Average Error: 5.1 → 0.1
Time: 10.0s
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 r8867822 = x;
        double r8867823 = y;
        double r8867824 = r8867823 * r8867823;
        double r8867825 = r8867822 / r8867824;
        double r8867826 = 3.0;
        double r8867827 = r8867825 - r8867826;
        return r8867827;
}
↓
double f(double x, double y) {
        double r8867828 = x;
        double r8867829 = y;
        double r8867830 = r8867828 / r8867829;
        double r8867831 = r8867830 / r8867829;
        double r8867832 = 3.0;
        double r8867833 = r8867831 - r8867832;
        return r8867833;
}

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 2019171 +o rules:numerics
(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))