\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
Test:
Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2
Bits:
128 bits
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
Time: 22.7 s
Input Error: 14.0
Output Error: 13.2
Log: ⚲
Profile: 🕒
\({\left(\sqrt[3]{\frac{230661.510616 \cdot y + \left({y}^{3} \cdot z + \left(t + \left({y}^{4} \cdot x + 27464.7644705 \cdot {y}^2\right)\right)\right)}{{y}^{3} \cdot a + \left(y \cdot c + \left({y}^{4} + \left(i + {y}^2 \cdot b\right)\right)\right)}}\right)}^3\)
  1. Started with
    \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
    14.0
  2. Using strategy rm
    14.0
  3. Applied add-cube-cbrt to get
    \[\color{red}{\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}} \leadsto \color{blue}{{\left(\sqrt[3]{\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}}\right)}^3}\]
    14.3
  4. Applied taylor to get
    \[{\left(\sqrt[3]{\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}}\right)}^3 \leadsto {\left(\sqrt[3]{\frac{230661.510616 \cdot y + \left({y}^{3} \cdot z + \left(t + \left({y}^{4} \cdot x + 27464.7644705 \cdot {y}^2\right)\right)\right)}{{y}^{3} \cdot a + \left(y \cdot c + \left({y}^{4} + \left(i + {y}^2 \cdot b\right)\right)\right)}}\right)}^3\]
    13.2
  5. Taylor expanded around 0 to get
    \[{\color{red}{\left(\sqrt[3]{\frac{230661.510616 \cdot y + \left({y}^{3} \cdot z + \left(t + \left({y}^{4} \cdot x + 27464.7644705 \cdot {y}^2\right)\right)\right)}{{y}^{3} \cdot a + \left(y \cdot c + \left({y}^{4} + \left(i + {y}^2 \cdot b\right)\right)\right)}}\right)}}^3 \leadsto {\color{blue}{\left(\sqrt[3]{\frac{230661.510616 \cdot y + \left({y}^{3} \cdot z + \left(t + \left({y}^{4} \cdot x + 27464.7644705 \cdot {y}^2\right)\right)\right)}{{y}^{3} \cdot a + \left(y \cdot c + \left({y}^{4} + \left(i + {y}^2 \cdot b\right)\right)\right)}}\right)}}^3\]
    13.2

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)))