Average Error: 4.9 → 0.1
Time: 15.0s
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 r280754 = x;
        double r280755 = y;
        double r280756 = r280755 * r280755;
        double r280757 = r280754 / r280756;
        double r280758 = 3.0;
        double r280759 = r280757 - r280758;
        return r280759;
}
↓
double f(double x, double y) {
        double r280760 = 1.0;
        double r280761 = y;
        double r280762 = r280760 / r280761;
        double r280763 = x;
        double r280764 = r280763 / r280761;
        double r280765 = r280762 * r280764;
        double r280766 = 3.0;
        double r280767 = r280765 - r280766;
        return r280767;
}

Error

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Bits error versus y

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Results

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Target

Original4.9
Target0.1
Herbie0.1
\[\frac{\frac{x}{y}}{y} - 3\]

Derivation

  1. Initial program 4.9

    \[\frac{x}{y \cdot y} - 3\]
  2. Using strategy rm

  3. Applied *-un-lft-identity4.9

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

  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 2019351 +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))