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

↓

\[\frac{1}{(\left((y \cdot \left((\left(y + a\right) \cdot y + b)_*\right) + c)_*\right) \cdot y + i)_*} \cdot (y \cdot \left((y \cdot \left((y \cdot \left((y \cdot x + z)_*\right) + 27464.7644705)_*\right) + 230661.510616)_*\right) + t)_*\]

Error

The X axis uses an exponential scale — Bits error versus `x`

Derivation

Initial program 28.2
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
Simplified28.2
\[\leadsto \color{blue}{\frac{(y \cdot \left((y \cdot \left((y \cdot \left((y \cdot x + z)_*\right) + 27464.7644705)_*\right) + 230661.510616)_*\right) + t)_*}{(\left((y \cdot \left((\left(y + a\right) \cdot y + b)_*\right) + c)_*\right) \cdot y + i)_*}}\]
Using strategy rm
Applied div-inv28.3
\[\leadsto \color{blue}{(y \cdot \left((y \cdot \left((y \cdot \left((y \cdot x + z)_*\right) + 27464.7644705)_*\right) + 230661.510616)_*\right) + t)_* \cdot \frac{1}{(\left((y \cdot \left((\left(y + a\right) \cdot y + b)_*\right) + c)_*\right) \cdot y + i)_*}}\]
Final simplification28.3
\[\leadsto \frac{1}{(\left((y \cdot \left((\left(y + a\right) \cdot y + b)_*\right) + c)_*\right) \cdot y + i)_*} \cdot (y \cdot \left((y \cdot \left((y \cdot \left((y \cdot x + z)_*\right) + 27464.7644705)_*\right) + 230661.510616)_*\right) + t)_*\]

Reproduce

herbie shell --seed 2019089 +o rules:numerics
(FPCore (x y z t a b c i)
  :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)))