do something off the top of one's head
extemporize
verb
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To perform or speak without prior planning or thought; to act in an impromptu manner; to improvise.
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To adapt, improvise, or devise action or speech in an impromptu or spontaneous manner.
How often have the words do something off the top of one's head and extemporize occurred in a corpus of books? (source: Google Ngram Viewer )