scratch

§ Geomeans and Ratios

created 2024-11-13 · last edited 2024-12-12
  • Suppose we are benching a tool that does rewrites and SAT solving.
  • We call the rewrite times RiR_iRi​ and the SAT solving times SiS_iSi​.
  • Now, how does ∑iRi/∑iSi\sum_i R_i / \sum_i S_i∑i​Ri​/∑i​Si​ compare against ∑i(Ri/Si)/N\sum_i (R_i / S_i) / N∑i​(Ri​/Si​)/N?
  • Clearly, we can write ∑iRi/∑iSi\sum_i R_i / \sum_i S_i∑i​Ri​/∑i​Si​ are (∑iRi/N)/(∑iSi/N)(\sum_i R_i / N) / (\sum_i S_i / N)(∑i​Ri​/N)/(∑i​Si​/N).
  • So we are asking, how does the ratio of the AMs compare to the AM of the ratio?
  • The interesting property
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