In a manner that is shockingly bad, appalling, or utterly hopeless; to an immeasurable degree.
Formed from 'abysmal' (adjective, meaning 'relating to or resembling an abyss' or 'shockingly bad') plus the adverbial suffix '-ly'; the meaning shifted from literal depth to moral/quality depth.
The word 'abysmally' originally described something as deep as an abyss, but now it just means 'really, really bad'—like when someone gets an abysmally low test score, they've fallen into the depths of poor performance!
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