(as) swift as an arrow
Incredibly swiftly or speedily. The karate expert had the would-be mugger unconscious on the ground as swift as an arrow. Swift as an arrow, Mary finished her exam and raced out of the classroom. The shopped ran through mall swift as arrows in search of great deals.
*swift as an arrow
and *swift as the wind; *swift as thoughtvery fast. (*Also: as ~.) The new intercity train is swift as an arrow. You won't have to wait for me long; I'll be there, swift as thought.