put the brakes on vs rein in

put the brakes on

verb
  • To stop (an event, action, or process) or to slow it down. 

  • To cease to perform one's current activity or to decrease one's level of activity. 

rein in

verb
  • To stop or slow something, by exercising control. 

  • To stop or slow a horse by pulling the reins 

How often have the words put the brakes on and rein in occurred in a corpus of books? (source: Google Ngram Viewer )