Stage 2 finished, the best 10 polynomials murphy_e ranges in 2.348e-19 - 2.129e-19. Not very impressing.

I ran stage 2 on 250k hits computed by RichD and myself, the best e-value was 2.0e-19, so not that great. Shi Bai ran the CADO stage 2 on the same dataset and has gotten better high scores (I think the best so far was 3.2e-19)

[QUOTE=jasonp;320043]I ran stage 2 on 250k hits computed by RichD and myself, the best e-value was 2.0e-19, so not that great. Shi Bai ran the CADO stage 2 on the same dataset and has gotten better high scores (I think the best so far was 3.2e-19)[/QUOTE]

As I recall from past comparisons (B200?), msieve typically has a ~10% lower score due to your more sophisticated integrator. How much of that better score is due to the differences in integration?

I was going to write that most of the time the e-values calculated by the two suites differ by less than 1%, and larger differences were actually because of bugs in Msieve that miscalculated the alpha value. But then to make sure I ran the best CADO polynomial through Msieve, and the difference in e-values was 4.78e-19 vs 3.493e-19!

For the record, the best polynomial I could find in the batch of 260k hits was
[code]
R0: -5876926706329267758590334567904669751467577
R1: 869332622169838859059
A0: 15018543190390770338953421520339801353757924940775872204660800
A1: 909208080136930262159142936022283921496280008021988680
A2: -13303473065609161166913597414184875440269406556
A3: -138145188131827120402436868843139274434
A4: 763752915545626483996372079531
A5: 4312543659621449260154
A6: 10000466830200
skew 133010468.05, size 3.823e-020, alpha -12.788, combined = 2.080e-019 rroots = 4
[/code]

Here's my slightly better (according to msieve) polynomial
[CODE]
SKEW 28338177.70
R0 -3626941552197564826492128852700460060642852
R1 48957407582916194761589
A0 -26101732745933806144485280988037796254029367990700826499285
A1 -2408464141902741608017790242140644715688145388490381
A2 -174314770228113076791419006080421369720970639
A3 28697722660097589508721192118263624637
A4 1036456362256909021188219944324
A5 -21292410351587764080336
A6 181000001476800
skew 28338177.70, size 4.381e-20, alpha -12.189, combined = 2.348e-19 rroots = 2
[/CODE]

jasonp, what score does CADO show for your or my polynomial?

I got it by myself: CADO's E.sage gives 1.84701205471987e-19 for your and 2.08696883313422e-19 for my polynomial.

The difference is that the CADO tools compute the size score by integrating in radial coordinates, whereas Msieve starts in radial coordinates and switches to computing the integral in rectangular coordinates. They don't compute the same numbers in general.

Msieve uses the rectangular integral because pol51opt did, and the GGNFS scripts had a table of precomputed 'good' scores to shoot for. Nonetheless, the radial score is more robust for some reason, i.e. it finds a better minimum a lot of the time.

Here are approx. 1.3 million stage 1 hits:
[URL="https://www.dropbox.com/s/spssx3ze8iagvpn/rsa896_1.dat.m.gz"]https://www.dropbox.com/s/spssx3ze8iagvpn/rsa896_1.dat.m.gz[/URL]

Edit: I restarted the stage 1 search at different values. I'm now running the size optimization on this file now, and I will run the root sieve on those with the smallest score.

So, the best murphy_e we have so far is about 2.5e-16, I wonder how CADO guys got murphy_e 2x larger than ours? Either their polynomial is quite extraordinary or they use different optimization algorihtms.

Is it possible we should run msieve stage 2 on their stage 1 results or their stage 2 on our stage 1 results?

I don't have access to the CADO stage 1 hits. We've collected 2.7M hits of our own, and they will all have stage 2 performed by both packages.

Keep 'em coming!

Ilya, I suspect a lot of the difference boils down to the more effective root sieve developed by Shi Bai for the CADO stage 2. From what I've seen it consistently produces better alpha scores without sacrificing as much polynomial size as Msieve needs.