pan out vs prove out

pan out

verb
  • To proceed according to plan; to result or end up. 

  • To separate and recover (valuable minerals) by swirling dirt or crushed rock in a pan of water, in the manner of a traditional prospector seeking gold. 

prove out

verb
  • To turn out to be feasible, accurate, true, satisfactory, as expected, hoped, stated, etc. 

  • To demonstrate the feasibility of; to show or be shown to be feasible, accurate, true, satisfactory, as expected, hoped, stated, etc. 

How often have the words pan out and prove out occurred in a corpus of books? (source: Google Ngram Viewer )