Average Error: 5.4 → 0.1
Time: 2.5s
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 r258759 = x;
        double r258760 = y;
        double r258761 = r258760 * r258760;
        double r258762 = r258759 / r258761;
        double r258763 = 3.0;
        double r258764 = r258762 - r258763;
        return r258764;
}
↓
double f(double x, double y) {
        double r258765 = x;
        double r258766 = y;
        double r258767 = r258765 / r258766;
        double r258768 = r258767 / r258766;
        double r258769 = 3.0;
        double r258770 = r258768 - r258769;
        return r258770;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original5.4
Target0.1
Herbie0.1
\[\frac{\frac{x}{y}}{y} - 3\]

Derivation

  1. Initial program 5.4

    \[\frac{x}{y \cdot y} - 3\]
  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 2020047 
(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))