Which is correct? "Blazing Fast Speed" or "Blazingly Fast Speed"?
In my opinion, the latter because one can't say, for one, "Amazing Fast Speed", right?
Admittedly NY Times use it a lot but...:
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Either blazing or blazingly could be valid.
We can use blazing to intensify fast, just as something can be burning hot or sopping wet, which sound redundant but are idiomatic. Blazingly, the usual adverbial form, would of course work in this manner.
We could alternatively read blazing and fast as parallel descriptors for speed, just as we can have soothing sweet tea or an amazing technicolor dreamcoat.
There are several intensifiers that end -ing, most of them swearing. I read blazing as replacing a similarly formed word which the NY Times would not deign to print.