Average Error: 5.0 → 0.1
Time: 9.9s
Precision: 64
\[\frac{x}{y \cdot y} - 3\]
↓
\[\frac{\frac{1}{\frac{y}{x}}}{y} - 3\]
\frac{x}{y \cdot y} - 3
↓
\frac{\frac{1}{\frac{y}{x}}}{y} - 3
double f(double x, double y) {
        double r9799725 = x;
        double r9799726 = y;
        double r9799727 = r9799726 * r9799726;
        double r9799728 = r9799725 / r9799727;
        double r9799729 = 3.0;
        double r9799730 = r9799728 - r9799729;
        return r9799730;
}
↓
double f(double x, double y) {
        double r9799731 = 1.0;
        double r9799732 = y;
        double r9799733 = x;
        double r9799734 = r9799732 / r9799733;
        double r9799735 = r9799731 / r9799734;
        double r9799736 = r9799735 / r9799732;
        double r9799737 = 3.0;
        double r9799738 = r9799736 - r9799737;
        return r9799738;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original5.0
Target0.1
Herbie0.1
\[\frac{\frac{x}{y}}{y} - 3\]

Derivation

  1. Initial program 5.0

    \[\frac{x}{y \cdot y} - 3\]
  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. Using strategy rm

  7. Applied associate-/r/0.1

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

  8. Applied associate-/r*0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019172 +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))