circumstantially vs by chance

circumstantially and by chance both are adverbs.

Word	Noun	Adjective	Verb	Adverb
circumstantially	No	No	No	Yes
by chance	No	No	No	Yes

As adverbs, circumstantially and by chance are synonyms defined as:

Other synonyms of circumstantially include accidentally, unexpectedly.

circumstantially (adverb)	by chance (adverb)
insofar as the circumstances are concerned	without advance planning
without advance planning	by accident
in minute detail	through chance
according to circumstances