Average Error: 5.1 → 0.1
Time: 2.2s
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 r224880 = x;
        double r224881 = y;
        double r224882 = r224881 * r224881;
        double r224883 = r224880 / r224882;
        double r224884 = 3.0;
        double r224885 = r224883 - r224884;
        return r224885;
}
↓
double f(double x, double y) {
        double r224886 = x;
        double r224887 = y;
        double r224888 = r224886 / r224887;
        double r224889 = r224888 / r224887;
        double r224890 = 3.0;
        double r224891 = r224889 - r224890;
        return r224891;
}

Error

Bits error versus x

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 *-un-lft-identity5.1

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

  4. Applied times-frac0.1

    \[\leadsto \color{blue}{\frac{1}{y} \cdot \frac{x}{y}} - 3\]
  5. Using strategy rm

  6. Applied associate-*r/0.1

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019308 
(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))