Let us say a MFLOP has an energetic cost of C. Then M * MFLOP * C is the training cost, and sqrt(M) * MFLOP * C is the query cost. As pointed out above, if the speed of the system serving the query is in the GFLOP/s range and it spends a few seconds on it, the square-root argument is not too outlandish, given that it took similar system days to train.