[QUOTE=fivemack;418819]I presume he's talking about the stage-2 score (the thing printed at the end of each line in msieve.dat.ms), which is a number of the order 3e+19.

You seem to have confused it with the Murphy scores, which are of the order 3e-12 (so forty-one orders of magnitude different, which I would have expected to make them hard to confuse). The Murphy scores are roughly a probability that a value of the polynomial is sufficiently smooth; I'm not exactly sure what the stage-2 score measures.[/QUOTE]

Ah. It's been many years since I've manually run a poly search -- :blush:

There's still the matter of 24 CPU hours doing better than 30 GPU hours though.

Best one I got for Alfred's C153
 

[CODE]R0: -176915602067131140978692131601
R1: 109404085563163
A0: -7302868581807259050515796513087069240
A1: 170933500834141158930455569890766
A2: 10928102934671700769536555
A3: -28459862608574595168
A4: -873208908832
A5: 1155960
skew 3350352.16, size 7.670e-015, alpha -7.874, combined = 3.635e-012 rroots = 5
elapsed time 04:00:06
[/CODE]

Murphy score is similar, but since A5 is smaller, the skew is higher. Probably still worth a test sieve.




Edit: As an experiment, I'm going to re-run this without any change in the chosen stage1 and stage2 norms to see how that affects the "best" polynomial. I'll post once it finishes.

@ Gimarel

Thank you very much for your polynomial.

Using the 14e siever and the parameters

[QUOTE]
rlim: 25000000
alim: 25000000
lpbr: 30
lpba: 30
mfbr: 60
mfba: 60
rlambda: 2.6
alambda: 2.6
[/QUOTE]

I get

[QUOTE]
total yield ~ 37000 (q-range 10k with starting values from 8e6 up to 18e6)
sec/rel ~ 0.0325
[/QUOTE]

If my choice of parameters is bad, let me know please.

[QUOTE=fivemack;418819]The Murphy scores are roughly a probability that a value of the polynomial is sufficiently smooth; I'm not exactly sure what the stage-2 score measures.[/QUOTE]
It's the integral of the square of the algebraic polynomial over a rectangular sieve region; lower is better, this is basically the RMS size of one sieve value.

[QUOTE=Alfred;418827]@ Gimarel

Thank you very much for your polynomial.

Using the 14e siever and the parameters



I get



If my choice of parameters is bad, let me know please.[/QUOTE]

(Use [code] tags instead of [quote] tags.)

I let Yafu choose parameters, and it gave these:

[code]n: 200342680339792084251385520743186501215219346823549163194073828377349727332880101003701005574557437974308702796632658776489876756467616443528718745464543
# norm 9.635214e-15 alpha -5.731471 e 3.859e-12 rroots 5
skew: 9910102.29
c0: 32499064344333747693836052278767798335
c1: 3126905685798081746601052320840
c2: -5075345682477287373503043
c3: 90439175992181516
c4: 59077950604
c5: 420
Y0: -862373527665808095417346348354
Y1: 665033345874870149

rlim: 29200000
alim: 29200000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.6
alambda: 2.6[/code]

Over a 2K range of q right at the factor base bound:

[code]nfs: commencing algebraic side lattice sieving over range: 29200000 - 29202000
gnfs-lasieve4I14e (with asm64): L1_BITS=15, SVN $Revision: 430 $
FBsize 1811797+0 (deg 5), 1811271+0 (deg 1)
total yield: 3809, q=29202001 (0.04913 sec/rel) ETA 0h00m)
105 Special q, 199 reduction iterations
...
nfs: found 3809 relations, need at least 44869960 (filtering ETA: 666h 10m)
[/code]

When I tried your parameters for 2K at the factor base bound, I get this:

[code]nfs: commencing algebraic side lattice sieving over range: 25000000 - 25002000
gnfs-lasieve4I14e (with asm64): L1_BITS=15, SVN $Revision: 430 $
FBsize 1566762+0 (deg 5), 1565926+0 (deg 1)
total yield: 8015, q=25002001 (0.02488 sec/rel) ETA 0h00m)
117 Special q, 221 reduction iterations
...
nfs: found 8015 relations, need at least 91912198 (filtering ETA: 679h 6m)[/code]

So it doesn't matter too much, but Yafu's param choice seems slightly better.

@ wombatman

Thank you very much.

[QUOTE]Murphy score is similar, but since A5 is smaller, the skew is higher. Probably still worth a test sieve.[/QUOTE]

A test (with identical parameters and three starting values for q) shows
[QUOTE]
total yield ~ 34k compared with Gimarel's ~ 37k.
[/QUOTE]

Yield doesn't matter, as long as it's not terribly small (say, under 2.0 relations per q). speed matters, as measured by sec/rel.

Yafu is pessimistic about how many relations will be needed for 30LP at 91M. In my opinion, this is closer to 31LP than 29. I'd expect a matrix to build with 80-82M relations with the parameters Alfred chose.

I'm also curious about Gimarel's find using CPU search; my experience was that it's worth using a GPU for any search 140 digits or higher, and I didn't think it was close. But I don't start from A1 = 1...

wombatman-
We should do some experiments with settings for the C198 requested this morning; I'm interested to try to figure out if altering stage1norm has merit in general.

Yeah, I think it would be worthwhile. Want to make sure we're not cutting potentially good candidates by making it too small/tight. Stage 2 norm could have an effect as well. I'll run from the lowest A1 with Stage 1 norm at msieve's chosen value / 10. Same for stage 2 norm. Then I can come back and rerun it with, say, Stage 1 at default and Stage 2 / 10. Something like that what you had in mind?

Conversely, don't the polys that CADO produces typically have substantially higher A1s (and lower skew)?

Dubslow-
Both CADO and msieve have A1 as a user-controlled parameter/search range. If you mean that CADO's best poly in a range often has higher A1 than msieve's best, I'm not sure- I've only used CADO for one poly search, and I ran a really wide range (like 0-20M).

[QUOTE=wombatman;418841]Yeah, I think it would be worthwhile. Want to make sure we're not cutting potentially good candidates by making it too small/tight. Stage 2 norm could have an effect as well. I'll run from the lowest A1 with Stage 1 norm at msieve's chosen value / 10. Same for stage 2 norm. Then I can come back and rerun it with, say, Stage 1 at default and Stage 2 / 10. Something like that what you had in mind?[/QUOTE]

Yes, though what is "better" is the issue. My measure of value is greatest number of -nps hits of norm better (sorry, lower) than {pick a number} per day. What stage1norm produces the highest rate of quality hits? Note I'm not talking about actual poly E-score; that's a crapshoot only lightly correlated with settings of stage1/stage2.

setting stage2norm merely alters the output that is kept for root-opt. It's not valuable to run root-opt on thousands of candidates, so some cutoff is useful for brevity. Default stage2norm produces *thousands* of candidates per hour, not helpful.

A few days of searching for the C198 should illuminate the worst stage2 size that produced a possibly-useful poly; we can set the cutoff for worthy candidates from -nps just above that number.