sum vs tot up

sum is a noun but tot up is not a noun.

Word	Noun	Adjective	Verb	Adverb
sum	Yes	No	Yes	No
tot up	No	No	Yes	No

As verbs, sum and tot up are synonyms defined as:

Other synonyms of sum include add, add together, add up, sum up, summate, tally, tot, total, tote up.

sum (noun)	tot up (noun)
the whole amount
the choicest or most essential or most vital part of some idea or experience
a quantity obtained by the addition of a group of numbers
the final aggregate
a set containing all and only the members of two or more given sets
a quantity of money

sum (verb)	tot up (verb)
determine the sum of	determine the sum of
be a summary of