All points in active until 31 (you reach this after using BP gained from Centipede) and then the rest in attack would net you the highest DPS by a decent margin.

This would take you into the last day of the game at 40 active BP and 65 dmg Micro UZ which is the highest yield of dps in the game, mathematically.

Not to mention it alleviates the burden of no QD on M10 if you get that weapon and continue the run (it's about the same). If you do get the M10, it yields higher DPS to dump ALL points into active BP and switch to the M8000 after receiving it. (Do not put RoF x2 or x3 on the M8000)

All tests done with Micro UZ (6 second base ATB charge)

With RoF calculated in already (Micro Uz) : Mixed route (65 dmg, 40 haste) = [58 / 3.2 = 18.13 dps] Full attack BP (75 attack, 30 haste) = [63 / 3.6 = 17.5 dps] Full active route (55 attack, 50 haste) = [53 / 3 = 17.66 dps]

As you can see, the full attack route is slowest by a bit and haste route is only marginally better. This is for each bullet. Calculate in x2 and 2x command and there's a large disparity between each turn.

The reason for this is that haste has diminishing returns. It gives less % time off of each hit with every additional active point. This makes it trivial to take past 40 as it only gives .25 per 10 additional points as opposed to the previous 10 points giving a whole .5 off.

Active time works like this : 10 = 1 second off 20 = .8 second 30 = .6 40 = .4 50 = .2

So by getting to 40 you save 2.8 seconds in total. Going to 50 you gain only 3.0 seconds in total. Those 10 points spent in attack give you 10 flat damage on hit (before x2/x3 or resistances like armadillos) and adds 5 to your crit multiplier WHICH SCALES.

Crits work off a very odd sequence of increase in attack. Damage works like this (single shot, no armor reduction, etc) :

10 dmg : 7 crit10 (3) 11 : 8 crit12 (4) 12 : 9 crit13 (4) 13 : 10 crit15 (5) 14 : 11 crit16 (5) 15 : 12 crit18 (6) 16 : 13 crit19 (6) 17 : 14 crit21 (7) 18 : 15 crit22 (7) 19 : 16 crit24 (8) 20 : 17 crit25 (8)

So, you can see that the more attack points only get MORE valuable as you spend them.

Thus, getting the most ATB charge % time off PER BP point takes you to 40, and getting an increase in damage (huge increase to crit for every 2 points) gets you extreme efficiency in place of the fall off.

Not to mention it conserves ammo as opposed to haste route, makes for a more efficient day5 and 6 since you don't use your BP until after each boss fight, and will do the overall most DPS.

TL;DR Spend BP on active time until you reach 31 points total. This is achieved, on average, after putting the 2 BP from Centipede into the active time. Afterwards, spend all remaining BP on attack. This is, mathematically, the most DPS you will have possible at your disposal.