Abstract: In a computing system, evaluating a mathematical expression in presented hierarchically according to the rules of precedence of operations, initial operations at the bottom of the hierarchy may yield values too large to be calculated conventionally, even if the ultimate value of the expression may represent a calculable value. The mathematical expression is evaluated top down to determine if portions of the mathematical expression are re-expressible to simplify the expression and avoid initial or intermediate calculations that would prevent calculation of the mathematical expression. Portions of the original mathematical expression are re-expressible by substituting known mathematical identities, applying arithmetic rules, or treating a portion of the mathematical expression as a variable on which other operations are performed. Once the mathematical expression has been re-expressed, the mathematical expression is simplified, and, if possible, its value calculated.