The definition I use for determinism is "same inputs and same order = same results", down to the compiler level. All modern compilers on all modern platforms that I've tested take steps to ensure that for everything except transcendental and special functions (where it'd be an unreasonable guarantee).

I'm somewhat less interested in correctness of the results, so long as they're consistent. rlibm and related are definitely neat, but I'm not optimistic they'll become mainstream.