Average Error: 4.8 → 0.1
Time: 2.4s
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 r338581 = x;
        double r338582 = y;
        double r338583 = r338582 * r338582;
        double r338584 = r338581 / r338583;
        double r338585 = 3.0;
        double r338586 = r338584 - r338585;
        return r338586;
}
↓
double f(double x, double y) {
        double r338587 = x;
        double r338588 = y;
        double r338589 = r338587 / r338588;
        double r338590 = r338589 / r338588;
        double r338591 = 3.0;
        double r338592 = r338590 - r338591;
        return r338592;
}

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 2020003 
(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))