The paper discusses various methods of adaptive spline approximations for the flow of function values. The number of K knots in the adaptive grid determines the required amount of memory for storage of compression results. The number of M knots of the original grid characterizes the number of operations required to obtain adaptive compression. In the case of access to the derivative values the number of digital operations is proportional to the number M. If it does not have access to the last ones then the number of required operations has the order of M2 (in the general case). If additionally the approximated flow is convex, then the number of required operations has the order of M log2M. In all cases the result requires the computer memory amount of the order of K.