come in vs go a long way

come in

verb
  • To become relevant, applicable, or useful. 

  • To begin transmitting. 

  • To enter. 

  • To finish a race or similar competition in a particular position, such as first place, second place, or the like. 

  • To finish a race or similar competition in first place. 

  • To become fashionable. 

  • To have a strong enough signal to be able to be received well. 

  • To join or enter; to begin playing with a group. 

  • To rise. 

  • To arrive. 

  • To fully develop. 

  • To become available. 

  • To give in; to yield. 

  • To surrender; to turn oneself in. 

  • To function in the indicated manner. 

go a long way

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

  • To achieve considerable success. 

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