Without getting too much into a polemic here, there's one point I think deserves defense:
"The processor I'm using may of course have non-deterministic aspects. Indeed it might be struck by a cosmic ray and do something bizarre. However, its expected behavior is described in sufficient detail that Intel and AMD chips can be claimed to be, at some level indistinguishable."
As far as I know none of the algorithms in Mathematica are outside reach the of ordinary mathematical knowledge. I believe that a big chunk of Mathematica could be reimplemented only with what's on maths handbooks. Their view on how to name functions, however, is much better than the usual on the numerical analysis community.