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

On an Algorithm for Comparing the Chromatic Symmetric Functions of Trees