With the increasing use of computers in what are called “mission critical situations,” it is becoming more and more necessary to be sure that both arithmetic and code do not contain hidden errors. It is to the former class of problems that the authors address themselves. The recent and deplorable incident of the Pentium divider and its quite rare bug is taken as an example. The authors give an exhaustive account of the most popular methods for detecting rare bugs and illustrate their thesis with examples drawn not only from the Pentium divider but also from such areas as matrix arithmetic. This is an interesting and worthwhile paper.