come through vs go a long way

come through

verb
  • To succeed. 

  • To come into a room or other space through a door or passageway. 

  • To survive, to endure. 

  • To be communicated or expressed successfully. 

  • To not let somebody down, keep or fulfil one's word or promise. 

  • Used other than figuratively or idiomatically: see come, through. 

go a long way

verb
  • To achieve considerable success. 

  • To be adequate or helpful for a significant amount of time. 

How often have the words come through and go a long way occurred in a corpus of books? (source: Google Ngram Viewer )