Average Error: 5.1 → 0.1
Time: 2.0s
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 r261927 = x;
        double r261928 = y;
        double r261929 = r261928 * r261928;
        double r261930 = r261927 / r261929;
        double r261931 = 3.0;
        double r261932 = r261930 - r261931;
        return r261932;
}
↓
double f(double x, double y) {
        double r261933 = x;
        double r261934 = y;
        double r261935 = r261933 / r261934;
        double r261936 = r261935 / r261934;
        double r261937 = 3.0;
        double r261938 = r261936 - r261937;
        return r261938;
}

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 associate-/r*0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2020036 
(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))