These are compound verbs. Using a noun (or even an adjective) to modify a verb is sometimes acceptable in English. The noun can either describe the manner in which the action is performed, or the object of the action.
Some examples include:
These words are often formed as neologisms, originating in common speech. I believe that these words are formed because there does not exist an adverb to describe the exact manner of the action. Also keep in mind that these are just a subset of compound verbs, as other forms exist. I got most of my examples from here: [https://examples.yourdictionary.com/compound-verb-examples.html]
I like to use hyphens to indicate that these words form a single verb, but sometimes they are depicted with a space rather than a hyphen. Sometimes, if they are around long enough, they become a single word, like stargaze. Sometimes all three methods are used inconsistently.
The hyphen method is particularly unwieldy in your example of "to Monte Carlo approximate", as Monte Carlo is already a compound proper noun and it would be arguably incorrect to add a hyphen between Monte and Carlo, but "Monte Carlo-approximate" looks very wrong. However, in the case of "to log-transform", I would use a hyphen.
I advise to use a hyphen with these words whenever possible to avoid confusion, as a hyphen is the default English construction of these words. I would not advise inventing new compound verbs that you have never heard in use before, especially in formal writing. If there is an adverb to describe the manner of the action, use it rather than a noun.