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 2021-08-15, 06:09 #3004 bur     Aug 2020 79*6581e-4;3*2539e-3 2×3×67 Posts The polynomials are apparently in the table polyselect1_bestpolynomials, but I can't figure out how they are sorted. The exp_E values don't seem to show any order. The columns are rowid, kkey, type and value. Rowid is just that, kkey was always rowid-1, type is always 0 and value is the polynomial with only #exp_E as score.
2021-08-17, 10:20   #3005
bur

Aug 2020
79*6581e-4;3*2539e-3

2·3·67 Posts

I was wondering, when going through a poly range, is it possible to entirely miss good polynomials? I.e. if someone would search the range again with smaller incr or yet larger nq or sopt-effort, could a significantly higher scoring polynomial be found or will it just result in slightly better scores?

Besides, this short script returns the highest scoring polynomial from the database (I don't know if the multiple grepping is really elegant, but it works). Just execute it with the db file as argument:
Quote:
 cp \$1 ./save.db sqlite3 -header -csv save.db "SELECT * FROM polyselect1_bestpolynomials;" > data.csv cat data.csv | grep "exp" | sort | head -1 | grep -f - data.csv -B 10 rm save.db rm data.csv

Last fiddled with by bur on 2021-08-17 at 11:16

2021-08-17, 12:37   #3006
charybdis

Apr 2020

2·251 Posts

Quote:
 Originally Posted by bur I was wondering, when going through a poly range, is it possible to entirely miss good polynomials? I.e. if someone would search the range again with smaller incr or yet larger nq or sopt-effort, could a significantly higher scoring polynomial be found or will it just result in slightly better scores?
Yes, you can completely miss good polys. This is less likely with sopteffort which improves polys that have already been found, as opposed to incr and nq which affect the range that is searched in stage 1.

 2021-08-17, 14:21 #3007 bur     Aug 2020 79*6581e-4;3*2539e-3 2×3×67 Posts So is it really worthwhile if I search a range with my moderate incr/nq combination? How likely is it that the range should be redone later on with more demanding parameters? Or is incr=420 and nq=46656 considered good enough for good? I think about that especially in light of users with a lot of ressources who could easily do the range with nq=6^7. Last fiddled with by bur on 2021-08-17 at 14:22
2021-08-17, 15:28   #3008
charybdis

Apr 2020

2·251 Posts

Quote:
 Originally Posted by bur So is it really worthwhile if I search a range with my moderate incr/nq combination? How likely is it that the range should be redone later on with more demanding parameters? Or is incr=420 and nq=46656 considered good enough for good? I think about that especially in light of users with a lot of ressources who could easily do the range with nq=6^7.
Yes, it's definitely worthwhile. You could miss a good polynomial, but if instead someone were to use lots of resources to run your range with incr=210 and nq=6^7, that would mean there's some higher range where they don't search (lots of resources =/= unlimited resources!) and there could be a good polynomial hiding there too.

Leading coefficients with more small prime factors are more likely to produce good polynomials, so incr=210 would take twice as long but probably won't find twice as many good polynomials in a given range. But there's a trade-off, because, all other things kept equal, smaller coefficients are better than larger ones. This is why VBCurtis uses larger incr values like 4620 for larger coefficients: in order to make up for the coefficients being larger, you need even more small prime factors.

As for nq, Gimarel showed that 6^7 finds polynomials more slowly than 6^6. The same trade-off applies, so perhaps larger nq is justified for smaller coefficients, but we might already have adjusted enough for this by using different incr values across the range.

 2021-08-17, 15:36 #3009 VBCurtis     "Curtis" Feb 2005 Riverside, CA 3×1,667 Posts I've done a couple of degree-6 poly searches before, and I've previously used 6^5 for nq; I consider 6^6 to be *very* thorough. While I used incr=210 on the very-smallest coefficient range, I can assure you that nobody will consider incr=420 / nq = 46656 as anything but exhaustively searched. Part of the "spin" that Max does is to take a posted poly and try size-opt and root-opt again with different settings (or with msieve instead of CADO, since they use slightly different procedures) in an attempt to get luckier than the original discovery. For a big job like this that Max is likely to help out with, that may make size-opt-effort something we don't really need to play with? (I'm not sure about this part, it just occured to me)
 2021-08-17, 15:41 #3010 bur     Aug 2020 79*6581e-4;3*2539e-3 2×3×67 Posts Ok, thanks, that's good to know. The yield so far isn't so good, best poly has cownoise 8E-17 at 85% done, so I got gloomy, haha. On the other hand I have no idea what is an average result for that range... Last fiddled with by bur on 2021-08-17 at 15:42
2021-08-17, 15:55   #3011
charybdis

Apr 2020

2·251 Posts

Quote:
 Originally Posted by bur Ok, thanks, that's good to know. The yield so far isn't so good, best poly has cownoise 8E-17 at 85% done, so I got gloomy, haha. On the other hand I have no idea what is an average result for that range...
Pay no attention to the scores of the polynomials produced by stage 1 and sizeopt. Rootopt will improve them *a lot*.

 2021-08-17, 23:35 #3012 swellman     Jun 2012 3,203 Posts Code: n: 5272066026958413205513021090082556639441277154855572268239336980532402881465013381219738819137405617219594641652778228990107677072837959240400905630530715435664638237254654768053674178165309345879869729405448588458952991 skew: 338136.855 c0: 189900042836812221982619647806688806023974608 c1: -2568098587555066549163576737385262919596 c2: 3958780384162120695641805109874764 c3: 72063043688644509410587348689 c4: -48639995036819186219299 c5: -355279972659030750 c6: -30550905000 Y0: -224860621784631260553024182454512411 Y1: 23949076096264622399754953 # MurphyE (Bf=3.436e+10,Bg=1.718e+10,area=8.590e+17) = 1.429e-09 # f(x) = -30550905000*x^6-355279972659030750*x^5-48639995036819186219299*x^4+72063043688644509410587348689*x^3+3958780384162120695641805109874764*x^2-2568098587555066549163576737385262919596*x+189900042836812221982619647806688806023974608 # g(x) = 23949076096264622399754953*x-224860621784631260553024182454512411 Which cownoise scores as 2.709e-16. Not really worth reporting but I got this result in only one day with a search over a range of 1M using nq=6^6. Is a rerun with nq=6^7 worth trying? A million ad per day is a decent search pace for a c220 but not worth doing if good polys are being missed.
2021-08-18, 00:39   #3013
charybdis

Apr 2020

2·251 Posts

Quote:
 Originally Posted by swellman Is a rerun with nq=6^7 worth trying? A million ad per day is a decent search pace for a c220 but not worth doing if good polys are being missed.
If you want to try something that isn't quite that long and doesn't duplicate the work you've already done, you could re-run the range with the P value doubled.

2021-08-18, 01:20   #3014
swellman

Jun 2012

3,203 Posts

Quote:
 Originally Posted by charybdis If you want to try something that isn't quite that long and doesn't duplicate the work you've already done, you could re-run the range with the P value doubled.
P was 10e6 for this recent run but I could double it.

I’ve got another Linux box finishing another task tonight, maybe I can vary nq and P simultaneously. I have no personal experience with a poly search of this size. Nothing to lose but time…

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