mersenneforum.org Reserved for MF - Sequence 4788
 Register FAQ Search Today's Posts Mark Forums Read

 2021-08-18, 09:23 #3015 bur     Aug 2020 79*6581e-4;3*2539e-3 13×31 Posts Root-opt did increase the score: Code: skew: 1860098.552 c0: -3427420519132645353382556907201718624117659312 c1: -52709839966423296709910539950475485051020 c2: 249681704899452712763350090243160 c3: 42123095563723982267747196055 c4: 880184122151042174607 c5: -5049619263096960 c6: 79732800 Y0: -423246853258132204806966803542792143 Y1: 2073030540718482278351646889 # MurphyE (Bf=3.436e+10,Bg=1.718e+10,area=8.590e+17) = 1.579e-09 Cownoise: 3.228e-16 Range 1e6-2e6 with P=10e6, nq=6^6, incr=420, keep=200, ropt-effort=50, sopt-effort=0. On a 10-core it took 4 days, so repeating with nq=6^7 is not really feasible for me, but maybe it would be interesting to compare results if someone has the hardware to do it faster? Also the influence of P would be interesting. I think keep=200 doesn't make sense, it'd probably be better to halve the value and maybe double ropt-effort? Root-opt took less than 4 hours on the 200 polys with ropt-effort 50, not much compared to the overall time of 95 hours. Would it be worthwhile to redo root-opt with higher effort on that specific poly? And how should I continue, range 2e6-3e6 with the same settings (just smaller keep)? From the screenlog (if of interest): Code: (size optimized): Aggregate statistics: (size optimized): potential collisions: 203998 (size optimized): raw lognorm (nr/min/av/max/std): 206980/65.780/77.170/78.620/0.998 (size optimized): optimized lognorm (nr/min/av/max/std): 193466/60.280/65.563/70.410/0.895 (size optimized): Total time: 3.13783e+06 [...] (root optimized): Best overall polynomial was 0-th in list after size optimization (root optimized): Aggregate statistics: (root optimized): Total time: 120654 (root optimized): Rootsieve time: 120652
2021-08-18, 11:56   #3016
swellman

Jun 2012

5×641 Posts

Quote:
 Originally Posted by bur Root-opt did increase the score: Code: skew: 1860098.552 c0: -3427420519132645353382556907201718624117659312 c1: -52709839966423296709910539950475485051020 c2: 249681704899452712763350090243160 c3: 42123095563723982267747196055 c4: 880184122151042174607 c5: -5049619263096960 c6: 79732800 Y0: -423246853258132204806966803542792143 Y1: 2073030540718482278351646889 # MurphyE (Bf=3.436e+10,Bg=1.718e+10,area=8.590e+17) = 1.579e-09 Cownoise: 3.228e-16 Range 1e6-2e6 with P=10e6, nq=6^6, incr=420, keep=200, ropt-effort=50, sopt-effort=0.
What did you use for adrange? 4*incr is an often used rule of thumb, and it has worked for me on many c19x poly searches (albeit deg 5).

You’ve found a very good value in an early search - suggesting P=10M is perfectly fine. I’m rerunning my job above with P=20M right now, and I should get results in a few days. Maybe that will shed more light on the effect of P. In my past testing I’ve had higher e-scores with lower P! I suspect CADO “tries harder” with higher P but internal time limits cloud the results(?)

I have never found a best poly that was worse than 8th on the list, so nrkeep=50 works for me. Tried a lot of experimentation last year or two and this has always held true though one cannot prove a negative. Others may have counter examples.

Also found higher incr values does not preclude good e-scores, and as you climb up the ad range the time to complete a search become unwieldy. You may want to move to the next range and try incr of 840 or even 1680 (with adrange =4x). But that’s just my two cents.

One last note - sopteffort has a minor effect on the total runtime and has the potential for bigger payoff. Using a value of 10 in my runs. I believe CADO uses 1+ the input value.

2021-08-18, 12:30   #3017
charybdis

Apr 2020

5·101 Posts

Quote:
 Originally Posted by bur I think keep=200 doesn't make sense, it'd probably be better to halve the value and maybe double ropt-effort?
Quote:
 Originally Posted by swellman I have never found a best poly that was worse than 8th on the list, so nrkeep=50 works for me. Tried a lot of experimentation last year or two and this has always held true though one cannot prove a negative. Others may have counter examples.
I've seen as low as 90th, though admittedly examples like this are uncommon. But we ought to remember that this was the 90th best over the entire search. If you set nrkeep=50 for a run that makes up 1% of the search, that would be like setting nrkeep=5000 over the whole search, which is overkill; it would probably be better spending most of that time doing more stage-1 searching instead.

The very best polynomials in the entire search will be either exceptionally good stage-1/sizeopt hits that get at least an average boost from rootopt, or okay sizeopt hits - possibly down as low as 200th over the whole search, hence the default CADO nrkeep value - that get an exceptionally good rootopt hit. If you're running a small range, setting nrkeep=6 or 12 might cause you to miss the best possible poly from your range, but since such a poly would not even be an "okay" sizeopt hit by the above definition, it would be extremely unlikely to be one of the top scoring polys in the whole search.

2021-08-18, 12:40   #3018
bur

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

13×31 Posts

To not make things too mixed up, I'll reserve 5e6 to 10e6, if that isn't too much (depends how ETA scales with range). VBCurtis had 0-1e6 and 2e6-5e6 and swellman 40e6-41e6. Does anyone keep track of the ranges?

Quote:
 Originally Posted by swellman What did you use for adrange? 4*incr is an often used rule of thumb, and it has worked for me on many c19x poly searches (albeit deg 5).

Quote:
 I have never found a best poly that was worse than 8th on the list, so nrkeep=50 works for me. Tried a lot of experimentation last year or two and this has always held true though one cannot prove a negative. Others may have counter examples.
Same here, whenever I saw it, cado said something about best poly was originally 1st or 2nd on the list. So I'll decrease it to 50 and increase ropt-effort to 200, whatever good that may do, but that step didn't take long anyway, so I might as well keep the time as it was.

Quote:
 Also found higher incr values does not preclude good e-scores, and as you climb up the ad range the time to complete a search become unwieldy. You may want to move to the next range and try incr of 840 or even 1680 (with adrange =4x). But that’s just my two cents.
I think Curtis wrote somewhere in here that he'd go to 2310 once the range was above 2e7. That large jump was due to a factor of 11 doing some good. I'll begin with incr=420 and if ETA is extreme I'll increase it to 840.

Quote:
 One last note - sopteffort has a minor effect on the total runtime and has the potential for bigger payoff. Using a value of 10 in my runs. I believe CADO uses 1+ the input value.
Yes, I think it should increase time linearly, but if the actual size opt is only a very small part, we might as well increase it.

So I'll test 5e6-6e6 next with adrange=1680,incr=420,nq=6^6,sopt-effort=10,keep=50,ropt-effort=200 next. If too slow, I'll try incr=840.

Last fiddled with by bur on 2021-08-18 at 13:11

 2021-08-18, 13:36 #3019 swellman     Jun 2012 5×641 Posts For the record, I am also repeating the range 40-41e6 with nq=6^7 and P=10M. It will take a week to complete but it should be interesting to see what CADO spits out. Personally I’m not expecting a big improvement (if any) but willing to hope. The search range reservations are easy enough to track within this thread, but perhaps a new thread should be started so that the input parameters and output e-score can be recorded for later reference? Could be useful to future searchers.
2021-08-18, 14:31   #3020
Gimarel

Apr 2010

2708 Posts

Quote:
 Originally Posted by bur Root-opt did increase the score: Code: skew: 1860098.552 c0: -3427420519132645353382556907201718624117659312 c1: -52709839966423296709910539950475485051020 c2: 249681704899452712763350090243160 c3: 42123095563723982267747196055 c4: 880184122151042174607 c5: -5049619263096960 c6: 79732800 Y0: -423246853258132204806966803542792143 Y1: 2073030540718482278351646889 # MurphyE (Bf=3.436e+10,Bg=1.718e+10,area=8.590e+17) = 1.579e-09 Cownoise: 3.228e-16 Range 1e6-2e6 with P=10e6, nq=6^6, incr=420, keep=200, ropt-effort=50, sopt-effort=0. [/CODE]
ropt of this poly gives:
Code:
### root-optimized polynomial 0 ###
n: 5272066026958413205513021090082556639441277154855572268239336980532402881465013381219738819137405617219594641652778228990107677072837959240400905630530715435664638237254654768053674178165309345879869729405448588458952991
Y0: -423267925613578608179326248033418828
Y1: 2073030540718482278351646889
c0: -773074974413028422431926573350819467006568232
c1: -7270194150193898049263463138887225927755
c2: -1256823921278067033708319813403655
c3: 42082087970958626673016315435
c4: 1136954599732427366607
c5: -5054482166568960
c6: 79732800
skew: 1718787.677
# lognorm 62.43, E 52.81, alpha -9.62 (proj -2.47), 6 real roots
# MurphyE(Bf=1.000e+07,Bg=5.000e+06,area=1.000e+16)=3.423e-16
### Best MurphyE so far is 3.423e-16, av. exp_E 53.32, av. E 52.81

 2021-08-18, 14:38 #3021 swellman     Jun 2012 C8516 Posts Nice! That makes it an arguably viable poly for the c220 but maybe better can be found?
2021-08-18, 14:42   #3022
VBCurtis

"Curtis"
Feb 2005
Riverside, CA

501010 Posts

Quote:
 Originally Posted by bur To not make things too mixed up, I'll reserve 5e6 to 10e6, if that isn't too much (depends how ETA scales with range). VBCurtis had 0-1e6 and 2e6-5e6 and swellman 40e6-41e6. Does anyone keep track of the ranges? ....... I think Curtis wrote somewhere in here that he'd go to 2310 once the range was above 2e7. That large jump was due to a factor of 11 doing some good. I'll begin with incr=420 and if ETA is extreme I'll increase it to 840.
Seems you are the one tracking ranges! :)

I don't think adding more 2's to incr is very useful. If 420 is too slow, I'd skip to 2310.
Glad to hear sizeopteffort doesn't add much time to the search; I guess I'll throw that in to my next range. I'll be done with 2e6 to 5e6 Thursday.

Nice poly find, bur! 3.42e-16 is serviceable. We'd like to beat it by 10% or so, and there's a reasonable chance we can do so.

2021-08-18, 15:26   #3023
charybdis

Apr 2020

5·101 Posts

Quote:
 Originally Posted by VBCurtis I'll be done with 2e6 to 5e6 Thursday.
Roughly how many thread-seconds is a 1M range taking? Should be able to start searching tomorrow and I'd like to have an idea how big a range I should take.

2021-08-18, 17:18   #3024
bur

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

13·31 Posts

Quote:
 Originally Posted by charybdis Roughly how many thread-seconds is a 1M range taking? Should be able to start searching tomorrow and I'd like to have an idea how big a range I should take.
The 1e6-2e6 with setting as posted above took 3137830 s (size) + 120654 s (root) = 3258484 s on an i9-10900k.

The 5e6-6e6 range with identical settings has an ETA that makes it seem similar.

Last fiddled with by bur on 2021-08-18 at 17:18

 2021-08-19, 15:36 #3025 VBCurtis     "Curtis" Feb 2005 Riverside, CA 2·3·5·167 Posts My first decent hit: Code: n: 5272066026958413205513021090082556639441277154855572268239336980532402881465013381219738819137405617219594641652778228990107677072837959240400905630530715435664638237254654768053674178165309345879869729405448588458952991 skew: 244493.103 c0: -5668839593972764105835315556201456845921004 c1: -31798709872233758681019267015167174947 c2: 1033507213021369650910017558429451 c3: -481752321251275723176492791 c4: -20937797913410105835205 c5: 1865890162275696 c6: 81285120 Y0: -338922499431150849187274538075964740 Y1: 404346679164023626048993733 # MurphyE (Bf=1.718e+10,Bg=1.718e+10,area=3.221e+17) = 1.238e-09 cownoise says skew 479764.36842 score 3.28788074e-16 Edit: And another! Code: n: 5272066026958413205513021090082556639441277154855572268239336980532402881465013381219738819137405617219594641652778228990107677072837959240400905630> skew: 1130398.647 c0: 1460970719324580302884397570964425573808852630 c1: -8446464120695272475513669260441719380443 c2: 5723620292044986192940398634388588 c3: 17612914952424667248800986219 c4: -13421101303146825222542 c5: -6930604474874388 c6: 379365840 Y0: -327885433653443790045728834604845926 Y1: 1080049699948936551530063521 # MurphyE (Bf=1.718e+10,Bg=1.718e+10,area=3.221e+17) = 1.254e-09 cownoise: skew 1200878.55688 score 3.29243504e-16 I split 2e6-5e6 in half and ran on two machines. Each poly was the best from its run. So, between bur and I we have at least three 3.2's (before spin) from 1e6-5e6. We just need better luck, next. EDIT2: Taking 10e6-15e6 at incr=420. Last fiddled with by VBCurtis on 2021-08-19 at 15:45

 Similar Threads Thread Thread Starter Forum Replies Last Post kar_bon Aliquot Sequences 136 2021-10-21 16:17 RichD Aliquot Sequences 476 2021-10-04 20:47 RichD Aliquot Sequences 524 2021-09-06 21:00 prism019 GPU to 72 6 2020-09-21 22:11 petrw1 Lone Mersenne Hunters 82 2010-01-11 01:57

All times are UTC. The time now is 06:03.

Wed Oct 27 06:03:24 UTC 2021 up 96 days, 32 mins, 0 users, load averages: 0.81, 0.89, 0.92