\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
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: 21.9 s
Input Error: 14.0
Output Error: 13.1
Log: ⚲
Profile: 🕒
\(\frac{(\left((\left((y * x + z)_*\right) * \left(y \cdot y\right) + \left((y * 27464.7644705 + 230661.510616)_*\right))_*\right) * y + t)_*}{\left((\left(y + a\right) * y + b)_* \cdot y\right) \cdot y + (y * c + i)_*}\)
  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. Applied simplify to get
    \[\color{red}{\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}} \leadsto \color{blue}{\frac{(\left((\left((y * x + z)_*\right) * \left(y \cdot y\right) + \left((y * 27464.7644705 + 230661.510616)_*\right))_*\right) * y + t)_*}{(\left(y \cdot y\right) * \left((\left(y + a\right) * y + b)_*\right) + \left((y * c + i)_*\right))_*}}\]
    14.1
  3. Using strategy rm
    14.1
  4. Applied fma-udef to get
    \[\frac{(\left((\left((y * x + z)_*\right) * \left(y \cdot y\right) + \left((y * 27464.7644705 + 230661.510616)_*\right))_*\right) * y + t)_*}{\color{red}{(\left(y \cdot y\right) * \left((\left(y + a\right) * y + b)_*\right) + \left((y * c + i)_*\right))_*}} \leadsto \frac{(\left((\left((y * x + z)_*\right) * \left(y \cdot y\right) + \left((y * 27464.7644705 + 230661.510616)_*\right))_*\right) * y + t)_*}{\color{blue}{\left(y \cdot y\right) \cdot (\left(y + a\right) * y + b)_* + (y * c + i)_*}}\]
    13.2
  5. Applied simplify to get
    \[\frac{(\left((\left((y * x + z)_*\right) * \left(y \cdot y\right) + \left((y * 27464.7644705 + 230661.510616)_*\right))_*\right) * y + t)_*}{\color{red}{\left(y \cdot y\right) \cdot (\left(y + a\right) * y + b)_*} + (y * c + i)_*} \leadsto \frac{(\left((\left((y * x + z)_*\right) * \left(y \cdot y\right) + \left((y * 27464.7644705 + 230661.510616)_*\right))_*\right) * y + t)_*}{\color{blue}{(\left(y + a\right) * y + b)_* \cdot {y}^2} + (y * c + i)_*}\]
    13.2
  6. Using strategy rm
    13.2
  7. Applied square-mult to get
    \[\frac{(\left((\left((y * x + z)_*\right) * \left(y \cdot y\right) + \left((y * 27464.7644705 + 230661.510616)_*\right))_*\right) * y + t)_*}{(\left(y + a\right) * y + b)_* \cdot \color{red}{{y}^2} + (y * c + i)_*} \leadsto \frac{(\left((\left((y * x + z)_*\right) * \left(y \cdot y\right) + \left((y * 27464.7644705 + 230661.510616)_*\right))_*\right) * y + t)_*}{(\left(y + a\right) * y + b)_* \cdot \color{blue}{\left(y \cdot y\right)} + (y * c + i)_*}\]
    13.2
  8. Applied associate-*r* to get
    \[\frac{(\left((\left((y * x + z)_*\right) * \left(y \cdot y\right) + \left((y * 27464.7644705 + 230661.510616)_*\right))_*\right) * y + t)_*}{\color{red}{(\left(y + a\right) * y + b)_* \cdot \left(y \cdot y\right)} + (y * c + i)_*} \leadsto \frac{(\left((\left((y * x + z)_*\right) * \left(y \cdot y\right) + \left((y * 27464.7644705 + 230661.510616)_*\right))_*\right) * y + t)_*}{\color{blue}{\left((\left(y + a\right) * y + b)_* \cdot y\right) \cdot y} + (y * c + i)_*}\]
    13.1
  9. Removed slow pow expressions

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)))