How fast is Mathematica?
A1. In most areas, Mathematica is extremely well optimised. In fact, it routinely beats custom C code–mainly because it is using much more sophisticated algorithms. You can think of Mathematica as having built-in functions that cover certain common chunks of computational functionality. Once you’re inside a chunk (such as, say, eigenvalues), Mathematica will go as fast as anything else–and often faster. But if you have lots of separate chunks, the generality of Mathematica can potentially slow it down since it has to do a lot of checking between each chunk. Version 3.0, however, has a sophisticated compiler that makes even these kinds of computations go spectacularly fast when the only objects involved are numbers.
