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 r266641 = x;
        double r266642 = y;
        double r266643 = r266642 * r266642;
        double r266644 = r266641 / r266643;
        double r266645 = 3.0;
        double r266646 = r266644 - r266645;
        return r266646;
}
↓
double f(double x, double y) {
        double r266647 = x;
        double r266648 = y;
        double r266649 = r266647 / r266648;
        double r266650 = r266649 / r266648;
        double r266651 = 3.0;
        double r266652 = r266650 - r266651;
        return r266652;
}

Error

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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 2020057 +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))