  Chebfun and related software projects for numerical computing with functions
are based on the idea that at each step of a computation, a function $f(x)$
defined on an interval $[a,b]$ is "rounded" to a prescribed precision by
constructing a Chebyshev series and chopping it at an appropriate point.
Designing a chopping algorithm with the right properties proves to be a
surprisingly complex and interesting problem. We describe the chopping
algorithm introduced in Chebfun Version 5.3 in 2015 after many years of
discussion and the considerations that led to this design.
