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A user wants my algebraic simplifier to spot real numbers which can be written in the form (fraction)*π^p. My first instinct is there'll be far too many false positives, even if we restrict to small p.
I did some testing (http://codepen.io/christianp/full/MpNExZ/) and weirdly, the false positive rate spikes at 50% when denominator of the fraction is limited to 1000. What's going on? That's nowhere near the good convergents for π, 333/106 and 355/113.
it's occurred to me that this is very sensitive to the way I find rational approximations, and changing the accuracy of that moves the spike about quite easily. So that pretty much explains what I saw.
