Average Error: 5.0 → 0.1
Time: 12.7s
Precision: 64
\[\frac{x}{y \cdot y} - 3\]
↓
\[\frac{1}{y} \cdot \frac{x}{y} - 3\]
\frac{x}{y \cdot y} - 3
↓
\frac{1}{y} \cdot \frac{x}{y} - 3
double f(double x, double y) {
        double r243756 = x;
        double r243757 = y;
        double r243758 = r243757 * r243757;
        double r243759 = r243756 / r243758;
        double r243760 = 3.0;
        double r243761 = r243759 - r243760;
        return r243761;
}
↓
double f(double x, double y) {
        double r243762 = 1.0;
        double r243763 = y;
        double r243764 = r243762 / r243763;
        double r243765 = x;
        double r243766 = r243765 / r243763;
        double r243767 = r243764 * r243766;
        double r243768 = 3.0;
        double r243769 = r243767 - r243768;
        return r243769;
}

Error

Bits error versus x

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

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

Reproduce

herbie shell --seed 2019305 +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))