Average Error: 5.0 → 0.1
Time: 13.3s
Precision: 64
\[\frac{x}{y \cdot y} - 3\]
↓
\[\frac{1}{y \cdot \frac{y}{x}} - 3\]
\frac{x}{y \cdot y} - 3
↓
\frac{1}{y \cdot \frac{y}{x}} - 3
double f(double x, double y) {
        double r347854 = x;
        double r347855 = y;
        double r347856 = r347855 * r347855;
        double r347857 = r347854 / r347856;
        double r347858 = 3.0;
        double r347859 = r347857 - r347858;
        return r347859;
}
↓
double f(double x, double y) {
        double r347860 = 1.0;
        double r347861 = y;
        double r347862 = x;
        double r347863 = r347861 / r347862;
        double r347864 = r347861 * r347863;
        double r347865 = r347860 / r347864;
        double r347866 = 3.0;
        double r347867 = r347865 - r347866;
        return r347867;
}

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 associate-/r*0.1

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

  5. Applied clear-num0.1

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

  6. Simplified0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2020042 
(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))