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For the algorithm, the problem is the implementation not the sort'n'subtract. With 4 values on top and 5 underneath, there are numerous ways in which the subtraction needs to be done.
That's why I simply enumerated each factorial's terms in increasing order and merged the streams, canceling in passing. It was a heck of a lot easier than writing a fast, robust representation of intervals, and yet this crude implementation is "fast enough": Less than 17 percent of my code's time is spent on this task (see profile report, below). Were I to eliminate this time entirely, I would gain only a one-fifth improvement in overall speed, and that fact suggests that this line of optimization has petered out.

Interesting tidbit: The entire pre-multiplication pipleline accounts for only 6 percent of the overall allocation cost, suggesting that the lazy build-and-merge-and-cancel operation works in near-constant space.

Cheers,
Tom

individual inherited COST CENTRE entries %time %alloc %time %alloc MAIN 0 0.0 0.0 100.0 100.0 main 1 0.0 0.0 90.5 82.4 pCutoff 1 0.0 0.0 90.5 82.4 toRatio 1 16.7 0.0 73.8 76.4 bigProduct 2 57.1 76.3 57.1 76.3 rpCutoff 1 0.0 0.0 16.7 6.0 <--- here rdivide 1 0.0 0.0 0.0 0.0 rtimes 1 0.0 0.0 0.0 0.0 rtimes 0 0.0 0.0 4.8 0.7 rdivide 1 0.0 0.0 4.8 0.7 cancel 113163 4.8 0.7 4.8 0.7 merge 2 0.0 0.0 0.0 0.0 facproduct 2 0.0 0.0 11.9 5.3 fac 9 4.8 2.8 4.8 2.8 rproduct 2 0.0 0.0 7.1 2.5 rtimes 9 0.0 0.0 7.1 2.5 cancel 9 0.0 0.0 0.0 0.0 merge 294870 7.1 2.5 7.1 2.5 CAF 1 0.0 0.0 9.5 17.6 sciformat 3 0.0 0.0 9.5 17.6 tosci 7031 9.5 17.4 9.5 17.6 digits 122 0.0 0.2 0.0 0.2 Note: All pre-multiplication logic, including merging and canceling, is contained within the inherited time marked "here".

In reply to Re^5: Algorithm for cancelling common factors between two lists of multiplicands by tmoertel
in thread Algorithm for cancelling common factors between two lists of multiplicands by BrowserUk

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