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Existing deep learning frameworks optimize the computation graph of a DNN model by performing greedy rule-based graph transformations, which generally only consider transformations that strictly improve runtime performance. We propose relaxed graph substitutions that enable the exploration of complex graph optimizations by relaxing the strict performance improvement constraint, which greatly increases the space of semantically equiv- alent computation graphs that can be discovered by repeated application of a suitable set of graph transformations. We introduce a backtracking search algorithm over a set of relaxed graph substitutions to find optimized networks and use a flow-based graph split algorithm to recursively split a computation graph into smaller subgraphs to allow efficient search. We implement relaxed graph substitutions in a system called MetaFlow and show that MetaFlow improves the inference and training performance by 1.1-1.6× and 1.1-1.2× respectively over existing deep learning frameworks.