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The thermodynamics of computation is well understood for computing engines (rdquoBrownian computersrdquo) that are ideal in the sense that they can make forward and backward steps along the intended computation path, but not transitions to unrelated states. The thermodynamics of error-prone computations and error-correcting mechanisms is less well understood. We explore the speed-error-dissipation tradeoff for a family of hypothetical coupled chemical reaction schemes loosely patterned on RNA and DNA polymerases, which suffer errors at some intrinsic hardware rate and, in the case of DNA polymerases, use proofreading - cyclic dissipative reaction path - to correct most of the errors initially introduced. Even simple non-proofreading systems exhibit nontrivial features, for example a regime where the copying process is pulled slowly forward, against a backward external driving force, by the entropy of incorporated errors.