Cat put out the compiler's busy (6)

I believe the answer is:

active

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'busy' is the definition.
(similar in meaning)

'cat put out the compiler's' is the wordplay.
'put out' indicates anagramming the letters.
'the compiler's' becomes 'ive' (I can't justify this - if you can you should believe this answer much more).
'cat' with letters rearranged gives 'act'.
'act'+'ive'='ACTIVE'

Can you help me to learn more?

(Other definitions for active that I've seen before include "Busy, energetic" , "In actual operation" , "Lively, working away" , "Energetic, moving" , "Moving about, functioning" .)

I've seen this clue in The Telegraph.

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