Average Error: 5.0 → 0.1
Time: 1.9s
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 r279811 = x;
        double r279812 = y;
        double r279813 = r279812 * r279812;
        double r279814 = r279811 / r279813;
        double r279815 = 3.0;
        double r279816 = r279814 - r279815;
        return r279816;
}
↓
double f(double x, double y) {
        double r279817 = x;
        double r279818 = y;
        double r279819 = r279817 / r279818;
        double r279820 = r279819 / r279818;
        double r279821 = 3.0;
        double r279822 = r279820 - r279821;
        return r279822;
}

Error

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Bits error versus y

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Results

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Target

Original5.0
Target0.1
Herbie0.1
\[\frac{\frac{x}{y}}{y} - 3\]

Derivation

  1. Initial program 5.0

    \[\frac{x}{y \cdot y} - 3\]
  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 2019353 +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))