speculate vs mull over

speculate and mull over both are verbs.

Word	Noun	Adjective	Verb	Adverb
speculate	No	No	Yes	No
mull over	No	No	Yes	No

As verbs, speculate and mull over are synonyms defined as:

Other synonyms of speculate include chew over, contemplate, excogitate, meditate, mull, muse, ponder, reflect, ruminate, think over.

speculate (verb)	mull over (verb)
reflect deeply on a subject	reflect deeply on a subject
to believe especially on uncertain or tentative grounds
talk over conjecturally, or review in an idle or casual way and with an element of doubt or without sufficient reason to reach a conclusion
invest at a risk