root about vs run after

root about

verb
  • To search for something in a similar manner. 

  • To rummage; to look for something in a somewhat aimless fashion. 

  • To forage by poking the snout here and there. 

run after

verb
  • To endeavour to find or obtain. 

  • To follow quickly, often in an effort to catch or catch up with (someone or something). 

  • To make a determined effort to win someone's affections or to have a sexual relationship with them. 

How often have the words root about and run after occurred in a corpus of books? (source: Google Ngram Viewer )