have a laugh vs laugh at

have a laugh

verb
  • To laugh. 

  • To joke; kid around. 

  • To enjoy oneself; have fun. 

laugh at

verb
  • Used other than figuratively or idiomatically: see laugh, at. 

  • To scorn or tease; to evince contempt or pity for someone, usually contrasted with laugh with. 

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