Average Error: 5.1 → 0.1
Time: 9.7s
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 r19071536 = x;
        double r19071537 = y;
        double r19071538 = r19071537 * r19071537;
        double r19071539 = r19071536 / r19071538;
        double r19071540 = 3.0;
        double r19071541 = r19071539 - r19071540;
        return r19071541;
}
↓
double f(double x, double y) {
        double r19071542 = x;
        double r19071543 = y;
        double r19071544 = r19071542 / r19071543;
        double r19071545 = r19071544 / r19071543;
        double r19071546 = 3.0;
        double r19071547 = r19071545 - r19071546;
        return r19071547;
}

Error

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Bits error versus y

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Results

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Target

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

Derivation

  1. Initial program 5.1

    \[\frac{x}{y \cdot y} - 3\]
  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 2019171 
(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))