cough up vs provide with

cough up

verb
  • to hand over, give. 

  • to expel from the lungs, throat, etc. by coughing 

  • to lose a competition by one's own mistakes, usually near the end of the contest 

  • to pay, disburse 

  • To spill, to fumble 

provide with

How often have the words cough up and provide with occurred in a corpus of books? (source: Google Ngram Viewer )