The developer documentation for the Intel math kernel library quite helpfully provides information on the approximate operation count for various LAPACK functions, which is apparently not available in the standard LAPACK documentation. E.g. for ?geqrf:

https://software.intel.com/en-us/mkl-developer-reference-fortran-geqrf

Unfortunately, it doesn't provide any time complexity estimates for ?syevr.

Does anybody have any details on, in particular, dsyevr? If available, I would also greatly appreciate a breakdown of the complexity for getting only a subrange of eigenpairs and/or the extra effort required for computing eigenvectors in addition to eigenvalues.