eat one's words vs recant

eat one's words

verb
  • To regret or retract what one has said. 

recant

verb
  • To withdraw or repudiate a statement or opinion formerly expressed, especially formally and publicly. 

  • To give a new cant (slant, angle) to something, in particular railway track on a curve. 

How often have the words eat one's words and recant occurred in a corpus of books? (source: Google Ngram Viewer )