Average Error: 4.9 → 0.1
Time: 14.3s
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 r14895689 = x;
        double r14895690 = y;
        double r14895691 = r14895690 * r14895690;
        double r14895692 = r14895689 / r14895691;
        double r14895693 = 3.0;
        double r14895694 = r14895692 - r14895693;
        return r14895694;
}
↓
double f(double x, double y) {
        double r14895695 = x;
        double r14895696 = y;
        double r14895697 = r14895695 / r14895696;
        double r14895698 = r14895697 / r14895696;
        double r14895699 = 3.0;
        double r14895700 = r14895698 - r14895699;
        return r14895700;
}

Error

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Bits error versus y

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Results

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Target

Original4.9
Target0.1
Herbie0.1
\[\frac{\frac{x}{y}}{y} - 3\]

Derivation

  1. Initial program 4.9

    \[\frac{x}{y \cdot y} - 3\]
  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 2019170 +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))