Average Error: 4.9 → 0.1
Time: 13.0s
Precision: 64
\[\frac{x}{y \cdot y} - 3.0\]
↓
\[\frac{\frac{x}{y}}{y} - 3.0\]
\frac{x}{y \cdot y} - 3.0
↓
\frac{\frac{x}{y}}{y} - 3.0
double f(double x, double y) {
        double r13102476 = x;
        double r13102477 = y;
        double r13102478 = r13102477 * r13102477;
        double r13102479 = r13102476 / r13102478;
        double r13102480 = 3.0;
        double r13102481 = r13102479 - r13102480;
        return r13102481;
}
↓
double f(double x, double y) {
        double r13102482 = x;
        double r13102483 = y;
        double r13102484 = r13102482 / r13102483;
        double r13102485 = r13102484 / r13102483;
        double r13102486 = 3.0;
        double r13102487 = r13102485 - r13102486;
        return r13102487;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original4.9
Target0.1
Herbie0.1
\[\frac{\frac{x}{y}}{y} - 3.0\]

Derivation

  1. Initial program 4.9

    \[\frac{x}{y \cdot y} - 3.0\]
  2. Using strategy rm

  3. Applied associate-/r*0.1

    \[\leadsto \color{blue}{\frac{\frac{x}{y}}{y}} - 3.0\]

  4. Final simplification0.1

    \[\leadsto \frac{\frac{x}{y}}{y} - 3.0\]

Reproduce

herbie shell --seed 2019162 +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))