In the course of searching for continued fraction identities, Raayoni (2021) and Elimelech et al. (2023) noticed that while
the numerator and denominator
of continued fraction convergents in general grow factorially ( for some positive integer ), the reduced numerator and
denominator and for grew at most exponentially ().

This phenomenon has been termed "factorial reduction" and, while it is extremely rare in general (Elimelech et al. 2023), it holds for all
identities originally found by the Ramanujan Machine (Raayoni et al. 2021,
Elimelech et al. 2023). It is illustrated above for the Apéry
constant continued fraction

Elimelech, R.; David, O.; De la Cruz Mengual, C.; Kalisch, R.; Berndt, W.; Shalyt, M.; Silberstein, M.; Hadad, Y.; and Kaminer, I. "Algorithm-Assisted
Discovery of an Intrinsic Order Among Mathematical Constants." 22 Aug 2023.
https://arxiv.org/abs/2308.11829.Raayoni,
G; Gottlieb, S.; Manor, Y.; Pisha, G.; Harris, Y.; Mendlovic, U.; Haviv, D.; Hadad,
Y.; and Kaminer, I. "Generating Conjectures on Fundamental Constants With the
Ramanujan Machine." Nature590, 67-73, 2021.