code generation and simplification

[Matthew Emmett]

Hi everyone,

I have some sympy code that generates Fortran code, and was wondering
if there a good way of simplifying the sympy expressions in order to
minimize the number of floating point operations that are required to
evaluate them numerically. Any suggestions?

Thanks,
Matt

[Aaron Meurer]

One thing you can try is to use the cse() function to group common
subexpressions so that they are only evaluated once.

Aaron Meurer

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[Matthew Rocklin]

SymPy may be able to help by counting operations in a given expression. I don't think you want it controlling the optimization search though.

I'm not very familiar with the relevant modules but I don't think it will be easy to perform this optimization within SymPy. To the best of my knowledge It is not easy to separate out the simplification rules and choose whether or not to apply each of them.

If you haven't already I recommend asking a non-sympy-specific version of this question on scicomp.stackexchange.com 

[Matthew Emmett]

Thanks Aaron and Matthew, I will take a look at the cse routine and
consider asking a general version of this on the scicomp site.

Matt

[Vinzent Steinberg]

There is Ignition [1], which uses Sympy for optimizing numerical expressions. See for example Andy's paper [2].

Vinzent

[1] http://andy.terrel.us/ignition/ 

[2] http://andy.terrel.us/ignition/downloads/Terrel2011.pdf

[Matthew Rocklin]

There is also the Theano project which is all about code generation on array expressions. They've optimized a lot of this stuff much more than SymPy has. It's a bit harder to get out a single code snippet with them though. They generate working C and CUDA code and then wrap it into python functions under the hood. 

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[Julien Rioux]

If you're working with polynomials, there is a function that returns the Horner form in the polys module, reducing the number of operations.

Cheers,
Julien