Average Error: 4.9 → 0.1
Time: 3.0s
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 r280165 = x;
        double r280166 = y;
        double r280167 = r280166 * r280166;
        double r280168 = r280165 / r280167;
        double r280169 = 3.0;
        double r280170 = r280168 - r280169;
        return r280170;
}
↓
double f(double x, double y) {
        double r280171 = x;
        double r280172 = y;
        double r280173 = r280171 / r280172;
        double r280174 = r280173 / r280172;
        double r280175 = 3.0;
        double r280176 = r280174 - r280175;
        return r280176;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original4.9
Target0.1
Herbie0.1
\[\frac{\frac{x}{y}}{y} - 3\]

Derivation

  1. Initial program 4.9

    \[\frac{x}{y \cdot y} - 3\]
  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 2020100 
(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))