Abstract: A method includes identifying multiple apportionments, where each apportionment identifies numbers of bit copies to be stored in at least one memory for at least some bits of a data value. The method also includes, for each apportionment, estimating a numerical error associated with use of the apportionment with a specified function, where the numerical error is estimated by creating errors in bit copies of multiple data values processed using the specified function. The method further includes combining portions of different ones of the apportionments having lower estimated numerical errors to create multiple derived apportionments. The method also includes, for each derived apportionment, estimating a numerical error associated with use of the derived apportionment with the specified function. In addition, the method includes selecting a final apportionment for use with the specified function, where the final apportionment includes or is based on at least one of the derived apportionments.