For those who use direct solving methods for 4x4x4,
For the diagonal 2-cycle case in 2 opposite dedges (in the last layer), this is one of many algorithms I found in the past for this case. It's the shortest algorithm in 3 out of the 4 common big cube move metrics (I have found 2 other solutions of the same length: all 3 are listed in the wiki). The only move metric it's longer in than other algorithms is STM, and only 1 more.
Uw Lw' Uw' l' Uw Lw Fw' Lw2 Uw' l' Uw Lw' L' Fw Uw' (16 SQTM, 15 STM, 18 qtm, 17 ftm)
I'm not a serious speedcuber, but I executed this algorithm a couple of days ago, and I realized that it might actually flow most of the way through (only the Lw' L' at the end needs to be dealt with). (Give it a chance, because it is so different to perform than algorithms you are used to.)
, and I was wondering if you could try to finger trick it and see if it is faster than all of the commonly practiced algorithms:
l' S2 U2 l U2 l' U2 r U2 r' F2 l B2 r z2 (21 SQTM, 14 STM, 30 qtm, 22 ftm)
r2 B2 U2 r U2 r2 B2 r' U2 r2 U2 B2 r' B2 (25 SQTM, 14 STM, 34 qtm, 20 ftm)
l2 B2 U2 l U2 l2 B2 l U2 l2 U2 B2 l B2 (25 SQTM, 14 STM, 34 qtm, 20 ftm):
l' U2 l U2 l U2 r' U2 l U2 l' U2 F2 l2 F2 r (25 SQTM, 16 STM, 34 qtm, 24 ftm)
Lw' U2 l U2 l U2 r' U2 l U2 l' U2 M' U2 l2 U2 Lw (26 SQTM, 17 STM, 34 qtm, 24 ftm)
And, although I mentioned this somewhere before, this case can be handled with a very intuitive algorithm.