Average Error: 5.4 → 0.1
Time: 11.3s
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 r351477 = x;
        double r351478 = y;
        double r351479 = r351478 * r351478;
        double r351480 = r351477 / r351479;
        double r351481 = 3.0;
        double r351482 = r351480 - r351481;
        return r351482;
}
↓
double f(double x, double y) {
        double r351483 = x;
        double r351484 = y;
        double r351485 = r351483 / r351484;
        double r351486 = r351485 / r351484;
        double r351487 = 3.0;
        double r351488 = r351486 - r351487;
        return r351488;
}

Error

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Bits error versus y

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Results

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Target

Original5.4
Target0.1
Herbie0.1
\[\frac{\frac{x}{y}}{y} - 3\]

Derivation

  1. Initial program 5.4

    \[\frac{x}{y \cdot y} - 3\]
  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 2020047 
(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))