Average Error: 5.0 → 0.1
Time: 7.5s
Precision: 64
\[\frac{x}{y \cdot y} - 3\]
↓
\[\frac{1}{y} \cdot \frac{x}{y} - 3\]
\frac{x}{y \cdot y} - 3
↓
\frac{1}{y} \cdot \frac{x}{y} - 3
double f(double x, double y) {
        double r200457 = x;
        double r200458 = y;
        double r200459 = r200458 * r200458;
        double r200460 = r200457 / r200459;
        double r200461 = 3.0;
        double r200462 = r200460 - r200461;
        return r200462;
}
↓
double f(double x, double y) {
        double r200463 = 1.0;
        double r200464 = y;
        double r200465 = r200463 / r200464;
        double r200466 = x;
        double r200467 = r200466 / r200464;
        double r200468 = r200465 * r200467;
        double r200469 = 3.0;
        double r200470 = r200468 - r200469;
        return r200470;
}

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 *-un-lft-identity5.0

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

  4. Applied times-frac0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019305 
(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))