Statistics.Sample:$skurtosis from math-functions-0.1.5.2

Average Error: 4.8 → 0.1

Time: 6.9s

Precision: binary64

• Falling back on racket egraph because egg-herbie package not installed

Math

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

↓

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

C

double code(double x, double y) {
	return ((double) ((x / ((double) (y * y))) - 3.0));
}

↓

double code(double x, double y) {
	return ((double) (((double) ((1.0 / y) * (x / y))) - 3.0));
}

Error

Bits error versus x

Bits error versus y

Target

Original	4.8
Target	0.1
Herbie	0.1

\[\frac{\frac{x}{y}}{y} - 3\]

Derivation

1. Initial program 4.8

   \[\frac{x}{y \cdot y} - 3\]
2. Using strategy rm

3. Applied *-un-lft-identity 4.8

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

4. Applied times-frac 0.1

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

5. Final simplification 0.1

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

Reproduce

herbie shell --seed 2020182 
(FPCore (x y)
  :name "Statistics.Sample:$skurtosis from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (- (/ (/ x y) y) 3.0)

  (- (/ x (* y y)) 3.0))