Calculation times

These are the times for various of our calculations, at different stages in the development of our algorithms.

The calculations were performed on a number of different machines, all running Linux. The machine speeds ranged from 350 MHz to 1.6GHz, and there were usually other processes running on the machines. The longer jobs were broken into pieces and the pieces were parcelled out among the machines. At times we had 42 machines working at the same time.

In order to get comparable times we tried to "normalize" all execution times to the same speed as our 1GHz machine, and of course we added the normalized times for jobs that were split into subjobs. So the times are not very precise, but should be roughly comparable to each other.

In the following table we list times for computing the volume only, and also for computing the entire polynomial. The different versions of the program correspond roughly to improvements in our algorithm:

• 0.5: The first working version. Always integrated starting with the lowest numbered variable, always using exterior residues.
• 0.6: The "branch count" method, to select the variable and direction (interior or exterior) that would generate the fewest terms.
• 0.7: Option to discard integrals which would not contribute to the volume calculation. Also the first version that could calculate the full polynomial.
• 0.8: "Factoring" option, to notice when integrals over two or more variables are identical; in this case just calculate one integral and raise the result to a power.
• 0.9: Code cleanup. (!)
• 1.0: Option for early detection of zero integrals.