To Rush Out
intransitive verb, godan verb
駆ける is "to gallop" and 出す is "to remove." So if you gallop out to remove yourself you are probably going to rush out a little fast. Calm down and slow down, man!
The readings come from 駆ける and 出す.
彼に質問を尋ねた時、駆け出しただけだ。
When I asked him a question he just ran off.