Before revision:  A method of order O(Nd) is also provided to compute the time derivative of the mass matrix. A numerical implementation of these algorithms in C/C++ is benchmarked showing computation times on the order of 10-20 \mus for the computation of the Coriolis matrix and 40-120 \mus for the computation of the Christoffel symbols for systems with 20 degrees of freedom.
After revision:  Implementation in C/C++ is benchmarked showing computation times on the order of 10-20 \mus for the computation of the Coriolis matrix and 40-120 \mus for the computation of the Christoffel symbols for systems with 20 degrees of freedom.