Merely looking at the written solve, the one thing that stands out immediately is that the solutions are very long. I normally expect each line/step to be 5-10 moves, with the exception of last layer algs. Point by point breakdown, starting from the scramble. Blue text indicates your solve, red text indicates my suggestions.
1. This scramble has no pre-made pairs at all, so it's not clear which colours one should use to build the initial 222 block. I see that the blue-yellow-red corner can join with either the blue-yellow edge or the red-yellow edge in one move, and there's also two correctly permuted cross edges on the blue face. Try for example:
x L2 // corner-edge pair
(U' D') // two 2×2×1 blocks
R' // join the blocks to get a 2×2×2
2. L' U' // edge
Two moves for a single edge is very inefficient, considering there are already multiple free/1-move edges all over the cube. Make use of edge-centre pairs when they show up (and they show up very often), but don't go out of your way to make them. Also, since you're following this up with a z2 rotation, you can also rotate first, executing it as z2 R' D' instead.
3. It looks like you're trying to solve the 222 block by doing a half-cross and then inserting an F2L pair.
F U' F' R U' R2 U' R' // insert white-orange
F' U' F U2 F' U F // white-green-orange F2L slot
Don't do this. (I don't know how to solve this specific situation well either, but I wouldn't have chosen this block anyway. Herein lies a strength of Petrus and other blockbuilding methods: you don't have to know how to solve every situation well, because 99% of the time you can just choose a different, easier starting block.) Even if you wanted to do it half-cross-then-slot, it would've been better to rotate to solve the F2L slot rather than use so many F moves in succession.
4.
y' F2 // white-red edge
L2 U L' U' R U R' // white-red-green F2L slot
Again, a CFOP-y approach, but here I don't see anything else obvious so this is acceptable.
5.
y2 U F' U' F R2 U2 F' U' F // EO
I would've just done a y' rotation, so that edge orientation can be done with R U* R' / L' U* L / R' F* R / L F* L' triggers, which are better than F' U* F and B U* B' triggers. Anyway, this EO case can be done in 5 moves:
y2 F R2 F2 U F
The five-move solution is very awkward to execute from this angle (orange in front), but if you'd done a y' rotation instead of a y2, it'd be like this:
y' Rw U2 Rw2 F Rw
Way better. I think you mostly just need to familiarise yourself with how to fix bad edges, because it looks like you're using only F' U' F to flip the UL and FR edges, when there are many other ways to flip two edges.
6.
U' R2 U R2 U' R U' R' U R // white-red-blue F2L slot
U R U R' U2 R U R' // white-orange-blue F2L slot
Not sure what the initial U' is for. I guess you were trying to influence the next slot, which isn't a bad idea in general, although this is pretty tricky and in this specific case, it just replaced a 7-move last slot case with another 7-move last slot case. Other than the initial U', this is fine, although you can also look at other ways to solve a square on the right face, e.g.
R' U' R' U2 R' U' R2 // white-orange-blue square, then
R U2 R2 U' R2 U' R' // white-red-blue slot
7.
y' F U R U' R' U R U2 R' U' R U R' F' // COLL (you typoed the rotation)
U M2 U' M U2 M' U' M2 U // EPLL
Do not ever do y rotations during the last layer. Rotations are a lot slower than AUFing. Other than that, this is fine, although I'm a bit concerned about why you know COLL when you're still having trouble with general efficiency.
1. This scramble has no pre-made pairs at all, so it's not clear which colours one should use to build the initial 222 block. I see that the blue-yellow-red corner can join with either the blue-yellow edge or the red-yellow edge in one move, and there's also two correctly permuted cross edges on the blue face. Try for example:
x L2 // corner-edge pair
(U' D') // two 2×2×1 blocks
R' // join the blocks to get a 2×2×2
2. L' U' // edge
Two moves for a single edge is very inefficient, considering there are already multiple free/1-move edges all over the cube. Make use of edge-centre pairs when they show up (and they show up very often), but don't go out of your way to make them. Also, since you're following this up with a z2 rotation, you can also rotate first, executing it as z2 R' D' instead.
3. It looks like you're trying to solve the 222 block by doing a half-cross and then inserting an F2L pair.
F U' F' R U' R2 U' R' // insert white-orange
F' U' F U2 F' U F // white-green-orange F2L slot
Don't do this. (I don't know how to solve this specific situation well either, but I wouldn't have chosen this block anyway. Herein lies a strength of Petrus and other blockbuilding methods: you don't have to know how to solve every situation well, because 99% of the time you can just choose a different, easier starting block.) Even if you wanted to do it half-cross-then-slot, it would've been better to rotate to solve the F2L slot rather than use so many F moves in succession.
4.
y' F2 // white-red edge
L2 U L' U' R U R' // white-red-green F2L slot
Again, a CFOP-y approach, but here I don't see anything else obvious so this is acceptable.
5.
y2 U F' U' F R2 U2 F' U' F // EO
I would've just done a y' rotation, so that edge orientation can be done with R U* R' / L' U* L / R' F* R / L F* L' triggers, which are better than F' U* F and B U* B' triggers. Anyway, this EO case can be done in 5 moves:
y2 F R2 F2 U F
The five-move solution is very awkward to execute from this angle (orange in front), but if you'd done a y' rotation instead of a y2, it'd be like this:
y' Rw U2 Rw2 F Rw
Way better. I think you mostly just need to familiarise yourself with how to fix bad edges, because it looks like you're using only F' U' F to flip the UL and FR edges, when there are many other ways to flip two edges.
6.
U' R2 U R2 U' R U' R' U R // white-red-blue F2L slot
U R U R' U2 R U R' // white-orange-blue F2L slot
Not sure what the initial U' is for. I guess you were trying to influence the next slot, which isn't a bad idea in general, although this is pretty tricky and in this specific case, it just replaced a 7-move last slot case with another 7-move last slot case. Other than the initial U', this is fine, although you can also look at other ways to solve a square on the right face, e.g.
R' U' R' U2 R' U' R2 // white-orange-blue square, then
R U2 R2 U' R2 U' R' // white-red-blue slot
7.
y' F U R U' R' U R U2 R' U' R U R' F' // COLL (you typoed the rotation)
U M2 U' M U2 M' U' M2 U // EPLL
Do not ever do y rotations during the last layer. Rotations are a lot slower than AUFing. Other than that, this is fine, although I'm a bit concerned about why you know COLL when you're still having trouble with general efficiency.
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