fill to the brim vs fill up

fill to the brim

fill up

verb
  • To satisfy the hunger of (someone). 

  • To annoy, or displease, by taunting, or by excessive nagging. 

  • To fill the tank of a vehicle with fuel. 

  • To become completely full. 

  • To make (something) completely full. 

  • To become tearful as a result of strong emotion. 

  • To fill in / fill out a form etc. 

  • To make a full house on the turn or the river. 

  • To satisfy one's hunger; to stop being hungry. 

How often have the words fill to the brim and fill up occurred in a corpus of books? (source: Google Ngram Viewer )