Program synthesis is a challenging problem in large part because of the difficulty of search in a large space of programs. Human programmers routinely tackle the task of writing complex programs by writing sub-programs and then analysing their intermediate results to compose them in appropriate ways. Motivated by this intuition, we present a new synthesis approach that leverages learning to guide a bottom-up search of programs. In particular, we train a model to prioritize compositions of intermediate values during search conditioned on a given set of input-output examples. This is a powerful combination because of several emergent properties: First, in bottom-up search, intermediate programs can be executed, providing semantic information to the neural network. Second, given the concrete values from those executions, we can exploit rich features based on recent work on Property Signatures. Finally, bottom-up search allows the system substantial flexibility in what order to generate the solution, allowing the synthesizer to build up a program from multiple smaller sub-programs. Overall, we find that the combination of learning and bottom-up search is remarkably effective, even with simple supervised learning approaches. We demonstrate the effectiveness of our synthesizer on a new data set for synthesis of spreadsheet programs.