Average Error: 5.3 → 0.1
Time: 2.5s
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 r337443 = x;
        double r337444 = y;
        double r337445 = r337444 * r337444;
        double r337446 = r337443 / r337445;
        double r337447 = 3.0;
        double r337448 = r337446 - r337447;
        return r337448;
}
↓
double f(double x, double y) {
        double r337449 = x;
        double r337450 = y;
        double r337451 = r337449 / r337450;
        double r337452 = r337451 / r337450;
        double r337453 = 3.0;
        double r337454 = r337452 - r337453;
        return r337454;
}

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 2020062 +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))