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Solvers

Solver	Language	Variations
nxopt	c++	nxopt11, nxopt21, nxopt31, nxopt22
vcube	c++	vcube104, vcube108, vcube112, vcube208, vcube308
reid's optimal solver	c	reid
Kociemba's optimal solver	python	kocpy
Cube Explorer	pascal	CE, CEhuge
Open Source Cube Explorer	pascal	kocce0, kocce1, kocce2
3ColorCube	javascript	3Color835M, 3ColorOpt
stickersolve	c++	sticker
h48	c	h48h0, h48h1, h48h2, h48h6
cubeopt	c++	cubeopt, cube48opt, cubenp

Space-node product

Pruning table size * number of nodes visited, less is better.

Average of 100 solves, in units of 1e15 Bytes (1PB).

Solver	Table size/MB	15f	16f	17f	inf
nxopt11	20.3366	0.085	1.030	13.757
nxopt21	325.386	0.147	1.367	16.563
nxopt31	2603.08	0.315	2.246	20.307	183.431
nxopt22	7809.26	0.664	2.936	28.020	216.542
vcube104	20.3366	0.087	1.028	13.720
vcube108	325.386	0.140	1.398	17.019
vcube112	2603.08	0.279	2.306	20.400	182.078
vcube208	7809.26	0.586	2.874	28.184	217.277
vcube308	22777.0	0.501	3.439	28.038	221.597
reid	35.2271 * 2	0.907	11.360	95.391
kocpy	833.172	0.916	11.057	110.312
kocce0	28.1816	0.166
kocce1	705.886	0.514	6.263
kocce2	1972.71	0.532	6.269	63.334
CE	28.1816	0.169	2.021	20.483
CEhuge	1972.71	0.509	6.269	63.334	436.803
3Color835M	1043.65	1.514	15.561	163.006
3ColorOpt	2959.11	1.497	14.085	138.270	763.862
sticker	12884.9	7.524	52.351	508.051
h48h0	29.3918 + 59.9050	1.218	14.502
h48h1	58.7837 + 59.9050	0.811	9.543
h48h2	117.567 + 59.9050	0.598	6.990	74.452
h48h3	235.135 + 59.9050	0.498	5.782
h48h4	470.270 + 59.9050	0.556	6.182
h48h5	940.540 + 59.9050	0.504	5.586	57.229	401.626
h48h6	1881.07 + 59.9050	0.483	5.307	53.678	376.395
cubeopt10	20.3366	0.076	0.920	12.304
cubeopt01	88.9728	0.155	1.911	21.347
cubeopt20	325.386	0.122	1.340	15.355
cubeopt11	1423.56	0.212	2.117	22.377	213.026
cubeopt30	2603.08	0.185	1.859	18.323	175.937
cube48opt1	30.4012	0.205	2.369	25.802
cube48opt2	121.605	0.203	2.083	23.104
cube48opt3	243.210	0.208	2.127	22.780
cube48opt4	486.420	0.230	1.948	21.867
cube48opt5	972.840	0.228	1.927	22.786
cube48opt6	1945.68	0.230	1.985	22.940	197.870
cube48opt7	3891.36	0.241	1.965	23.780	199.615
cube48opt8	7782.72	0.335	2.483	26.780	197.300
cubenp10	22.7620	0.052	0.634	8.532
cubenp01	99.5841	0.112	1.318	15.085
cubenp20	364.193	0.083	0.870	10.307
cubenp11	1593.34	0.158	1.585	16.383
cubenp30	2913.54	0.125	1.227	12.718	114.453

Number of nodes visited

Average of 100 solves, in units of 1 million, less is better.

"X-move" denotes random-move scramble of specific number of moves, "inf-move" denotes random-state scramble.

Solver	15-move	16-move	17-move	inf-move
nxopt11	4.180	50.627	676.488
nxopt21	0.451	4.200	50.902
nxopt31	0.121	0.863	7.801	70.467
nxopt22	0.085	0.376	3.588	27.729
vcube104	4.295	50.568	674.668
vcube108	0.431	4.297	52.306
vcube112	0.107	0.886	7.837	69.947
vcube208	0.075	0.368	3.609	27.823
vcube308	0.022	0.151	1.231	9.729
reid	12.877	161.25	1353.948
kocpy	1.100	13.271	132.400
kocce0	5.899
kocce1	0.729	8.873
kocce2	0.270	3.178	32.105
CE	6.004	71.721	726.827
CEhuge	0.258	3.178	32.105	221.423
3Color835M	1.451	14.910	156.188
3ColorOpt	0.506	4.760	46.727	258.139
sticker	0.584	4.063	39.430
h48h0	13.645	162.41
h48h1	6.836	80.400
h48h2	3.371	39.384	419.518
h48h3	1.689	19.598
h48h4	1.049	11.661
h48h5	0.504	5.584	57.204	401.447
h48h6	0.249	2.734	27.655	193.921
cubeopt10	3.733	45.261	605.024
cubeopt01	1.743	21.482	239.927
cubeopt20	0.375	4.119	47.191
cubeopt11	0.149	1.487	15.719	149.643
cubeopt30	0.071	0.714	7.039	67.588
cube48opt1	6.747	77.913	848.722
cube48opt2	1.666	17.132	189.996
cube48opt3	0.855	8.746	93.665
cube48opt4	0.472	4.005	44.955
cube48opt5	0.234	1.981	23.422
cube48opt6	0.118	1.020	11.790	101.697
cube48opt7	0.062	0.505	6.111	51.297
cube48opt8	0.043	0.319	3.441	25.351
cubenp10	2.302	27.869	374.873
cubenp01	1.125	13.239	151.479
cubenp20	0.229	2.388	28.302
cubenp11	0.099	0.995	10.282
cubenp30	0.043	0.421	4.365	39.283

Average time per node

Average of 100 solves, in units of 1 nanosecond, less is better.

Please note that the following results are highly dependent on the executing environment.

Intel Core i7-10750H (6-core 12-thread)

Single-thread results (ns/node)

Solver	15-move	16-move	17-move	inf-move
nxopt11	139.539
nxopt21	185.758	176.827	173.381
nxopt31	225.167	201.615	191.337	201.617
nxopt22	282.246	270.800	269.386	269.140
vcube104	93.216	89.018
vcube108	131.679	128.264	126.622
vcube112	183.137	150.037	143.185	145.752
vcube208	244.820	216.474	207.608	208.546
reid	61.377	62.623
kocpy	332.935
kocce0	110.500
kocce1	212.563	212.754
kocce2	164.995	172.858	162.854
h48h0	112.491
h48h1	116.153
h48h2	118.351
h48h6	143.903	136.752	137.878	136.723
cubeopt10	80.814
cubeopt20	98.198	91.771	88.475
cubeopt30	106.758	105.099	99.448	101.621
cube48opt1	46.721	44.572
cube48opt2	53.585	52.058
cube48opt6	58.653	59.028	55.392	55.650
cube48opt7	67.161	69.245	66.025	64.136
cube48opt8	76.337	73.434	73.832	73.117
cubenp10	139.656	138.462
cubenp20	158.640	148.907	145.633
cubenp30	161.857	167.441	158.515	159.037

12-thread results

Solver	ns/node	time/s	time*space/s/GB
nxopt31*	23.824	1.679	4.371
nxopt22*	31.850	0.883	6.896
CEhuge*	19.570	4.333	8.548
vcube112*	19.736	1.380	3.592
vcube208*	28.324	0.788	6.154
vcube308*	33.007	0.321	7.311
h48h6*	18.630	3.613	7.013
cubeopt30*	16.927	1.144	2.978
cube48opt6*	9.538	0.970	1.887
cube48opt7*	10.151	0.521	2.027
cube48opt8*	10.734	0.272	2.117
cubenp30*	25.410	0.998	2.908

Apple M1 Pro (10-core)

10-thread results

Solver	ns/node	time/s	time*space/s/GB
nxopt31*	25.367	1.788	4.654
nxopt22*	30.026	0.833	6.505
cubeopt30*	14.149	0.958	2.494
cube48opt6*	8.427	0.861	1.675
cubenp30*	20.401	0.802	2.337