at any rate vs leastwise

at any rate and leastwise both are adverbs.

Word	Noun	Adjective	Verb	Adverb
at any rate	No	No	No	Yes
leastwise	No	No	No	Yes

As adverbs, at any rate and leastwise are synonyms defined as:

at any rate and leastwise: if nothing else (`leastwise' is informal and `leastways' is colloquial)

Other synonyms of at any rate include at least, leastways.

at any rate (adverb)	leastwise (adverb)
used to indicate that a statement explains or supports a previous statement	if nothing else (`leastwise' is informal and `leastways' is colloquial)
if nothing else (`leastwise' is informal and `leastways' is colloquial)