as it happens vs circumstantially

as it happens

adv
  • By coincidence, incidentally 

circumstantially

adv
  • In respect to circumstances; not essentially; accidentally. 

  • in a circumstantial manner 

  • In every circumstance or particular; minutely. 

How often have the words as it happens and circumstantially occurred in a corpus of books? (source: Google Ngram Viewer )