My dissertation research centers on application of machine learning techniques to speed up problem solving. In fact, many speed-up learning systems suffer from the utility problem; time after learning is greater than time before learning. Discovering how to assure that learned knowledge will in fact speed up system performance has been a focus of research in explanation-based learning (EBL). One way of finding a solution which can guarantee that cost after learning is bounded by cost of problem solving is to analyze all the sources of cost increase in the learning process and then eliminate these sources. I began on this task by decomposing the learning process into a sequence of transformations that go from a problem solving episode, through a sequence of intermediate problem solving/rule hybrids, to a learned rule. This transformational analysis itself is important to understand the characteristics of the learning system, including cost changes through learning.