Average Error: 4.6 → 0.1
Time: 9.4s
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 r13719599 = x;
        double r13719600 = y;
        double r13719601 = r13719600 * r13719600;
        double r13719602 = r13719599 / r13719601;
        double r13719603 = 3.0;
        double r13719604 = r13719602 - r13719603;
        return r13719604;
}
↓
double f(double x, double y) {
        double r13719605 = x;
        double r13719606 = y;
        double r13719607 = r13719605 / r13719606;
        double r13719608 = r13719607 / r13719606;
        double r13719609 = 3.0;
        double r13719610 = r13719608 - r13719609;
        return r13719610;
}

Error

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Bits error versus y

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Results

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Target

Original4.6
Target0.1
Herbie0.1
\[\frac{\frac{x}{y}}{y} - 3\]

Derivation

  1. Initial program 4.6

    \[\frac{x}{y \cdot y} - 3\]
  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 2019174 
(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))