exact science vs formal science

exact science

noun
  • A mathematical science, i.e. a field of science such as mathematics or mathematical physics which is capable of perfectly exact results based on rigorously formal methods. 

  • A field of science such as physics or chemistry that is not perfectly exact, but still capable of highly quantitative results based on methods that are are not strictly rigorous, but still systematic and scrupulous. 

  • Used contrastively to characterize something as imprecise or relying on intuition or heuristics. 

formal science

noun
  • A study that is concerned with theoretical formal systems, such as logic, mathematics, systems theory and the theoretical branches of computer science, information theory, microeconomics, statistics, and linguistics. 

How often have the words exact science and formal science occurred in a corpus of books? (source: Google Ngram Viewer )