Easing Functions Cheat Sheet

I'm not sure why or how it came up with cubic-bezier(0.445, 0.05, 0.55, 0.95) for easeInOutSine.

A more accurate representation of this piece of sin(t) would be cubic-bezier((pi - 2)/pi, 0, 1 - (pi - 2)/pi, 1) which evaluates to cubic-bezier(0.3633802276324187, 0, 0.6366197723675813, 1). (round where necessary)

This way, the tangents at the start and end remain horizontal. This also matches the function (1 - cos (pi x)) / 2 with a root mean square error of only about 0.000224528.

If you want to optimize excessively (why not?), you can minimize this error to about 0.00013 with cubic-bezier(0.364212423249, 0, 0.635787576751, 1). However, there is no closed form for these values as you end up attempting to integrate the cosine of a cubic polynomial.