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The flop counts returned from the flop_counts function appear to be incorrect for GEQRF (op == 'q') and POTRF (op == 'c'). The correct formulas from LAPACK Working Note 41 are:

• *GEQRF if m ≥ n:
  • multiplications: mn^2 - 1/3n^3 + mn + 1/2n^2 + 23/6n
  • additions: mn^2 - 1/3n^3 + 1/2n^2 + 5/6n
  • total: 2mn^2 - 2/3n^3 + mn + n^2 + 14/3n
  • current (incorrect): 2mn^2 - 2/3n^3 + 2mn + 17/3n
• *POTRF:
  • multiplications: 1/6n^3 + 1/2n^2 + 1/3n
  • additions: 1/6n^3 - 1/6n
  • total: 1/3n^3 + 1/2n^2 + 1/6n
  • current (incorrect): 1/3n^3 - 1/2n^2 + 1/6n

The current formula for GEQRF in src/misc/descutil/flop_counts.c appears to have been mistakenly copied from GERQF (RQ factorization instead of QR) in LAWN41, while that for POTRF simply has an incorrect sign and was presumably a typo.

Aside, my understanding is that the SVD is computed using iterative method, so the flops are input-dependent; how did you determine the current 22n^3 formula?