20210825, 09:31  #3070  
Aug 2020
79*6581e4;3*2539e3
13·31 Posts 
Quote:


20210825, 11:52  #3071 
Apr 2020
504_{10} Posts 
In previous searches (mostly degree 5), larger incr has been used to compensate for the disadvantage of searching at higher leading coefficients. Roughly speaking, polys with larger coeffs tend to have worse size properties, and using an incr value with more small prime factors gives a small boost to the root properties to make up for this.

20210825, 14:39  #3072 
Aug 2020
79*6581e4;3*2539e3
13×31 Posts 
Ah, I thought incr controlled how thoroughly a range is searched and larger incr resulted in shorter search times. So it is the other way around? Would it have a slight advantage to use larger incr even for smaller coefficients (regardless of whether it's worth it)?

20210825, 15:00  #3073 
Apr 2020
504_{10} Posts 
You've got it right: the leading coefficients that are searched are the multiples of incr, so a 1M range at incr=2310 will be much quicker than a 1M range at incr=420. We don't use larger incr from the start because we don't want to get to large coefficients too quickly.

20210825, 18:02  #3074  
Aug 2020
79*6581e4;3*2539e3
13×31 Posts 
At the risk of looking like an idiot, but I still don't get it.
Quote:
Quote:
Last fiddled with by bur on 20210825 at 18:04 

20210825, 19:00  #3075 
Apr 2020
2^{3}×3^{2}×7 Posts 
The rate at which we find raw polynomials stays roughly constant (assuming fixed P), so we want the average score of the polynomials we find to be as high as possible through the search. In general, we observe:
1. If incr is kept constant, lower leading coeffs give higher average scores. 2. Among leading coeffs of similar size, those with more small prime factors give higher average scores. Note that this is why we choose incr values like 420 in the first place. It's not hard to see the effects of point 2: look at the leading coefficients of the best polynomials from your searches, and see how smooth they tend to be, even given that they're multiples of 420. For example, the current leading poly came from a stage 1 hit with c6 = 18572400 = 2^4 * 3^2 * 5^2 * 7 * 11 * 67, so it would still have been found with incr = 2310 or 4620. So if we started off at a larger incr, we would start off finding better polynomials than with incr=420 due to point 2... but we would run into the effects of point 1 much more quickly. Once we get to leading coeffs high enough that scores have dropped noticeably due to point 1, the theory is that increasing incr to 2310 or 4620 will then give a temporary boost to the average score. I don't think we're seeing much of the effect of point 1 yet, which is why I've stuck with incr=420 for the 25M to 40M range. It's possible that incr=2310 or 4620 over a much larger range would have been better, but that's difficult to test in advance. I wouldn't mind CADO adding an option to put a smoothness bound on the leading coefficients... Last fiddled with by charybdis on 20210825 at 19:05 
20210826, 21:18  #3076 
Jun 2012
5·641 Posts 
4145M best poly found was only 2.921e16. 10th best was 2.506e16.
I should be finished with 4550M late Friday. 
20210827, 07:48  #3077 
Aug 2020
79*6581e4;3*2539e3
13·31 Posts 
So large incr gives better polys on average due to the many small factors, but it skips a lot of coefficients of which it isn't a multiple? If so, then I finally understood.
6e67e6 is at 75%, should be finished in about 30 hours. 
20210827, 08:25  #3078 
"Curtis"
Feb 2005
Riverside, CA
5×7×11×13 Posts 

20210827, 17:02  #3079 
Aug 2020
79*6581e4;3*2539e3
13×31 Posts 

20210827, 17:19  #3080 
Apr 2020
504_{10} Posts 
Going over a range with larger incr would be repeating work on the coefficients that are multiples of both incr values. If the new incr (say 4620) was a multiple of the old incr (say 420), you wouldn't be doing any new work at all.

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