Programming sound synthesizers is a complex and time-consuming task. Automatic synthesizer programming involves finding parameters for sound synthesizers using algorithmic methods. Sound matching is one application of automatic programming, where the aim is to find the parameters for a synthesizer that cause it to emit as close a sound as possible to a target sound. We describe and compare several sound matching techniques that can be used to automatically program the Dexed synthesizer, which is a virtual model of a Yamaha DX7. The techniques are a hill climber, a genetic algorithm and three deep neural networks that have not been applied to the problem before. We define a sound matching task based on six sets of sounds, which we derived from increasingly complex configurations of the Dexed synthesis algorithm. A bidirectional, long short-term memory network (LSTM) with highway layers performed better than any other technique and was able to match sounds closely in 25% of the test cases. This network was also able to match sounds in near real time, once trained, which provides a significant speed advantage over previously reported techniques that are based on search heuristics. We also describe our open source framework which makes it possible to repeat our study, and to adapt it to different synthesizers and algorithmic programming techniques.