Average Error: 5.3 → 0.1
Time: 9.9s
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 r12836937 = x;
        double r12836938 = y;
        double r12836939 = r12836938 * r12836938;
        double r12836940 = r12836937 / r12836939;
        double r12836941 = 3.0;
        double r12836942 = r12836940 - r12836941;
        return r12836942;
}
↓
double f(double x, double y) {
        double r12836943 = x;
        double r12836944 = y;
        double r12836945 = r12836943 / r12836944;
        double r12836946 = r12836945 / r12836944;
        double r12836947 = 3.0;
        double r12836948 = r12836946 - r12836947;
        return r12836948;
}

Error

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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 2019192 
(FPCore (x y)
  :name "Statistics.Sample:$skurtosis from math-functions-0.1.5.2"

  :herbie-target
  (- (/ (/ x y) y) 3.0)

  (- (/ x (* y y)) 3.0))