Hi Bruno, Till now, it can only work with polynomial and trigonometric functions. and I have a good idea of simplifying a expression. as you said, if N is compile time known, it should be int_<N>, then the expression with it can be simplified. As the hypersphere talked before, if N=2, and the volume expression will be simplified from (int_<N>^(int_<N>/int_<2>)*var(r)^int_<N>) / gamma(int_<N>/int_<2> + int_<1>) to int_<pi>*var(r)^int_<2> if gamma() has been specialized. Till now, (_x*_x*_x) is a functor, it can be simplified to something like pow(_x, int_<3>). without using d(...), it can be used to simplify expression as we talked before. this is another use of it. You know, there are too many functions in math, so I think I can't implement all of them, the functions included in standard library is enough for me. and I will make it easy to be extended. what do you think about it, I mean how many functions should I implement. My main purpose is calculating derivative easily, of course simplify expression is a important part, I am working on it. Dongfei.