TITLE: (Computationally) Simple sigmoid
QUESTION [8 upvotes]: I'm looking for the analytic expression of a computationally cheap sigmoid that passes through the points (0, 1) and (1, 0). Thoughts?

REPLY [9 votes]: An extremely cheap option is the cubic spline with zero derivatives at both endpoints:
$$f(x)=1-3x^2+2x^3.$$