  In computer aided geometric design a polynomial is usually represented in
Bernstein form. The de Casteljau algorithm is the most well-known algorithm for
evaluating a polynomial in this form. Evaluation via the de Casteljau algorithm
has relative forward error proportional to the condition number of evaluation.
However, for a particular family of polynomials, a curious phenomenon occurs:
the observed error is much smaller than the expected error bound. We examine
this family and prove a much stronger error bound than the one that applies to
the general case. Then we provide a few examples to demonstrate the difference
in rounding.
