1. A method for use in a computer system having a hierarchical memory system with at least first and second memory tiers, the first memory tier being faster than the second memory tier, the method enabling more data to be stored in the first memory tier so as to be more quickly accessed by a processor, the method being performed by a processor and comprising: performing an operation with two operands to determine an initial result of the operation, each operand being associated with a sensitivity value, wherein each sensitivity value indicates a number of bits of at least a portion of an associated data value that are not garbage bits, and wherein the initial result is computed without regard to the sensitivity value of either of the operands; determining a sensitivity value for a final result based at least on the sensitivity values of each of the operands; developing the final result as a function of the initial result and the determined sensitivity value for the final result; compressing only that portion of the final result that does not correspond to garbage bits as indicated by the sensitivity value of the final result; and storing the compressed final result and a representation of its sensitivity value in the first memory tier.