Average Error: 4.5 → 0.1
Time: 12.6s
Precision: 64
\[\frac{x}{y \cdot y} - 3.0\]
↓
\[\frac{\frac{1}{\frac{y}{x}}}{y} - 3.0\]
\frac{x}{y \cdot y} - 3.0
↓
\frac{\frac{1}{\frac{y}{x}}}{y} - 3.0
double f(double x, double y) {
        double r10784779 = x;
        double r10784780 = y;
        double r10784781 = r10784780 * r10784780;
        double r10784782 = r10784779 / r10784781;
        double r10784783 = 3.0;
        double r10784784 = r10784782 - r10784783;
        return r10784784;
}
↓
double f(double x, double y) {
        double r10784785 = 1.0;
        double r10784786 = y;
        double r10784787 = x;
        double r10784788 = r10784786 / r10784787;
        double r10784789 = r10784785 / r10784788;
        double r10784790 = r10784789 / r10784786;
        double r10784791 = 3.0;
        double r10784792 = r10784790 - r10784791;
        return r10784792;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original4.5
Target0.1
Herbie0.1
\[\frac{\frac{x}{y}}{y} - 3.0\]

Derivation

  1. Initial program 4.5

    \[\frac{x}{y \cdot y} - 3.0\]
  2. Using strategy rm

  3. Applied associate-/r*0.1

    \[\leadsto \color{blue}{\frac{\frac{x}{y}}{y}} - 3.0\]
  4. Using strategy rm

  5. Applied clear-num0.1

    \[\leadsto \color{blue}{\frac{1}{\frac{y}{\frac{x}{y}}}} - 3.0\]
  6. Using strategy rm

  7. Applied associate-/r/0.1

    \[\leadsto \frac{1}{\color{blue}{\frac{y}{x} \cdot y}} - 3.0\]

  8. Applied associate-/r*0.1

    \[\leadsto \color{blue}{\frac{\frac{1}{\frac{y}{x}}}{y}} - 3.0\]

  9. Final simplification0.1

    \[\leadsto \frac{\frac{1}{\frac{y}{x}}}{y} - 3.0\]

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(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))