Performance evaluation of programs for the error and complementary error functions

This paper presents methods for performance evaluation of computer programs for the functions erf(<italic>x</italic>), erfc(<italic>x</italic>), and e<supscrpt><italic>x</italic><supscrpt>2</supscrpt></supscrpt> erfc(<italic>x</italic>). Accuracy estimates are based on comparisons using power series expansions and an expansion in the repeated integrals of erfc(<italic>x</italic>). Some suggestions for checking robustness are also given. Details of a specific implementation of a test program are included.