(to) ad-lib
Defined: a person who deviates from a written score or script
Example: Comedian Jerry Lewis was forced to ad-lib for over 20 minutes when the 1959 Academy Award® ceremony finished 20 minutes ahead of schedule.
When an actor departs from the playwright's lines, or a comedian adds a new joke to his prepared script, they are said to be "ad-libbing." "Ad-lib" is an abbreviation of the Latin words ad libitum (at pleasure). The term was first used by composers in written scores to mark a point in the piece of music where the performing musician could substitute or add to the piece. From music, the term spread to the stage, and, ultimately, to radio and television.
