Average Error: 5.1 → 0.1
Time: 1.7s
Precision: 64
\[\frac{x}{y \cdot y} - 3\]
↓
\[\frac{1}{\frac{y}{\frac{x}{y}}} - 3\]
\frac{x}{y \cdot y} - 3
↓
\frac{1}{\frac{y}{\frac{x}{y}}} - 3
double f(double x, double y) {
        double r281678 = x;
        double r281679 = y;
        double r281680 = r281679 * r281679;
        double r281681 = r281678 / r281680;
        double r281682 = 3.0;
        double r281683 = r281681 - r281682;
        return r281683;
}
↓
double f(double x, double y) {
        double r281684 = 1.0;
        double r281685 = y;
        double r281686 = x;
        double r281687 = r281686 / r281685;
        double r281688 = r281685 / r281687;
        double r281689 = r281684 / r281688;
        double r281690 = 3.0;
        double r281691 = r281689 - r281690;
        return r281691;
}

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. Using strategy rm

  5. Applied clear-num0.1

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

  6. Final simplification0.1

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

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))