  Hyperbolic geometry has recently found applications in social networks,
machine learning and computational biology. With the increasing popularity,
questions about the best representations of hyperbolic spaces arise, as each
representation comes with some numerical instability. This paper compares
various 2D and 3D hyperbolic geometry representations. To this end, we conduct
an extensive simulational scheme based on six tests of numerical precision
errors. Our comparisons include the most popular models and less-known mixed
and reduced representations. According to our results, polar representation
wins, although the halfplane invariant is also very successful. We complete the
comparison with a brief discussion of the non-numerical advantages of various
representations.
