An arithmetic expression is evaluated in a form most suitable to a given computing structure. To select this “suitable form” restructuring algorithms using laws of associativity, commutativity, and distributivity have been proposed. This raises the question of how different ways of evaluating an expression influence the propagation of errors due to round-off. An error model consisting of “error vectors” is developed to obtain the absolute error bound satisfied by the computation of a given expression. An error vector algebra is presented that vastly simplifies the calculation of error bounds; yet this model yields the same bounds as other models. The model is used to analyze the error accumulation for different evaluations of division-free arithmetic expressions. With error complexity defined to be the minimum error bound incurred under all modes of evaluation of an expression, a restructuring algorithm is given that minimizes error complexity.