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Comment by Houshalter | Hacker News Reader

There is an amazing, easy to use peice of software for doing stuff like this called Eureqa (http://www.nutonian.com/products/eureqa/). I've used it to find approximations for a lot of different functions.

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Am I correct when I think of this as a curve/surface fitting tool that tries to automatically find a low complexity equation together with parameters that fits some provided data?

Yes, that's exactly it.

The term for this is called "Symbolic Regression".

On the flip side of the coin, there's ries, which takes a number and finds a mathematical expression that approximates it: http://mrob.com/pub/ries/

That's really cool, I've been looking for something like that.

I had a program for my HP-48GX that use to do something similar. It was especially useful when I knew that my decimal answer had some numerical constant, such as sqrt(2), and I wanted to convert it to something more reasonable. It would only return a single value, so I had to be careful that I didn't just use it every time, since just because an answer could approximate a multiple of Pi, it might only be a coincidence and not a good answer.

Some of that was actually built-in to the calculator. The "→Q" and "→Q𝛑" functions took a floating-point number and return a rational number or rational expression in terms of pi. The tolerance for the approximation was determined by how many significant digits the calculator was configured to display. It was pretty nice for a calculator that didn't include a computer algebra system.

It was specifically an improved library of those functions. I'll have to dig around on hpcalc.org and see if I can find it again. You could do algebraic calculations if you wrapped the statement in quotes, but once you got used to RPN that made little sense to do.

It was specifically this library: http://www.hpcalc.org/details.php?id=1403.

Eureqa seems a wonderful software for this specific application. If only I could get 2,500$ for a one-year license...

It has a 30 day free trial and you can use it for free if you limit to a few hundred datapoints (not ideal but workable.)

It's not perfect for this application though because it doesn't bitwise operations or use execution time as a fitness function.

There are cheaper ones such as GeneXproTools.

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