Average Error: 5.3 → 0.1
Time: 26.6s
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 r241461 = x;
        double r241462 = y;
        double r241463 = r241462 * r241462;
        double r241464 = r241461 / r241463;
        double r241465 = 3.0;
        double r241466 = r241464 - r241465;
        return r241466;
}
↓
double f(double x, double y) {
        double r241467 = x;
        double r241468 = y;
        double r241469 = r241467 / r241468;
        double r241470 = r241469 / r241468;
        double r241471 = 3.0;
        double r241472 = r241470 - r241471;
        return r241472;
}

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 2019323 
(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))