hell-bent for leather vs like a bat out of hell

hell-bent for leather

adv
  • determinedly recklessly, in a manner that lacks restraint. 

  • Synonym of hell-bent (“(recklessly) determined”) 

  • Synonym of hell-for-leather (“very fast”) 

like a bat out of hell

prep
  • With crazy or excessive intensity or speed. 

How often have the words hell-bent for leather and like a bat out of hell occurred in a corpus of books? (source: Google Ngram Viewer )