quarterfinal vs semifinal

quarterfinal

noun
  • A competition that narrows a field of contestants (quarterfinalists) to a set of semifinalists, for a subsequent final. 

  • One of the four competitions in a knockout tournament whose winners go on to play in the two semifinals. 

semifinal

noun
  • A competition that narrows a field of contestants (semifinalists) to a set of finalists, for a subsequent final. 

  • A playoff in the round with only four players or teams left, the stage before the final. 

How often have the words quarterfinal and semifinal occurred in a corpus of books? (source: Google Ngram Viewer )