In the pgfplots manual it says:
\addplot+[smooth] Smooth plots interpolate smoothly between successive points.
In order to choose the right sampling of points from a function evaluation for plotting, I need to know with some detail what is the "interpolation" that "smooth plot" actually pgfplots (or tikz) implements.
For example, is it cubic splines (probably not), Akima splines, home brew? If it is not a standard one, what properties does it have? continuity, continuity of first derivative, second derivative, monotonicity, maximum tolerated curvature?