# 4x4x4 FMC (computer and human)

#### Stefan

##### Member
Thanks for hosting the contest!

I used Shuang Chen's 4x4x4 solver for reduction to 3x3x3, and then the huge optimal solver of Cube Explorer 5.01s. With a script of my own in between.

I slightly modified Shuang Chen's solver to feed our scrambles into it, to search more (multiplying the numbers like PHASE1_SOLUTIONS by 100 or 1000), and to print not just one solution but keep printing solutions that are not more than three moves longer than the shortest so far (counting in OBTM, as that's what that solver uses). I stopped it when I had around 1000 OBTM-short reductions (or rather, solutions containing them) for each scramble.

Then I used a (messy and quite possibly buggy) script of my own to extract the reductions (and 3x3 parts), minimize them for OBTM (some cancellations were possible) and BTM (much was possible, as Shuang Chen's solver doesn't use BTM), sort them by resulting move count and produce input files for Cube Explorer that looked like this:
Code:
L U R' B U' F2 B D' U R F2 L2 U2 R' U2 R' D2 B2 // line4 BTM 22 redux: Dw Fw D' Lw2 B Uw Lw U2 Fw2 2U2 D' B2 U2 Lw D' R2 F Uw2 Rw2 D L2 Bw2
F2 L U R' B U' F2 B D' U R F2 L2 U2 R' U2 R' D2 B2 // line4 BTM 22 redux: Dw Fw D' Lw2 B Dw y Lw U2 Fw2 2U2 D' B2 U2 Lw D' R2 F Dw2 y2 Lw2 x2 D L2 2F2 z2
B2 L U R' B U' F2 B D' U R F2 L2 U2 R' U2 R' D2 B2 // line4 BTM 22 redux: Dw Fw D' Lw2 B Dw y Lw U2 Fw2 2U2 D' B2 U2 Lw D' R2 F Dw2 y2 Lw2 x2 D L2 2B2
B' L2 B' U2 D2 L2 F R2 B L U2 F D B' L' U R2 F' B' L' // line13 BTM 22 redux: R2 Dw2 Bw' U' Rw' 2B' S2 L' F2 Uw D B' L2 Uw L D2 2B2 Dw2 R' B' Rw2 Dw2
U2 B' L2 B' U2 D2 L2 F R2 B L U2 F D B' L' U R2 F' B' L' // line13 BTM 22 redux: R2 Dw2 Fw' z U' Lw' x' 2F' S' L' F2 Dw y D B' L2 Dw y L D2 2B2 Dw2 R' B' Lw2 x2 2U2 y2
D2 B' L2 B' U2 D2 L2 F R2 B L U2 F D B' L' U R2 F' B' L' // line13 BTM 22 redux: R2 Dw2 Fw' z U' Lw' x' 2F' S' L' F2 Dw y D B' L2 Dw y L D2 2B2 Dw2 R' B' Lw2 x2 2D2
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.
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This is the start of my input file for scramble 1 for BTM. Each line is a 3x3x3 part that I want Cube Explorer to optimize, and in the comment the already "optimized" reduction leading to that 3x3x3 part (gets shown in Cube Explorer as "Pattern Name"). Note that most of the time each reduction gets "tripled" because when the reduction for example ends in Bw2, you can append a B2 or F2 for free (doesn't change the BTM length as they just turn the Bw2 into 2B2 or 2F2 z2). This gives you three times as many 3x3x3 chances to try.

Then in a Cube Explorer clickfest, I tried the cubes from the shortest reductions first, and stopped searches when they couldn't lead to a shorter solution than I had already found at that point. Only tried the first few dozen or so for each scramble, gave up when I would've needed like 14 HTM to improve. Oh and for BTM I used the "Allow Slice Moves" option, which I somehow hadn't known existed.
Tom, one thing I'm curious about: How did you produce the scrambles? Looks like 3x3+reduction+random, but the 3x3 part is pretty long and the reduction part is pretty short. Doesn't look like Shuang Chen's solver, so I'm wondering...

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#### Renslay

##### Member
Congrats to everyone! Impressive numbers.

#### ch_ts

##### Member
Tom, will the actual solutions be posted anywhere? Or should we share our own solutions here?

#### cmhardw

Wow, impressive numbers from the computer and from the human competition! Very exciting, and congrats to the winners!

#### goodatthis

##### Member
Wow, impressive! I'm really curious to see the solutions to the human solutions, especially how they were able to obtain them.

#### ch_ts

##### Member
These were my solutions:

Human FMC:

Scramble 1

Scramble 2

Scramble 3

Scramble 4

Scramble 5

Scrambles 1, 3, 4, 5 were done using cmowla's reduction method described here. Initially they were all done centers first then edge pairing, about 55 moves for reduction and I thought that was pretty good. But then Tom updated the leaderboard and I found cmowla's method and used it to try to get ahead of Bruce. If I had known his actual score, I don't know if i would have tried as hard as I did.

Computer solutions were done using my reduction method (4 reduction steps) using single slices for the BTM metric and using wide turns for the OBTM metric. One ugly hack I tried was to check at end of step 1 if step 2 was also accidentally solved, otherwise find another solution, and if it worked I would use it for steps 3 and 4. It didn't find anything after 15 minutes so I stopped the search.

3x3x3 solutions were found using Cube Explorer.

Computer BTM: (used single slice turns during reduction)

Scramble 1

Scramble 2

Scramble 3

Scramble 4

Scramble 5

Computer OBTM: (used wide turns during reduction)

Scramble 1

Scramble 2

Scramble 3

Scramble 4

Scramble 5

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#### cuBerBruce

##### Member
Here are my explanations for my "human" solutions. Due to length, I've used a spoiler.

I note that as far as solving the centers are concerned, all face turns (single-layer) can be considered to be commuting moves. That potentially allows for "one" centers solution to essentially produce many different configurations for the edge pieces for the start of the edge pairing phase. This can hopefully be used to get a few edges paired up before even starting the edge pairing phase. Being allowed to use Tom's applet was especially helpful to do this fairly efficiently.

In some ways, I'm somewhat disappointed that only one other person competed in this category. My 3x3x3 phase solves were not particularly super by today's standards (and there was no 1-hour time limit, obviously) so I think a good FMC'er should have been able to beat my solutions.

Code:
Scramble 1:

First center: Uw2 F' Rw R' Fw' (5)
2nd center: F' Uw' L' Fw' R2 Fw (11)
3rd center: F Uw' R' Uw' (15)
4th center: Fw2 R2 Fw2 (18)
Finish centers: F2 Uw L Uw' (22)
2 dedges already paired
3rd - 9th dedges: B' (R' U' R) Dw (L U' L') (R' U2 R) (R' D' R) (L D2 L') Dw' (40 - 2 = 38)
10th - 12th dedges: F Dw2 R' D R Dw2 y (44)

3x3x3 phase (explained in terms of 3x3x3)
2x2x1: F' U'  (2)
2x2x2: . R D * R (5)
Insert at ".": D (6)
2x2x3: L B L B' (10)
Pseudo F2L minus 1 slot: L' F L F2 (14)
Use premove F' to correct for pseudo F2L minus 1 slot.
Tripod: L2 U L U' L2 (19)
All but 2 corners, 2 edges: U L' U' L (23)
Premove correction: F' (24)
Insert cyclic-shifted J-perm to solve final 4 pieces.
Insert at "*": D L' D' L2 B2 R' U' R B2 L' (34-3 = 31)

OBTM: 44 + 31 = 75
BTM: 42 + 30 = 72

Solution:
Uw2 F' 2R Fw' F' Uw'
L' Fw' R2 Fw F Uw' R' Uw'
Fw2 R2 2F2 Uw L Uw'
B' R' U' R Dw L U' L' R' U2 D' R L D2 L' Dw'
F Dw2 R' D R Dw2 y
F' E' y' R D2 L' D' L2 B2 R' U' R B2
R B L B' L' F L F2
L2 U L U' L2 U L' U' L F'

Scramble 2:

First 2 centers: R L D Fw' D F Uw Rw' D' L' R2 Fw' (12)
3rd-4th centers: F Uw' F R Uw B2 R Uw (20)
Finish centers: R2 Fw2 L2 Fw2 (24)
2 dedges already paired
3rd-6th dedges: Dw' (L U2 L') (L D L') Dw (32-2 = 30)
6th-12 dedges: R2 F R Bw' (D F' D') (R' B2 R) (R' U F' R U') Bw x' y' (46-2 = 44)

3x3x3 phase:

Premoves: D' R' (2)
2x2x2: L' D R U' (6)
2x2x3: D' . B2 D B2 L B * L' D2 (14)
C-E pair extension: D' B D (17-1 = 16)
F2L minus 1 slot: D L2 D' (19-1 = 18)
Tripod: B (19)
Edges: L U' L' U (23)
Premove correction: D' R' (moves already counted)
This leaves 4 corners, solved by two insertions.
Insert at ".": D F' D' B2 D F D' B2 (31-6 = 25)
Insert at "*": F' R' F L' F' R F L (33-2 = 31)

OBTM: 44+31 = 75
BTM: 43+29 = 72

Solution:
R L D Fw' D F Uw Rw' D' L' R2 2F' Uw' F R Uw B2 R Uw R2 Fw2 L2 Fw2
Dw' L U2 D L' Dw R2 F R Bw' D F' D' R' B2 U F' R U' Bw x' y'
L' D R U' F' D' B2 D F B2 L S z' R' F L' F' R F D B D2 L2 D' B
L U' L' E y R'

Scramble 3:

First 2 centers: R' L' Dw' B2 Lw' F' Dw' L' Dw2 B2 Dw (11)
3rd center: D' Lw F' U B2 Rw (17)
4th center: F Rw' F2 Rw (21)
Finish centers: Uw2 F2 Uw2 (24)
3 dedges already paired
4th-9th dedges: F' (U R') (R' U R) Dw (D' R D) (R' F D' F') (F U' F') Dw' (42-3 = 39)
10th-12th dedges: D Lw' L D L' D' Lw (46)

3x3x3 phase:

1x2x3: F' D R' D' U R' F . (7)
2x2x3: R L2 F R2 (11)
Edges: L2 B2 D' * B D L B2 L' B (20)
A 5-cycle of corners remains.
Insert at ".": F' R' B' R F R' B R  (28-4 = 24)
Insert at "*": R2 B L' B' R2 B L B' (32-2 = 30)

OBTM: 46+30 = 76
BTM: 42+27 = 69

Solution:
R' L' Dw' B2 Lw' F' Dw' L' Dw2 B2 2D Lw F' U B2 Rw F Rw' F2 Rw Uw2 F2 Uw2
F' U R2 U R 2D R D R' F D' U' F' 2D' 2L' D L' D' Lw
F' D R' E y R2 B' R F R' B M2 x2 F M2 x2 B2 D' R2 B L' B' R2 B L D L B2 L' B

Scramble 4:

Full solution:
First center: D' Rw Bw (3)
2nd center (adj.): F' U Rw2 B' Rw' (8)
3rd center: R Fw Dw' F2 Dw Fw' (14)
Finish centers: Fw D' R' Fw D U2 Bw2 (21-2 = 19)
2 dedges already paired
3rd - 4th dedges: Bw2 R' B2 R Bw2  (24-2 = 22)
5th - 10th dedges: D' F (F L F') Rw' (F' R F) (F' L F) (U R2 U') Rw (38-3 = 35)
11th - 12th dedges: D' R' Dw' R' B U' R B' Dw y' (44)

Solving inverse for 3x3x3 phase.

2x2x2: D F' R2 B'  (4)
2x2x3: R U2 R2     (7)
F2L - 1: F U F2   (10)
Edges: L' U' B' U2 B2 . L' B' L2  (18)
Insert at ".": F' L' B' L F L' B L (18+8-5 = 21)
Insert at end: L' B L F' L' B' L F (21+8-2 = 27)
Use inverse as solution to 3x3x3 phase.

OBTM: 44+27 = 71
BTM: 41+26 = 67

Solution:
D' Rw 2F z' U Rw2 B' 2R' Fw Dw' F2 2D R' Fw D U2
R' B2 R Bw2 D' F2 L F' Rw' F' R L F U R2 U' Rw D' R' Dw' R' B U' R B' Dw y'
L2 B L B2 U2 B U L F2 U' L F' R2 F L' F' U2 R' B2 L' B' R2 B L S' z D'

Scramble 5:

First 2 centers: F' D2 L B' U Uw Lw Fw' L2 Fw' (10)
Paired center pieces: B' F' U Rw (14)
Finish centers: F D2 Rw' D2 Rw2 (19)
4 dedges already paired
5th-7th dedges: U2 Rw2 (F' R F) (U R' U') Rw2 (28)
8th-12th dedges: B' L' Dw (R' U2 R) (R U' R') Dw' x' y2 (38-1 = 37)

3x3x3 phase:
2x2x2: R B' D2 F2 (4)
Siamese 2x2x2's: D' B2 L2 D2 B L B' (11)
F2L minus 1 slot: D' L' F L F' (16)
All but 2 corners, 2 edges: R D' R' . B' D2 B (22)
Insert at ".": R D2 R' D' R D2 L' D R' D' L (33-3 = 30)
(sub-optimal J-perm)

OBTM: 37+30=67
BTM: 37+30=67

Solution:
F' D2 L B' U Uw Lw Fw' L2 Fw' B' F' U Rw F D2 Rw' D2 Rw2
U2 Rw2 F' R F U R' U' Rw2 B' L' Dw R' U2 R2 U' R' Dw' x' y2
R B' D2 F2 D' B2 L2 D2 B L B' D' L' F L F'
R D R' D' R D2 L' D R' D' L B' D2 B

#### rokicki

##### Member
Thanks for hosting the contest!
My pleasure!

How did you produce the scrambles? Looks like 3x3+reduction+random, but the 3x3 part is pretty long and the reduction part is pretty short. Doesn't look like Shuang Chen's solver, so I'm wondering...
I used Shuang Chen's solver as integrated into tnoodle to generate the scrambles.
Then I inserted four random clockwise quarter turns at the front and at the back
(making some efforts to avoid cancellations). I figured this was a reasonable
compromise between getting truly random positions, having overly long scrambles,
and having the scrambles provided be as good as a computer could do.

Oh, the Cube Explorer allow-slice-move option! Very nice; I had not even thought
of that.

#### Stefan

##### Member
Ok, I guess the reduction parts are just short by accident then (they were shorter than what I got for the scrambles, despite my much more extensive search). I don't think they improved the solver in tnoodle, only added dependencies making it harder to compile (that's why I used his original standalone version, very easy to use and modify).

#### Stefan

##### Member
Charlie, your second and fourth computer BTM solutions contain "D2 U2". I guess you didn't use the slice moves option?

#### cuBerBruce

##### Member
I noticed some of Charlie's solutions "should" have been one move less in BTM. (Related to Stefan's comment.) This is because of sequences such as "F B'" or "U2 D2" which could be rewritten as "S' z" or "E2 y2" so as to be counted as a single move. Unfortunately (in my view), the applet and the code Tom used to score the submissions did not automatically detect such optimizable situations in counting BTM moves. So for my own submissions, at least, I tried to make sure I converted any such sequences before submitting to be sure I got proper BTM credit for them. This can be likened to the situation in 3x3x3 FMC where someone writes "R y F" instead of "R2 y" and getting it counted as two moves when only one was needed. (I guess I messed up once on a solution that ended up counting for OBTM only anyway.)

I spent most of the contest period working on my "human" solutions, and didn't get started on the "computer" solutions until around the last week. I figured the solver code that is used for the WCA scrambles might be hard to beat (assuming 3x3x3 phase replaced with optimal solve). I assumed Shuang Chen was already making use of that (or some improvement on it) and I didn't know if I wanted to spend time trying to compile the tnoodle code myself.

Instead, I mainly opted to see what I could come up with using the following 4-phase approach.

1. Solve tricolor centers and make edge piece permutation parity even.
2. Finish solving centers and pair up at least N dedges using <U, D, L, R, F, B, Uw2, Lw2, Fw2>, with N typically 8.
3. Finish reducing to 3x3x3 (no reduction parities) without computer search.
4. Optimally solve the remaining pseudo-3x3x3 configuration (treating it as a 3x3x3) with Cube Explorer.

For Scramble #2 (BTM), I used Charlie's 8-step solver, replacing the last four steps with an optimal solution from Cube Explorer.

See spoiler for my actual "computer" solves.

Code:
BTM

Scramble #1
Tricolor centers: Uw L2 B 2U' Rw U2 Fw' Dw (8)
Centers + 8 dedges: F R U Lw2 U B R2 Uw2 F' R Fw2 (19)
Finish Reduction: Rw' F L2 F' Rw2 B U' L B' U Rw' y2 (30)
3x3x3 solve: D2 F2 L D' L F2 R2 F' L U' D2 F' U F' D2 L2 (46)

Scramble #2
Tsai Step 1: B' U 2F2 2D R' U 2B' (7)
Tsai Step 2: 2L2 R D2 F' 2U2 F Rw (14)
Tsai Step 3: F L2 U' B 2R2 B 2U2 2R2 2U2 (23)
Tsai Step 4: L2 U2 2F2 L2 D' 2L2 (29)
3x3x3 phase: U' L' D F2 D' L' E2 F2 M' D' R' U2 L2 B2 M' (44)
(Charlie used the same first four steps except I used a different last move to cancel out the first move of the optimal slice-turn metric 3x3x3 solve. Hmm... Charlie seems to have used a sub-optimal FTM 3x3x3 solve.)

Scramble #3
Tricolor centers: 2L' 2B 2L' B 2D' R 2B' 2R2 D 2R (10)
Centers + 8 dedges: D B' L2 Uw2 F2 L' D F Lw2 F' Uw2 (21)
Finish Reduction: Fw L' F' L Fw' U Fw D R' B D' R 2F' x2 (34)
3x3x3 solve: D S' R U2 F2 L2 U S L2 F' U D F E2 M (49)

Scramble #4
Tricolor centers: Uw2 B Lw D' Fw2 R B2 Dw' 2L' (9)
Centers + 9 dedges: F' L' B U' Fw2 U Lw2 D F R' Fw2 (20)
Finish Reduction: U' Rw' B L' B' Rw (26)
3x3x3 solve: F2 U L2 B R' L2 F E y R2 F' B' R2 F L' U' (41)
Note: tricolor center solve also formed 5 dedges.

Scramble #5
Tricolor centers: U' L2 2F' 2U' L2 F 2L' 2F (8)
Centers + 8 dedges: D B Uw2 L U' Lw2 U Lw2 F2 U' Uw2 Fw2 Lw2 (21)
Finish Reduction: Fw R' F R Fw2 B' U B U' Fw y2 (31)
3x3x3 solve: L E2 B' U' R B2 F R D2 M U' F' D' B D' (46)

OBTM
Scramble #1
Same solution as for BTM.
Tricolor centers: Uw L2 B 2U' Rw U2 Fw' Dw (9)
Centers + 8 dedges: F R U Lw2 U B R2 Uw2 F' R Fw2 (20)
Finish Reduction: Rw' F L2 F' Rw2 B U' L B' U Rw' y2 (31)
3x3x3 solve: D2 F2 L D' L F2 R2 F' L U' D2 F' U F' D2 L2 (47)
Note: 3x3x3 phase is both 16f* and 16s*.

Scramble #2
Tricolor centers: Fw' Uw2 R Bw' Rw Uw' B2 R Uw (9)
Centers + 8 dedges: L Uw2 L' B2 Lw2 U R Fw2 B' R2 Uw2 (20)
Finish Reduction: L B' Lw F R2 F' Lw' F2 Rw F D' L F' D L Rw' y2 (36)
3x3x3 solve: B' R B2 L' U D2 R' U' L' D' R' U' B2 D' B R' L' (53)
Note: For BTM, the L Rw' at end of reduction could be optimized. For OBTM, the L is really part of 3x3x3 solve.

Scramble #3
Tricolor centers: F' Uw' Lw' Uw' Lw D Fw2 U Rw Uw (10)
Centers + 8 dedges: U F U D Uw2 L2 B Uw2 R' F Lw2 D' Fw2 (23)
Finish Reduction: R' Uw' L' D L Uw U F Uw' B R' U B' R Uw (38)
3x3x3 solve: F' E y B R D2 L' B2 D B' R2 F2 U2 B L2 U2 R' D2 (56)

Scramble #4
Same solution as for BTM.
Tricolor centers: Uw2 B Lw D' Fw2 R B2 Dw' 2L' (10)
Centers + 9 dedges: F' L' B U' Fw2 U Lw2 D F R' Fw2 (21)
Finish Reduction: U' Rw' B L' B' Rw (27)
3x3x3 solve: F2 U L2 B R' L2 F E y R2 F' B' R2 F L' U' (43)
Note: 3x3x3 phase is optimal in both FTM and STM.

Scramble #5
Same solution as for BTM.
Tricolor centers: U' L2 2F' 2U' L2 F 2L' 2F (12)
Centers + 8 dedges: D B Uw2 L U' Lw2 U Lw2 F2 U' Uw2 Fw2 Lw2 (25)
Finish Reduction: Fw R' F R Fw2 B' U B U' Fw y2 (35)
3x3x3 solve: L E2 B' U' R B2 F R D2 M U' F' D' B D' (52)

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#### ch_ts

##### Member
Yeah, originally I wasn't going to submit any OBTM solutions, my single slice solutions were going to serve as both BTM and OBTM solutions, since I thought Shaung's solver would be difficult to beat. In the end, I added 1 line of code to also turn the outer layer whenever turning an inner layer so at least my solutions would be ~50 moves instead of ~60 moves in OBTM. And that's all I did for that.

I think it's unnecessary to search Dw, Lw, or Bw since they don't really reach any new positions that can't be reached with Uw, Rw, and Fw. (This is not the case in single slice turn metric: 2D, 2L, and 2B do reach new positions.) It seems like Shuang's solver/scrambler doesn't search these moves, I haven't checked the code, but the solutions don't seem to use these moves. My solver did use these moves since I didn't put in any extra effort to convert it from single slice to wide turns.

#### Stefan

##### Member
The "U2 D2" were in the 3x3x3 parts, though, where you said you used Cube Explorer, and it would've improved your BTM scores, not your OBTM scores. I just ran the 3x3 parts of your BTM solutions through Cube Explorer, it found solutions 2, 3, 0, 2 and 1 moves shorter.

My solutions for OBTM:
41 Dw Bw R' Dw2 B Rw Bw D2 Rw2 D' 2U2 R2 U2 Fw L' F2 U Lw2 Fw2 R F2 Dw2 F L B' D L' D U2 M' D B2 U2 L2 D' L2 D' R2 F2
41 U2 D 2F E' Bw' Rw' Bw' L D2 Rw2 Uw' F' Uw2 B R U2 B2 Uw2 F Bw2 L' Uw2 R' B2 L' F R' U' B2 R' S U2 B2 L' U' B E
42 L' Dw' Bw2 Lw Bw' Dw B2 2D' L U' F' Lw B U2 R' D' Bw2 D' Lw2 Dw2 F2 D 2R2 F D' B D' F' R' D' B' U' L' F U F L B' L' B2
40 Lw2 U' R' B Fw2 U2 L2 Lw' Dw' D2 L U2 F' R Fw' F2 R2 U' R' B2 Fw2 R 2D2 F R2 F R' F2 D F L2 U R' B D U2 L' B' L
41 Lw D B Uw Fw U Lw' Uw F Lw2 D L2 B' Fw' E 2R2 B U F' U Rw2 Uw2 F2 D' F2 B D M' S U' L U' R' U B U' B2

My solutions for BTM:
38 Dw Bw R' Dw2 B Rw Bw D2 Rw2 D' 2U2 R2 U2 Fw L' F2 U Lw2 Fw2 R F2 2D2 L E2 R2 D' L D' R D2 F' U2 M2 B D2 R L U2
37 same as for OBTM
38 L' Dw' Fw2 Lw Dw' Lw U2 2L' F R' D' Bw L U2 B' D' Rw2 U' Bw2 Dw2 L2 U 2B2 S R' F2 R2 L U R' B D2 B' L' D' R2 S' M'
37 Dw2 2R2 F Lw' Bw2 L' Bw L2 F' 2L D' L' U B' R2 D2 Fw2 U' F L2 Uw2 Lw2 F' L B U2 S' E2 R' F U R' D' F' D' L2 U'
37 same as for OBTM

And here's my main script:
It BTM-optimizes algorithms by replacing consecutive moves on the same axis with as few equivalent moves as possible. I didn't see an obvious smart way (does anyone?), so I brute-forced it. The hash function takes consecutive moves on the same axis and turns them into a number like 21030, the first digit telling the axis and the last four telling the angles that the four layers on that axis get turned. Then for each of the three axes, I went through all 4^8 possible such combinations of moves (without repetitions like Dw Dw2, of course), computed the hash, and kept the best move combination for each hash. That was then used later to optimize the algs. And I have a removeRotations function that removes the cube rotations present in Shuang Chen's solutions and those that my BTMizing inserts (they don't increase the move count, but I dislike them).

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#### qq280833822

##### Member
Although the context has finished, I'm going to continue optimizing the solution to see how short it can be.

Scramble 1:
R2 u' L2 f2 u' L' f' R D2 R2 D' u2 R2 u f F r2 F L2 r2 D' r2 (22 OBTM reduction)
+ D F2 R2 B' U2 F2 U L2 D' R' D2 B L2 U2 L U B' (39 OBTM)

Scramble 2:
U' F2 f' D' B2 u' L2 f' r' D2 u' f U F' f y U' F' r2 U' D B U' f2 (23 OBTM reduction)
+ D' F R' B' L2 D2 B U2 L2 U' B L' R2 U2 B' F2 D2 (40 OBTM)

Scramble 3:
f' r' f R' f R' U2 D L' f' u' F' y R2 U R2 D' F2 r2 D B u2 f2 r2 (23 OBTM reduction)
+ D' R' F L F2 R D' R2 B D2 U' B R B' F2 D L' (40 OBTM)

Scramble 5:
B f U' F' R' f u' B2 u2 L' D' f' r2 f2 D F R2 r2 B' D' f2 (21 OBTM reduction)
+ U2 R2 D R' B' U2 F' D U2 L2 D U F' L' R2 F2 R2 D' (39 OBTM)

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#### ch_ts

##### Member
The "U2 D2" were in the 3x3x3 parts, though, where you said you used Cube Explorer, and it would've improved your BTM scores, not your OBTM scores. I just ran the 3x3 parts of your BTM solutions through Cube Explorer, it found solutions 2, 3, 0, 2 and 1 moves shorter.
OK, I see what you mean. No, I didn't notice the slice moves option in Cube Explorer.

#### Stefan

##### Member
Sweet, how did you find that one? Did you improve your solver? Or just found a better search limit configuration? The best reduction I found using your old one was 24 moves (and I only found one), and this is 23.

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#### cuBerBruce

##### Member
The "U2 D2" were in the 3x3x3 parts, though, where you said you used Cube Explorer, and it would've improved your BTM scores, not your OBTM scores. I just ran the 3x3 parts of your BTM solutions through Cube Explorer, it found solutions 2, 3, 0, 2 and 1 moves shorter.
Stefan, you neglected checking for step boundary optimizations. My solution for scramble #2 was 4 moves shorter than Charlie's, not 3. See my solutions.

In addition to not selecting "Allow slice moves" (only in Cube Explorer 5.00 and later), he (at least on scramble #2) apparently didn't check the "optimal" check box either, using a 19f instead of the 17f* solution.

#### qq280833822

##### Member
Well, after my losing the context, I'm going to write a new solver optimized towards the length of solution without concerning the memory cost or solving time.
I try to merge step 1 and step 2, and now it's a two-phase reduction solver. Although the solver is much slower and cost more memory than the three-phase reduction solver, tt's practical to see how short the reduction can be.

#### rokicki

##### Member
Well, after my losing the context, I'm going to write a new solver optimized towards the length of solution without concerning the memory cost or solving time.
I try to merge step 1 and step 2, and now it's a two-phase reduction solver. Although the solver is much slower and cost more memory than the three-phase reduction solver, tt's practical to see how short the reduction can be.
Wow, you've got a two-phase 4x4x4 solver going? I tried doing this last
month, but my first phase didn't complete on random positions in any
reasonable length of time (I gave it a day for a random position). I also
thought it is practical to do the reduction phase optimally, but (so far)
have not succeeded. Can you describe your approach?

#### Stefan

##### Member
No, he means two-phase reduction (instead of his previous three-phase reduction).

Still cool, though. Congratulations on that sub40 solve!