Numbers of that magnitude combined with sixth and eighth powers should get you thinking 'hey, something's fishy here'.

Also, here's a good reference: http://epubs.siam.org/doi/book/10.1137/1.9780898718027

And I'm too headachey to bother trying, but I wonder what happens if you ignore that x/2y part and put the rest of the thing into Horner's form.