My PG sib, who is a STEM worker, never "memorized" trig identities, because it was more efficient to re-derive them from the law of sines and law of cosines than it was to brute-force memorize them, and then retrieve them from the arbitrary storage location that would have resulted from rote memorization. My sib does also have an enormous memory span, but apparently decided that processing speed won out over memory on this task. This same sib would undoubtedly score poorly on any measure of processing speed that involved fine-motor dexterity, although silent reading speed has been clocked at ~800 wpm. Needless to say, my mother introduced typing at age 8.
I have another sib who has relatively weaker working memory, and thus poor rote memory, but a very retentive memory for concepts, more like those described upthread. One of my children is like this, too. One of the interesting manifestations of this is that, when performing in drama (or music), there can be verbatim inaccuracies which retain the sense and emotional impact (or chord, melodic, and figural structure, for music) with sufficient quality that only someone who had the script/score in front of them (or who had otherwise memorized it themselves) would be likely to pick up on the alterations.
And, our most commonly-used processing speed measures are, at best, mixed measures.
