run away vs search for

run away

verb
  • To leave home, or other place of residence, usually unannounced, or to make good on a threat, with such action usually performed by a child or juvenile. 

  • To become a runaway. 

  • To flee by running. 

search for

How often have the words run away and search for occurred in a corpus of books? (source: Google Ngram Viewer )