About tradeoff, would it be possible to add an option to choose the quality of the accuracy? For example, a flag to choose between "fast nth root" or "accurate nth root".

Python already has two kind of numbers: Decimal and float. Maybe the "flag" should be the type of input numbers, Decimal or float?

I'm asking because I looked at http://lipforge.ens-lyon.fr/www/crlibm/ a few years ago, and such library is designed for accuracy, not for speed. crlibm is based on the scslib library which compose a number using multiple float numbers to get a better precision. To get correct rounding, crlibm requires more loop iterations and more floating point number operations, so as expected, it is slower.

FYI my old blog article (in french!): http://www.haypocalc.com/blog/index.php/2009/02/20/188-bibliotheque-mathematique-arrondi-exact-crlibm