Average Error: 5.3 → 0.1
Time: 29.9s
Precision: 64
\[\frac{x}{y \cdot y} - 3\]
↓
\[\frac{1}{y} \cdot \frac{x}{y} - 3\]
\frac{x}{y \cdot y} - 3
↓
\frac{1}{y} \cdot \frac{x}{y} - 3
double f(double x, double y) {
        double r13197688 = x;
        double r13197689 = y;
        double r13197690 = r13197689 * r13197689;
        double r13197691 = r13197688 / r13197690;
        double r13197692 = 3.0;
        double r13197693 = r13197691 - r13197692;
        return r13197693;
}
↓
double f(double x, double y) {
        double r13197694 = 1.0;
        double r13197695 = y;
        double r13197696 = r13197694 / r13197695;
        double r13197697 = x;
        double r13197698 = r13197697 / r13197695;
        double r13197699 = r13197696 * r13197698;
        double r13197700 = 3.0;
        double r13197701 = r13197699 - r13197700;
        return r13197701;
}

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. Using strategy rm

  5. Applied div-inv0.1

    \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{1}{y}} - 3\]

  6. Final simplification0.1

    \[\leadsto \frac{1}{y} \cdot \frac{x}{y} - 3\]

Reproduce

herbie shell --seed 2019168 
(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))