Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Average Error: 28.4 → 27.7

Time: 8.7s

Precision: binary64

Math

\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

↓

\[\begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.764470499998\right) + 230661.510616000014\right) + t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} \le 2.1057622161334481 \cdot 10^{285}:\\ \;\;\;\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.764470499998\right) + 230661.510616000014\right) + t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return ((double) (((double) (((double) (((double) (((double) (((double) (((double) (((double) (((double) (x * y)) + z)) * y)) + 27464.7644705)) * y)) + 230661.510616)) * y)) + t)) / ((double) (((double) (((double) (((double) (((double) (((double) (((double) (y + a)) * y)) + b)) * y)) + c)) * y)) + i))));
}

↓

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double VAR;
	if ((((double) (((double) (((double) (y * ((double) (((double) (y * ((double) (((double) (y * ((double) (((double) (x * y)) + z)))) + 27464.7644705)))) + 230661.510616)))) + t)) / ((double) (((double) (y * ((double) (((double) (y * ((double) (((double) (y * ((double) (y + a)))) + b)))) + c)))) + i)))) <= 2.105762216133448e+285)) {
		VAR = ((double) (((double) (((double) (y * ((double) (((double) (y * ((double) (((double) (y * ((double) (((double) (x * y)) + z)))) + 27464.7644705)))) + 230661.510616)))) + t)) / ((double) (((double) (y * ((double) (((double) (y * ((double) (((double) (y * ((double) (y + a)))) + b)))) + c)))) + i))));
	} else {
		VAR = 0.0;
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus i

Derivation

1. Split input into 2 regimes

2. if (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)) < 2.1057622161334481e285

   1. Initial program 5.0

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

   if 2.1057622161334481e285 < (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))

   1. Initial program 63.4

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

   2. Taylor expanded around 0 61.7

      \[\leadsto \color{blue}{0}\]
3. Recombined 2 regimes into one program.

4. Final simplification 27.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.764470499998\right) + 230661.510616000014\right) + t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} \le 2.1057622161334481 \cdot 10^{285}:\\ \;\;\;\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.764470499998\right) + 230661.510616000014\right) + t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Reproduce

herbie shell --seed 2020184 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2"
  :precision binary64
  (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))