Average Error: 5.4 → 0.1
Time: 11.9s
Precision: 64
\[\frac{x}{y \cdot y} - 3\]
↓
\[\frac{1}{\frac{y}{x} \cdot y} - 3\]
\frac{x}{y \cdot y} - 3
↓
\frac{1}{\frac{y}{x} \cdot y} - 3
double f(double x, double y) {
        double r243905 = x;
        double r243906 = y;
        double r243907 = r243906 * r243906;
        double r243908 = r243905 / r243907;
        double r243909 = 3.0;
        double r243910 = r243908 - r243909;
        return r243910;
}
↓
double f(double x, double y) {
        double r243911 = 1.0;
        double r243912 = y;
        double r243913 = x;
        double r243914 = r243912 / r243913;
        double r243915 = r243914 * r243912;
        double r243916 = r243911 / r243915;
        double r243917 = 3.0;
        double r243918 = r243916 - r243917;
        return r243918;
}

Error

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Bits error versus y

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Results

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Target

Original5.4
Target0.1
Herbie0.1
\[\frac{\frac{x}{y}}{y} - 3\]

Derivation

  1. Initial program 5.4

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

  3. Applied associate-/r*0.1

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

  5. Applied *-un-lft-identity0.1

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

  6. Applied *-un-lft-identity0.1

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

  7. Applied times-frac0.1

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

  8. Applied associate-/l*0.1

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

  9. Simplified0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2020047 +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))