Not everything can be compiled, and very simple code might not benefit, but complex low-level numerical code can get a really big speedup. This takes away some of the flexibility of the Mathematica language, but freed from having to worry about “What if the argument was symbolic?” and the like, Mathematica can optimize the program and create a byte code to run on its own virtual machine. The Compile function takes Mathematica code and allows you to pre-declare the types (real, complex, etc.) and structures (value, list, matrix, etc.) of input arguments. It only takes one exact value to cause the whole dataset to have to be held in a more flexible but less efficient form. When working with lists of data, be consistent in your use of reals. For example, solving this polynomial symbolically before substituting the values in causes Mathematica to produce a five-page-long intermediate symbolic expression.īut do the substitution first, and Solve will use fast numerical methods. If you don’t care about the symbolic answer and are not worried about stability, then substitute numerical values as soon as you can.

The same is true for symbolic computation. And in this case it gets the same result. Here is a simple example where working with floating-point numbers is nearly 50.6 times faster than doing the computation exactly and then converting the result to a decimal afterward. In Mathematica any number with a decimal point and less than 16 digits of input is automatically treated as a machine float, so always use the decimal point if you want speed ahead of accuracy (e.g. 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.

Mathematica code online