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Inferring a phylogenetic tree, which describes the evolutionary relationships among a set of organisms, genes, or genomes, is a fundamental step in numerous evolutionary studies. With the aim of making tree inference feasible for problems involving more than a handful of sequences, current algorithms for phylogenetic tree reconstruction utilize various heuristic approaches. Such approaches rely on performing costly likelihood optimizations, and thus evaluate only a subset of all potential trees. Consequently, all existing methods suffer from the known tradeoff between accuracy and running time. Here, we train a machine-learning algorithm over an extensive cohort of empirical data to predict the neighboring trees that increase the likelihood, without actually computing their likelihood. This provides means to safely discard a large set of the search space, thus avoiding numerous expensive likelihood computations. Our analyses suggest that machine-learning approaches can make heuristic tree searches substantially faster without losing accuracy and thus could be incorporated for narrowing down the examined neighboring trees of each intermediate tree in any tree search methodology.