Jeff Tupper's program GrafEq is a wonderful demonstration of the
power of interval arithmetic for graphing functions:
http://www.peda.com/grafeq/
Especially see his "Rogues' Gallery" of equations that other software
packages that don't use interval arithmetic can graph drastically
incorrectly:
http://www.peda.com/grafeq/gallery/rogue.html
Hopefully everyone here has read his master's thesis on graphing
equations with interval arithmetic (which also compares affine
arithmetic and other techniques.) If you haven't read it, please do so.