Enumeration of all Addition Chains with Five Small Steps

It took a few months of work to get the enumeration program to seemingly handle this case. Runtime was a couple of weeks to generate an output file of 147GB. This contains a lot of duplication as filtering by the generation program is minimal.

I use an offline program to filter the output and cut it down by removing overlaps etc. I decided to split it down such that I process all the 6-bit numbers followed by the 7-bit and so on through 32-bit numbers.

I managed to get each bucket down to the smallest size possible (you can't remove an entry without missing numbers) by removing entries that overlap. These have been checked against a large range of data.

Any 6-bit number can be generated with 5 small steps via the binary method. So that case is trivial:

// 24745
1 6 6 @(a)+@(b)+@(c)+@(d)+@(e)+@(f)

5 Small 6-bit

The remaining possible bit counts of 7-32 are in different files:

5 Small 7-bit      5 Small 8-bit      5 Small 9-bit     5 Small 10-bit

5 Small 11-bit    5 Small 12-bit    5 Small 13-bit   5 Small 14-bit

5 Small 15-bit    5 Small 16-bit    5 Small 17-bit   5 Small 18-bit

5 Small 19-bit    5 Small 20-bit    5 Small 21-bit   5 Small 22-bit

5 Small 23-bit    5 Small 24-bit    5 Small 25-bit   5 Small 26-bit

5 Small 27-bit    5 Small 28-bit    5 Small 29-bit   5 Small 30-bit

5 Small 31-bit    5 Small 32-bit

The following tables shows the distribution of convex sets for each bit count: