  It is a long-standing question of Stanley whether or not the chromatic
symmetric function (CSF) distinguishes unrooted trees. Previously, the best
computational result, due to Russell, proved that it distinguishes all trees
with at most $25$ vertices. In this paper, we present a novel probabilistic
algorithm which may be used to check more efficiently that the CSF
distinguishes a set of trees. Applying it, we verify that the CSF distinguishes
all trees with up to $29$ vertices.
