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

↓

\[\frac{y \cdot \left(230661.510616 + \sqrt[3]{y} \cdot \left(\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right)\right)\right) + t}{y \cdot \left(c + \left(b + y \cdot \left(y + a\right)\right) \cdot y\right) + i}\]

Error

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

Derivation

Initial program 28.3
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
Using strategy rm
Applied add-cube-cbrt28.4
\[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot \color{blue}{\left(\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}\right)} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
Applied associate-*r*28.4
\[\leadsto \frac{\left(\color{blue}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)\right) \cdot \sqrt[3]{y}} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
Final simplification28.4
\[\leadsto \frac{y \cdot \left(230661.510616 + \sqrt[3]{y} \cdot \left(\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right)\right)\right) + t}{y \cdot \left(c + \left(b + y \cdot \left(y + a\right)\right) \cdot y\right) + i}\]

Reproduce

herbie shell --seed 2019100 
(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)))