The adverb has 2 meanings:
Meaning #1:
in an immoderate manner
Synonym: without moderation
Antonym: moderately (meaning #2)
Derived from adjective: immoderate (meaning #1)
Meaning #2:
to a degree that exceeds the bounds or reason or moderation
Synonym: unreasonably
Antonym: moderately (meaning #1)
Derived from adjective: immoderate (meaning #1)
