Average Error: 5.0 → 0.1
Time: 17.5s
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 r10140216 = x;
        double r10140217 = y;
        double r10140218 = r10140217 * r10140217;
        double r10140219 = r10140216 / r10140218;
        double r10140220 = 3.0;
        double r10140221 = r10140219 - r10140220;
        return r10140221;
}
↓
double f(double x, double y) {
        double r10140222 = x;
        double r10140223 = y;
        double r10140224 = r10140222 / r10140223;
        double r10140225 = r10140224 / r10140223;
        double r10140226 = 3.0;
        double r10140227 = r10140225 - r10140226;
        return r10140227;
}

Error

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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. Final simplification0.1

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

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))