Thanks! Let me follow up by exploring a specific use case: scoring in a Lucene-style search engine, where arbitrarily complex queries repeatedly scale a floati

Thanks! Let me follow up by exploring a specific use case: scoring in a Lucene-style search engine, where arbitrarily complex queries repeatedly scale a floating point "score" value which measures document relevancy against a query. Sometimes documents which ought to produce equal scores against a given query (if scoring were evaluated using real number math) do not produce equal scores in practice because of floating point limitations such as not supporting associativity or commutativity. Let's assume we are willing to sacrifice performance for correctness to address this issue. 1) If scores were tracked as expression trees, could this problem be eliminated entirely? If so, I'd hazard a guess that while you'd eventually run into edge case issues such as needing arbitrarily large integers, in practice the CPU cost to track scores as expression trees rather than floats would be increased by a roughly constant factor. 2) If scores were tracked using a rational instead of a float, could the problem of tied scores be eliminated? I suspect that the answer to that is no, because you will quckly run up against integer precision limitations in the numerator/denominator of the rational type.