Average Error: 5.1 → 0.1
Time: 10.9s
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 r321781 = x;
        double r321782 = y;
        double r321783 = r321782 * r321782;
        double r321784 = r321781 / r321783;
        double r321785 = 3.0;
        double r321786 = r321784 - r321785;
        return r321786;
}
↓
double f(double x, double y) {
        double r321787 = x;
        double r321788 = y;
        double r321789 = r321787 / r321788;
        double r321790 = r321789 / r321788;
        double r321791 = 3.0;
        double r321792 = r321790 - r321791;
        return r321792;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

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

Derivation

  1. Initial program 5.1

    \[\frac{x}{y \cdot y} - 3\]
  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 2020060 
(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))