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Comment by vlmutolo | Hacker News Reader

An interesting tool to help preserve floating point precision is Herbie (https://herbie.uwplse.org/), which takes an expression as input and outputs an optimized version of it that will retain precision.

The example they give on their site is:

    sqrt(x+1) - sqrt(x)  =>  1/(sqrt(x+1) + sqrt(x))

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For those curious, this tool uses arbitrary precision floating-point arithmetic (up to 3000 bits) to sample the input space and measure the error of different implementations of the function, then some clever numerical program synthesis to generate candidates and search for the most accurate implementation.

Seems like this should be solvable with something like symbolic manipulation or (e.g. Taylor) series expansion.

It is, there is an entire field called Numerical Analysis about this, but instead of spending a year learning numerical analysis throwing it at a tool that spits out something pretty decent after 15 minutes is probably a better ROI.

I'm glad that there's a tool to automatically do this. When I was in university, this was something that was on tests/assignments.

Somebody has to make the tool :-)

And so it shall remain!

This tool is a really cool mix of hard math and soft reality. You need some pretty advanced tools to symbolically manipulate expressions like this, and then it takes the results and throws it on the wall to see what sticks best.

does it generate erfc(x) from 1-erf(x)?

Apparently it does.

http://herbie.uwplse.org/demo/042341d0fe3004d56ba86a30344299...

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