at all vs by any chance

at all

adv
  • Indicating degree, quantity or frequency greater than zero: to the slightest degree, in any way, at any time or in any circumstance. 

by any chance

prep
  • Used other than figuratively or idiomatically: see by, any, chance. 

  • Possibly; perhaps. 

How often have the words at all and by any chance occurred in a corpus of books? (source: Google Ngram Viewer )