half-moon vs old moon

half-moon

noun
  • The moon in its first or last quarter when only half the visible face is illuminated; a quarter moon. 

  • A semicircular or crescent-shaped Filipino butter cookie. 

  • Anything shaped like a crescent, especially the base of a fingernail. 

  • Synonym of black and white (“type of cookie”) 

old moon

noun
  • The phase of the moon when it is waning. 

  • The moon when it is waning. 

How often have the words half-moon and old moon occurred in a corpus of books? (source: Google Ngram Viewer )