back down vs walk back

back down

verb
  • To withdraw from a commitment or position. 

  • To take a less aggressive position in a conflict than one previously has or has planned to. 

walk back

verb
  • To withdraw or backpedal on a statement or promise. 

  • Used other than figuratively or idiomatically: see walk, back. 

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