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

↓

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

Error

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

Derivation

Initial program 28.7
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
Taylor expanded around inf 28.7
\[\leadsto \frac{\left(\left(\color{blue}{\left(z \cdot y + x \cdot {y}^{2}\right)} + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
Simplified28.7
\[\leadsto \frac{\left(\left(\color{blue}{(y \cdot x + z)_* \cdot y} + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
Final simplification28.7
\[\leadsto \frac{t + \left(y \cdot \left(27464.7644705 + (y \cdot x + z)_* \cdot y\right) + 230661.510616\right) \cdot y}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(a + y\right) + b\right)\right)}\]

Runtime

herbie shell --seed 2018248 +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)))