<p><b>Abstract</b>—A new technique for the a priori calculation of rigorous error bounds for floating-point computations is introduced. The theorems given in the paper combined with interval arithmetic lead to the implementation of reliable software routines, which enable the user to compute the desired error bounds automatically by a suitable computer program. As a prominent example, a table-lookup algorithm for calculating the function exp(<it>x</it>) <tmath>$-$</tmath> 1 that has been published by Tang [<ref rid="bibt075016" type="bib">16</ref>] is analyzed using these new tools. The result shows the high quality of the new approach.</p>