Results for Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

Test:: Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2
Bits:: 128 bits

Time: 19.4 s

Input Error: 14.5

Output Error: 13.3

Log: ⚲

Profile: 🕒

\(\frac{\left(\left({y}^2 \cdot z + {y}^{3} \cdot x\right) + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\)

Started with
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

14.5
Applied taylor to get
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \leadsto \frac{\left(\left({y}^2 \cdot z + {y}^{3} \cdot x\right) + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

13.3
Taylor expanded around inf to get
\[\frac{\left(\color{red}{\left({y}^2 \cdot z + {y}^{3} \cdot x\right)} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \leadsto \frac{\left(\color{blue}{\left({y}^2 \cdot z + {y}^{3} \cdot x\right)} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

13.3

Original test:


(lambda ((x default) (y default) (z default) (t default) (a default) (b default) (c default) (i default))
  #:name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2"
  (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))