extemporize
verb
[ ɪkˈstɛmpərʌɪz ]
• compose or perform something such as music or a speech without preparation; improvise.
• "he extemporized at the piano"
Similar:
improvise,
ad lib,
play it by ear,
think on one's feet,
make it up as one goes along,
take it as it comes,
busk it,
wing it,
do something off the cuff,
