[UWR] 128x128x128 solve

Still working on the blue center :p I'm now at 21:49:52.452 and 127141 moves. I did this part at 1.596 moves/second.
9O7HcWv.png


EDIT: Something weird happened with the movecount (it wasn't supposed to be 138620). I loaded the save and got a new screenshot. I thought 3.191 moves/second was unrealistic!
 
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I'm now done with the blue center! The time is 23:33:13.796, and I've done 137779 moves. This session was done at 1.715 moves/second. After finishing orange, about 1/3 of blue was already solved, so I solved about 10584 centers. That means that I did the blue center stage at 1.613 moves/second, about 2.627 moves/piece, and about 1.629 seconds/piece.
NmyCcwV.png
 
TraciAG said:
how many breaks have you taken so far?
Click to expand...
I've been doing it in roughly-2-hour chunks once a day (with some days skipped due to technical difficulties or a competition). I couldn't do something like this in one sitting, I would worry about repetitive motion injury.

IRNjuggle28 said:
I have a feeling this UWR will stand for quite a while...

Out of curiosity, what made you choose 128?
Click to expand...
We'll have to see, the 111 only stood for like 6 months :p

I wanted to do an even cube this time (since they're easier with my method), and it had to be above the 121, but not too big. 128 seemed like a nice number since it's not too much higher and (as guysensei1 said) it's also a power of 2.
 
mns112: Clearing is basically a step that has the goal of quickly solving a large portion of the center in relatively few moves. It does that by only solving centers that are in particular positions on the cube. Solving the center in two steps (clearing and then any pieces not solved yet) turns out to be significantly faster and more efficient than just solving all the pieces directly with commutators.

I'm now roughly 2/3 through the last 2 centers, at 25:32:13.765 and 151220 moves. I did this part at about 1.883 moves/second. There should be about an hour left at this point, so I should be done tomorrow (and then I might show off a pretty pattern or two :p).
uxpaurD.png
 
I'm done! :D The final result was 26:25:18.515 and 157318 moves. I'll post some more detailed statistics later but for now here's what I got...

The last two centers were done in just under 3 hours and 19539 moves. About 7938 green centers needed to be solved, so I was solving green at a rate of 2.039 moves/second, about 2.459 moves/piece, and about 1.206 seconds/piece. Of course that is only taking into account the unsolved green centers, so if you count all 31752 green and red center pieces, you get much better numbers :p
E7ixKPU.png


I also made a cube in cube pattern for Randomno :)
lCqL5w2.png

8KoWvpi.png
 
Congrats. Now finally update the thread title :D

And next time sub-24h? What's the record for largest cube solved on one day?
 
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Imgur album of progress: http://imgur.com/a/izVLF

Youtube playlist of the entire solve: https://www.youtube.com/playlist?list=PLEeuqKEdptAM0DpOuhWpsi6HRkrTRcHHc

Updated historical WR list:
2x2x2 - January 12, 2000, by David Barr, in 35.600
3x3x3 - January 12, 2000, by David Barr, in 1:23.600
4x4x4 - January 12, 2000, by David Barr, in 5:52.460
5x5x5 - January 12, 2000, by David Barr, in 9:20.180
6x6x6 - January 13, 2000, by David Barr, in 16:42.830
7x7x7 - January 21, 2000, by David Barr, in 23:33.450
11x11x11 - March 12, 2000, by David Barr, in 1:20:15.566
11x11x11 - June 12, 2000, by Chris Hardwick, in 56:32.298
11x11x11 - February 20, 2001, by fl, in 5:24:40.242
11x11x11 - April 11, 2001, by fl, in 6:57:35.728
11x11x11 - May 25, 2001, by fl, in 2:23:04.975
11x11x11 - May 31, 2001, by vfr, in 1:36:03.768
20x20x20 - June 12, 2001, by Chris Hardwick, in 4:24:54 (solving time) or 8:13:56 (total time)
20x20x20 - March 16, 2002, by Richard Carr, in 3:53:39.573
20x20x20 - June 25, 2002, by Richard Carr, in 3:05:27.722
20x20x20 - September 7, 2002, by Richard Carr, in 2:46:48.822
21x21x21 - October 28, 2002, by Grant Tregay, in 72:38:11.378
31x31x31 - January 1, 2003, by Richard Carr, in 7:43:15.493
35x35x35 - October 1, 2003, by Joe Allen, in 103:26:10.140
39x39x39 - October 8, 2003, by Joe Allen, in 113:48:13.052
40x40x40 - February 17, 2004, by Chris Moyer-Grice, in 23:35:xx (solving time)
55x55x55 - March 18, 2004, by Joe Allen, in 23:00:24 (solving time)
100x100x100 - December 20, 2008, by Ravi Fernando and Peter Greenwood, in 820:13:11.220
111x111x111 - May 19, 2013, by Michael Gottlieb, in 29:51:02.641 (solving time) or 246:48:xx (total time)
121x121x121 - September 30, 2013, by Adrian Acosta, in 89:02:26.601 (solving time) or ~2106 hours (total time)
128x128x128 - November 19, 2014, by Michael Gottlieb, in 26:25:18.515 (solving time) or 361:36:xx (total time)

Whole-cube statistics:
- Total solve time: 26:25:18.515, or 95,118.515 seconds
- Total moves: 157,318
- Number of pieces: 96,776
- Number of positions: 7.8 * 10^63054
- Seconds per piece: 0.983 (compared to 1.480 for the 111)
- Moves per piece: 1.626 (compared to 2.781 for the 111)
- Moves per second: 1.654 (compared to 1.878 for the 111)
- Real time spent: about 15 days 1 hour 36 minutes (from 7:09 PM on the 4th, until 8:45 PM on the 19th)
- Percent of time spent working: 7.3%

Stage by stage statistics:
Note that for "pieces solved" here I mean the number of new pieces I deliberately solved in this stage. There are many pieces which accidentally solve themselves - for instance, the entire sixth center, or about 1/6th of all centers which are solved after edges. I didn't include those here because just keeping track of the pieces I solved on purpose gives more useful numbers for moves/piece and time/piece.

Code: 
Stage           Time          Moves   Pieces  mov/sec mov/pc  sec/pc
Edges + 3x3x3   1:21:58.421   2951     1520   0.600   1.941   3.236
1st Clearing    3:11:49.688   13416   ~7439   1.166   1.803   1.547
1st Finishing   3:17:26.514   23408   ~5791   1.976   4.042   2.046
2nd Clearing    3:09:21.844   16458   ~8228   1.449   2.000   1.381
2nd Finishing   2:41:25.516   17854   ~4473   1.843   3.992   2.165
3rd Clearing    1:41:08.375   11796   ~5670   1.944   2.080   1.070
3rd Finishing   3:22:41.267   24088   ~6237   1.980   3.862   1.950
4th             4:47:22.171   27808   ~10584  1.613   2.627   1.629
5th & 6th       2:52:04.719   19539   ~7938   1.892   2.461   1.301

And if we combine the clearing+finishing stages to get a better sense of how long each center took:

Code: 
Stage           Time          Moves   Pieces  mov/sec mov/pc  sec/pc
Edges + 3x3x3   1:21:58.421   2951     1520   0.600   1.941   3.236
1st             6:29:16.202   36824   ~13230  1.577   2.783   1.765
2nd             5:50:47.360   34312   ~12701  1.630   2.702   1.657
3rd             5:03:47.642   35884   ~11907  1.968   3.014   1.531
4th             4:47:22.171   27808   ~10584  1.613   2.627   1.629
5th & 6th       2:52:04.719   19539   ~7938   1.892   2.461   1.301

The method I used:
Anything underlined is new since the 111x111x111. The rest is the same.

First, some basics. I solved most faces in two steps: "clearing" and finishing up. The idea of clearing a face is to solve as many pieces as possible as quickly as possible. After that step, which typically solves 50% or more of the face, I can go through the longer step of putting each of the remaining pieces of that color into the center, one at a time or in blocks. As for notation, I'll be using something like SiGN (xR means turn the xth layer on the R face, or the first layer if x is absent), except that I'll also be using lowercase p and q as variables to better describe classes of commutators.

1) Solve the edges. I do edges first for large computer cubes because reduction (centers first) scales badly, and because having solved edges actually lets me use them to keep track what part of the puzzle I'm working on. A lot of the time I do a pR' move or something to start working on a row of one center, and the incorrect edge reminds me which row it is. With so many layers it's impossible to do it by counting or visual inspection alone. Anyway, for the first 9 edges I did basically the same thing as with other cubes. For the last three edges I used moves like pR U2 pR' (for the 10th edge only), pR2 U2 pR U2 pR2, and pR' F U' R F' U pR. Instead of solving one orbit at a time like on my keyboard solves, I went for an edge at a time and solved pieces in the same position in groups. For instance on the last 3 edges there are only 6 possible positions for each piece, so with 126 pieces in each edge there are a lot of pieces in the same position which can be solved in the same way, all at once, by replacing a pR move with a whole bunch of slice moves along the same layer. This took about an hour and twenty minutes in total.

2) Clean the first center. I used white. Hold the white face on U, and then for each row (perpendicular to the F face), we do something like this: move white centers out of the way on the corresponding row on F using pU moves, then qR', then solve as many white centers into that layer as possible using only pU-axis moves, then qR. By "solve as many white centers ... as possible" I mean I basically look at that row on R, B, and L, and for every white center I see, move that layer the right amount. Note that these rows are vertical, which is something I did because of the way Iso is set up (when zoomed in, it's easy to scroll through a vertical row on F or R using just the up/down arrow keys). You could do any of this from a different angle if you wanted. A typical layer might be something like (2U 4U 7U ...) 3R' y (3U 6U 8U ...) y (U2 4U2 8U2 ...) y (2U' 3U' 4U' ...) y 3R. Each center on white corresponds to 5 stickers, and a white center on any of those 5 stickers means the center gets solved. About 63.5% of the center ends up solved.

3) Finish the first center. Now I can hold the center on F and look at R. If I see a white center anywhere, I can solve it using pF qU' pF' qU. Four-move commutators are fast! However, I can't just do that randomly, but instead, I have to do it so that the center moves into a place on the white center that didn't have a solved center already. I often do y' y to see what pieces can be moved into holes in the white center, and a lot of pieces can be solved this way before I need to rotate the white center and check again. You'll see this type of checking often as I continue. Note that this requires centers to be adjacent, and since we're solving from all five, we have to swap two adjacent centers. On the 4x4x4 the algorithm for this is r U2 r' l' U2 l, which you then have to properly undo later.

4) Clear the second center. I used yellow. This is the same idea as the first center - hold yellow on U (so, white on D) and proceed row by row. However, instead of using pR' moves to move a row onto the F face, I used pR U2 pR' moves. This does solve the layers in a different order, but that's okay. For the middle layer I used U pR U' pR'. Each center on yellow again corresponds to 5 stickers (any yellow piece in one of those 5 places means that piece gets solved), and about 71.8% of the center ends up solved after this.

5) Finish the second center. Again I swap yellow with another center, so I can hold yellow on F, white on U, and the solved center on R. The commutator this time is pF2 qU' pF2 qU (or pF2 qU pF2 qU' for the mirror). Since I can't just do x rotations and keep going, I have to do some extra center swaps to bring each of the four non-white/yellow centers into the right place. There was also plenty of y' y to check if there's room to put a piece.

6) Clear the third center. I used orange (for visibility). Place orange on U and white/yellow on L/R. Now we can do pU2 moves but not pU moves. So I do something like the white center clearing, where I do pU2 moves to move orange centers out of the way, then a qR' move to bring the row down, then do more pU2 moves to solve as many orange centers as possible, then a qR move. A typical row clear might look something like (2U2 4U2 7U2 ...) 3R' y2 (2U2 3U2 4U2 ...) y2 3R. Each center on orange corresponds to only 3 stickers, solving about 60.7% of the center.

7) Solve the third center. This is just like what I do on yellow, with the pF2 qU' pF2 qU moves, since they keep U and D solved, and again I use plenty of y' y moves. In fact, there are fewer center swaps than last time, since the D center can stay where it is.

8) Solve the fourth center. As a general rule you want this to be adjacent to the third center, so I chose blue. However, I want to set up the blue center opposite orange for the algorithms I use, so I do a center swap. Now the idea is to move all blue centers out of both F and B, one column at a time. I use pU2 moves to move as many blue centers as possible off F, then qR U2 qR' to move a column of the blue center down to F, and then more pU2 moves to bring as many blue centers onto that colun as possible. Then I undo the qR U2 qR' to put the blue center column back, and do a U turn. This is a lot like the clearing stages, except that for each column we repeat the process as necessary (at most 4 times, for the 4 possible orientations of the U center) to solve all blue centers on that column. Then we just move onto the next column, and so on until all blue centers are on U.

9) Solve the last two centers. Swap the fourth center back into place first, so the two centers are adjacent. Place blue on F, red on U, and green on B; we again want to solve one center (green) column by column. Do a qR' y2 to bring a row down, and then use a pU2 move on all the red centers in that column, and then a y2 again. Now you have a lot of unsolved rows with red pieces in that column. Do qR U qR', and if you see any green centers in that column on one of those unsolved rows, solve it with a pU2. Repeat the same thing two more times, and almost all of those rows should be solved. The remaining rows are ones where no amount of qR U qR' will put a green center there. There are a few ways to fix this; for this solve I did y2 (U2 qR U2 qR'), then pU2 moves to solve all the rows at once, then (qR U2 qR' U2) y2. Then just do a qR to finish that column, and you can start the next column by bringing a row down. Once all the columns are done, everything is solved and you just have to fix the U face.

Stefan said:
And next time sub-24h? What's the record for largest cube solved on one day?
Click to expand...
As far as I know, the record for solving within one real day is 40x40x40 (by Joe Allen (in 8 hours in 2006) and me (in 2.6 hours in 2013)) and the record for solving in <= 24 hours of solving time is 55x55x55 (by Joe Allen (in 23 hours over a few weeks in 2004)). Neither of these records are particularly hard to beat though. The one-hour limit record is a bit more optimized though: I did a 24x24x24.
 
I feel there should be some sort of rules/time limits for higher order cubes. I could start on a ridiculously massive cube, and spend several hundred hours total time solving it, and if I did it over a long time (say year), it wouldn't really be too much effort.
 
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