Average Error: 5.3 → 0.1
Time: 9.2s
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 r354220 = x;
        double r354221 = y;
        double r354222 = r354221 * r354221;
        double r354223 = r354220 / r354222;
        double r354224 = 3.0;
        double r354225 = r354223 - r354224;
        return r354225;
}
↓
double f(double x, double y) {
        double r354226 = x;
        double r354227 = y;
        double r354228 = r354226 / r354227;
        double r354229 = r354228 / r354227;
        double r354230 = 3.0;
        double r354231 = r354229 - r354230;
        return r354231;
}

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 2020046 
(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))