That difference can be pretty important when you hit nasty, numerically unstable problems, but in the majority of tasks, floating-point numbers are good enough and, importantly, much faster. In most numerical software, there is no such thing as exact arithmetic. Unnecessary use of exact arithmetic is the most common case. Of the most common issues that I see when I review slow code is that the programmer has inadvertently asked Mathematica to do things more carefully than needed. Use floating-point numbers if you can, and use them early.
I thought I would share the list of things that I look for first when trying to optimize Mathematica code.ġ.
When people tell me that Mathematica isn’t fast enough, I usually ask to see the offending code and often find that the problem isn’t a lack in Mathematica‘s performance, but sub-optimal use of Mathematica.
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