Average Error: 5.0 → 0.1
Time: 2.3s
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 r221849 = x;
        double r221850 = y;
        double r221851 = r221850 * r221850;
        double r221852 = r221849 / r221851;
        double r221853 = 3.0;
        double r221854 = r221852 - r221853;
        return r221854;
}
↓
double f(double x, double y) {
        double r221855 = x;
        double r221856 = y;
        double r221857 = r221855 / r221856;
        double r221858 = r221857 / r221856;
        double r221859 = 3.0;
        double r221860 = r221858 - r221859;
        return r221860;
}

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2020002 +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))