The optimization of short sequences of loop-free, fixed-point assembly code sequences is an important problem in high-performance computing. However, the competing constraints of transformation correctness and performance improvement often force even special purpose compilers to produce sub-optimal code. We show that by encoding these constraints as terms in a cost function, and using a Markov Chain Monte Carlo sampler to rapidly explore the space of all possible code sequences, we are able to generate aggressively optimized versions of a given target code sequence. Beginning from binaries compiled by 11vm –O0, we are able to produce provably correct code sequences that either match or outperform the code produced by qcc –O3, icc –O3, and in some cases expert handwritten assembly.