdot y} - 3.0
↓
\frac{\frac{x}{y}}{y} - 3.0
double f(double x, double y) {
        double r16667351 = x;
        double r16667352 = y;
        double r16667353 = r16667352 * r16667352;
        double r16667354 = r16667351 / r16667353;
        double r16667355 = 3.0;
        double r16667356 = r16667354 - r16667355;
        return r16667356;
}
↓
double f(double x, double y) {
        double r16667357 = x;
        double r16667358 = y;
        double r16667359 = r16667357 / r16667358;
        double r16667360 = r16667359 / r16667358;
        double r16667361 = 3.0;
        double r16667362 = r16667360 - r16667361;
        return r16667362;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original4.6
Target0.1
Herbie0.1
\[\frac{\frac{x}{y}}{y} - 3.0\]

Derivation

  1. Initial program 4.6

    \[\frac{x}{y \cdot y} - 3.0\]
  2. Using strategy rm

  3. Applied associate-/r*0.1

    \[\leadsto \color{blue}{\frac{\frac{x}{y}}{y}} - 3.0\]

  4. Final simplification0.1

    \[\leadsto \frac{\frac{x}{y}}{y} - 3.0\]

Reproduce

herbie shell --seed 2019158 
(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))