Average Error: 4.8 → 0.1
Time: 2.2s
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 r366496 = x;
        double r366497 = y;
        double r366498 = r366497 * r366497;
        double r366499 = r366496 / r366498;
        double r366500 = 3.0;
        double r366501 = r366499 - r366500;
        return r366501;
}
↓
double f(double x, double y) {
        double r366502 = x;
        double r366503 = y;
        double r366504 = r366502 / r366503;
        double r366505 = r366504 / r366503;
        double r366506 = 3.0;
        double r366507 = r366505 - r366506;
        return r366507;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original4.8
Target0.1
Herbie0.1
\[\frac{\frac{x}{y}}{y} - 3\]

Derivation

  1. Initial program 4.8

    \[\frac{x}{y \cdot y} - 3\]
  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 2020001 
(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))