Numeric.SpecFunctions:$slogFactorial from math-functions-0.1.5.2, A

Average Error: 0.6 → 0.2

Time: 6.3s

Precision: binary64

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

Math

\[\frac{1}{x \cdot x}\]

↓

\[\frac{\frac{1}{x}}{x}\]

C

double code(double x) {
	return (1.0 / ((double) (x * x)));
}

↓

double code(double x) {
	return ((1.0 / x) / x);
}

Error

Bits error versus x

Target

Original	0.6
Target	0.2
Herbie	0.2

\[\frac{\frac{1}{x}}{x}\]

Derivation

1. Initial program 0.6

   \[\frac{1}{x \cdot x}\]
2. Using strategy rm

3. Applied associate-/r* 0.2

   \[\leadsto \color{blue}{\frac{\frac{1}{x}}{x}}\]

4. Final simplification 0.2

   \[\leadsto \frac{\frac{1}{x}}{x}\]

Reproduce

herbie shell --seed 2020182 
(FPCore (x)
  :name "Numeric.SpecFunctions:$slogFactorial from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (/ (/ 1.0 x) x)

  (/ 1.0 (* x x)))