Average Error: 5.1 → 0.1
Time: 2.6s
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 r297321 = x;
        double r297322 = y;
        double r297323 = r297322 * r297322;
        double r297324 = r297321 / r297323;
        double r297325 = 3.0;
        double r297326 = r297324 - r297325;
        return r297326;
}
↓
double f(double x, double y) {
        double r297327 = x;
        double r297328 = y;
        double r297329 = r297327 / r297328;
        double r297330 = r297329 / r297328;
        double r297331 = 3.0;
        double r297332 = r297330 - r297331;
        return r297332;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

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

Derivation

  1. Initial program 5.1

    \[\frac{x}{y \cdot y} - 3\]
  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 2019354 
(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))