write down vs write out

write down

verb
  • To write (something) in a simple or condescending style. 

  • Used other than figuratively or idiomatically: see write, down. 

  • To produce or set (something) down in writing; to record something. 

  • To make a downward adjustment in the value of an asset. 

  • To condemn in writing; to document the faults, offenses, or wrongdoing of. 

write out

verb
  • To write at full length or in expanded form. 

  • To exclude (a character in a TV show, etc.) by writing the script so as to explain their disappearance (through death, moving away, etc.). 

  • To write a ticket or citation; to fill out a ticket or citation. 

  • To exclude someone from a narrative or history. 

  • To exhaust one's mental capacity by too much writing. 

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