The vagaries of floating point mean this "terrible" scenario essentially happens already. For example, a "double" variable isn't the same from one machine to a

The vagaries of floating point mean this "terrible" scenario essentially happens already. For example, a "double" variable isn't the same from one machine to another. And debug vs release versions of the same numerical code, built with the same compiler and run on the same machine, can arrive at different answers. These things lead to much gnashing of teeth in the scientific programming community already. I have a numerical code that I cross-compile with gcc -O0, gcc -O3, clang, icc, and MS Visual C, all on the same machine. Each version can give slightly different results. The fact that they don't give wildly different results is mainly down to the stability (in the ODE sense) of the problems run. Unstable problems would definitely give different results.