No single ERI algorithm is available to efficiently handle all integral
classes; rather, each tends to have specific integral classes where the
specific algorithm outperforms the alternatives. The PRISM algorithm
Int. J. Quantum Chem.
(1991), 40, pp. 753. is an intricate collection of pathways and steps in which the path chosen is that which is the most efficient for a given class. It appears that the most appropriate path for a given integral class depends on the relative position of the contraction step (lowly contracted bra-kets prefer late contraction, highly contracted bra-kets are most efficient with early contraction steps).
Careful studies have provided FLOP counts which are the current basis of
integral algorithm selection, although care must be taken to ensure that
algorithms are not rate limited by MOPs.
Chem. Phys. Lett.
(1993), 206, pp. 225. Future algorithm selection criteria will take greater account of memory, disk, chip architecture, cache size, vectorization and parallelization characteristics of the hardware, many of which are already exist within Q-Chem.