Average Error: 4.8 → 0.1
Time: 2.1s
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 r286425 = x;
        double r286426 = y;
        double r286427 = r286426 * r286426;
        double r286428 = r286425 / r286427;
        double r286429 = 3.0;
        double r286430 = r286428 - r286429;
        return r286430;
}
↓
double f(double x, double y) {
        double r286431 = x;
        double r286432 = y;
        double r286433 = r286431 / r286432;
        double r286434 = r286433 / r286432;
        double r286435 = 3.0;
        double r286436 = r286434 - r286435;
        return r286436;
}

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))