We consider the problem of program synthesis from input-output examples via stochastic search. We identify a robust feature of stochastic synthesis: The search often progresses through a series of discrete \emph{plateaus}. We observe that the distribution of synthesis times is often heavy-tailed and analyze how these distributions arise. Based on these insights, we present an algorithm that speeds up synthesis by an order of magnitude over the naive algorithm currently used in practice. Our experimental results are obtained in part using a new program synthesis benchmark for superoptimization distilled from widely used production code.