[pklo]

Sorry--forgot to specify the values for the polynomial: 77617 and 33096. In Maxima, the effects of precision can be simulated thus:

  for fpprec:10 step 5 thru 50 do print (rp(77617.0b0, 33096.0b0));

1.17260394b0 1.17260394005318b0 1.8014398509481985173b16 1.172603940053178631858835b0 1.17260394005317863185883490452b0 1.1726039400531786318588349045201837b0 -8.27396059946821368141165095479816291999b-1 -8.27396059946821368141165095479816291999033116b-1 -8.2739605994682136814116509547981629199903311578439b-1

google will find you more info about Rump's polynomial..

[GFK_of_xmaspast]

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.