Average Error: 5.0 → 0.1
Time: 9.9s
Precision: 64
\[\frac{x}{y \cdot y} - 3\]
↓
\[\frac{x}{y} \cdot \frac{1}{y} - 3\]
\frac{x}{y \cdot y} - 3
↓
\frac{x}{y} \cdot \frac{1}{y} - 3
double f(double x, double y) {
        double r205795 = x;
        double r205796 = y;
        double r205797 = r205796 * r205796;
        double r205798 = r205795 / r205797;
        double r205799 = 3.0;
        double r205800 = r205798 - r205799;
        return r205800;
}
↓
double f(double x, double y) {
        double r205801 = x;
        double r205802 = y;
        double r205803 = r205801 / r205802;
        double r205804 = 1.0;
        double r205805 = r205804 / r205802;
        double r205806 = r205803 * r205805;
        double r205807 = 3.0;
        double r205808 = r205806 - r205807;
        return r205808;
}

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 *-un-lft-identity5.0

    \[\leadsto \frac{\color{blue}{1 \cdot x}}{y \cdot y} - 3\]

  4. Applied times-frac0.1

    \[\leadsto \color{blue}{\frac{1}{y} \cdot \frac{x}{y}} - 3\]

  5. Final simplification0.1

    \[\leadsto \frac{x}{y} \cdot \frac{1}{y} - 3\]

Reproduce

herbie shell --seed 2019196 
(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))