I have the book and I know the theoretical complexities, however, the effective complexity of LAPACK functions that MKL provides is of course not there :) this is not really a simple matrix multiplication because it has to implicitly recover the Q first and apply it automagically to some matrix or vector. This is not covered in that book. Likewise the darfl type of functions that generate one column reflector to annihilate the non zero elements of a new column is not easy to find out unless you are a LAPACK Fortran guru.
It is impossible to know if e.g. some updates are improving the situation if I have no idea what flop count every MKL function I call has.