The Chebfun system provides "numerical computing with functions." Many familiar MATLAB
commands are extended to appropriate interpretations for functions of one
variable, and Chebfun often feels symbolic but runs
at the speed of numerics. More precisely our vision is to achieve for
functions what floating-point arithmetic achieves for numbers: rapid
computation in which each successive operation is carried out exactly
apart from a rounding error that is very small in relative terms.