cake with mud vs mire

cake with mud

mire

verb
  • To cause or permit to become stuck in mud; to plunge or fix in mud. 

  • To sink into mud. 

  • To weigh down. 

  • To soil with mud or foul matter. 

noun
  • An undesirable situation, a predicament. 

  • Deep mud; moist, spongy earth. 

How often have the words cake with mud and mire occurred in a corpus of books? (source: Google Ngram Viewer )