pull someone's chestnuts out of the fire vs pull someone's fat out of the fire

pull someone's chestnuts out of the fire

verb
  • Synonym of pull someone's bacon out of the fire (“rescue someone, especially at the last moment”) 

  • To do another person's difficult work. 

pull someone's fat out of the fire

How often have the words pull someone's chestnuts out of the fire and pull someone's fat out of the fire occurred in a corpus of books? (source: Google Ngram Viewer )