Average Error: 5.3 → 0.1
Time: 8.2s
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 r181989 = x;
        double r181990 = y;
        double r181991 = r181990 * r181990;
        double r181992 = r181989 / r181991;
        double r181993 = 3.0;
        double r181994 = r181992 - r181993;
        return r181994;
}
↓
double f(double x, double y) {
        double r181995 = x;
        double r181996 = y;
        double r181997 = r181995 / r181996;
        double r181998 = r181997 / r181996;
        double r181999 = 3.0;
        double r182000 = r181998 - r181999;
        return r182000;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

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

Derivation

  1. Initial program 5.3

    \[\frac{x}{y \cdot y} - 3\]
  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 2019235 +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))