Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, A

Average Error: 0.0 → 0.0

Time: 1.0s

Precision: 64

Math

\[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673003\]

↓

\[\left(x \cdot y + 0.918938533204673003\right) - \left(1 \cdot x + 0.5 \cdot y\right)\]

C

double code(double x, double y) {
	return (((x * (y - 1.0)) - (y * 0.5)) + 0.918938533204673);
}

↓

double code(double x, double y) {
	return (((x * y) + 0.918938533204673) - ((1.0 * x) + (0.5 * y)));
}

Error

Bits error versus x

Bits error versus y

Derivation

1. Initial program 0.0

   \[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673003\]
2. Using strategy rm

3. Applied sub-neg 0.0

   \[\leadsto \left(x \cdot \color{blue}{\left(y + \left(-1\right)\right)} - y \cdot 0.5\right) + 0.918938533204673003\]

4. Applied distribute-lft-in 0.0

   \[\leadsto \left(\color{blue}{\left(x \cdot y + x \cdot \left(-1\right)\right)} - y \cdot 0.5\right) + 0.918938533204673003\]

5. Applied associate--l+ 0.0

   \[\leadsto \color{blue}{\left(x \cdot y + \left(x \cdot \left(-1\right) - y \cdot 0.5\right)\right)} + 0.918938533204673003\]

6. Applied associate-+l+ 0.0

   \[\leadsto \color{blue}{x \cdot y + \left(\left(x \cdot \left(-1\right) - y \cdot 0.5\right) + 0.918938533204673003\right)}\]

7. Simplified 0.0

   \[\leadsto x \cdot y + \color{blue}{\left(0.918938533204673003 - \left(1 \cdot x + 0.5 \cdot y\right)\right)}\]
8. Using strategy rm

9. Applied associate-+r- 0.0

   \[\leadsto \color{blue}{\left(x \cdot y + 0.918938533204673003\right) - \left(1 \cdot x + 0.5 \cdot y\right)}\]

10. Final simplification 0.0

    \[\leadsto \left(x \cdot y + 0.918938533204673003\right) - \left(1 \cdot x + 0.5 \cdot y\right)\]

Reproduce

herbie shell --seed 2020100 
(FPCore (x y)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (+ (- (* x (- y 1)) (* y 0.5)) 0.918938533204673))