Are you looking for the fastest ease-in ease-out function?

look no further…

y = x*x*(3-2*x);

it a polynomial function, that’s 0 at 0, 1 and 1 and has zero derivative at both ends;

its the unique polynomial of degree 3 with those properties.

This function is also called “smoothstep”

Here a more expensive variation, called Smootherstep:

y = x*x*x*(10+x*(6*x-15))

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