python3.10.8のmpmath+gmpy2での限界は10^10^10^3

>>> from mpmath import *
>>> mp.dps = 100
>>> mpf(10)**mpf(10)**mpf(10)**mpf(3)
mpf('9.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999943
e+9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999984493709296336270566404385672161952742743241077733906187326297062909459664001826973141810503397202159853574555183445082156953368883108213243229772021602804766641722704203262413734241333411365614458601908322865200493192636312582037682767645237966125765805256875029004536890655834102400229718644017216501252596867887442045999489634872310669534925852305535782846779461514469698383199727433918223034540569653324627097250571246263386526133059665528573402546754675434946969226578757310823884398028968736089087803775734402381580569598009776563746459210344899539783573284379615937067498964991783503126373585178862779650798892646201847617089469658445302973770961477148459478332746920890500973443735335941245245180222137010994201118213211414011804988731030921949395465478056516257394288702414602573352453845977806031162071614309099336317761633932590351749875182709820978219128175120194198568092237926978551807')

しかし誤差がすごいことに。