God's algorithm distribution
Depth              New            Total
    0                1                1
    1                8                9
    2               32               41
    3              128              169
    4              512              681
    5             2048             2729
    6             8176            10905
    7            32400            43305
    8           128608           171913
    9           509927           681840
   10          2021092          2702932
   11          8003554         10706486
   12         31678834         42385320
   13        125307530        167692850
   14        495157495        662850345
   15       1953478687       2616329032
   16       7682157029      10298486061
   17      29984818955      40283305016
   18     114831820323     155115125339
   19     417957132495     573072257834
   20    1325871801018    1898944058852
   21    2934550836931    4833494895783
   22    2736869164561    7570364060344
   23     427540149248    7997904209592
   24       1770867597    7999675077189
   25             7595    7999675084784
   26               16    7999675084800
   27                0    7999675084800

Date: 2024-09-14 to 2024-09-22
Time: ~7 days 3 hours

Generators of all depth 25 positions
Depth 26 positions are listed below

2018-03-05:

2^20 random scrambles solved optimally:

Depth	Frequency
10  	1
11  	0
12  	5
13  	13
14  	66
15  	273
16  	995
17  	3940
18  	14949
19  	54581
20  	173415
21  	385091
22  	358877
23  	56148
24  	222

3^7 pure corner twists:

Depth   Frequency
0       1
16      198
17      330
18      98
19      424
20      174
21      320
22      274
23      242
24      110
25      0
26      16

Depth 26 positions:

U R U' R2' U R U2' R2' U2' R' U' R U' R2 U R' U2' R' U2' R' U R2' U R2 U2 R'
U R U2 R U' R' U2 R2 U2 R' U2 R2' U R2 U' R' U R2' U R' U' R2 U R2 U' R2
U R2 U2' R2 U' R2 U' R' U' R2' U R2' U2' R U' R2 U2' R2' U R2' U' R2' U R U2' R2
U R2 U R U2 R' U2 R U2 R' U' R U2' R U' R2 U' R2 U2' R U2 R' U2 R2 U' R'
U R U2 R2' U' R' U R' U' R' U' R2 U2' R' U2 R2 U2 R2 U R2' U' R' U2 R2 U' R2'
U R U2' R2 U R2 U2' R2 U' R2 U' R' U' R2' U R2' U2' R U' R2 U2' R2' U R2' U' R2'
U R U' R2 U2 R U2' R U' R2' U' R2' U' R U2 R' U R' U' R2' U2' R2' U R U2' R'
U R U R U2' R2 U R2' U2' R2' U2' R' U2 R U R2' U2' R U2 R' U' R2' U2 R U R'
U R U2 R' U2 R U2 R' U' R U2' R U' R2 U' R2 U2' R U2 R' U2 R2 U' R' U R2
U R U2 R U2' R U R' U R2 U' R2' U R2' U2 R U' R2 U2 R' U R2 U' R2 U R'
U R U R2 U' R2 U2 R' U R2' U2 R2 U' R2 U R2 U' R' U2 R2' U' R2' U2 R2' U R2'
U R U2' R2' U R2' U' R2 U2' R U2' R U' R2 U' R U R2' U' R2' U R2' U' R' U2' R'
U R U2 R' U2 R2 U' R U2' R2 U2 R' U2 R U2 R' U' R2 U2' R' U2' R2 U2' R U2' R
U R U R2' U R2' U2 R2' U' R2' U2 R' U' R2 U R2 U' R2 U2 R2' U R' U2 R2 U' R2
U R U R2' U2 R U2' R2' U2' R2' U' R2 U R U2' R2' U R2 U' R' U2' R2 U R U' R
U R U R U' R U R2 U2' R' U' R2 U R2' U2' R U R2 U' R2' U2' R2' U2' R U2 R2'