That material efficiency formula doesn't work for me.

Taking a 50% material efficiency CT from my storage at ICS Alpha:
Base Titanium is 400. My shown relation bonus is 6%
I have 12 levels in the material efficiency extensions, so a 24% bonus.

Using your method:
400 / 0.5 - 400 = 400 waste.
400 / (1+(.001*6)) =397.61
log(0.1*24)=0.3802
397.61 *  0.3802 = 151.171 total saved
400 - 151.171 = 249 waste

So theoretically it should require 649 titanium, but ingame for me it requires 632. The difference is too large to be accounted for by rounding problems (with CT at 50.5% and relation at 6.5% the figure is still too big at 644).

This is the material equation I'm using in my spreadsheet at the moment.

Amount Required = Base Amount / CT Efficiency / (1+(Material Efficiency Extensions / 50)) / (1+( Sum of Corp Relations / 3))

For the above example 400 / 0.5 / (1 + (12 / 50)) / (1+(5.61/3)) = 633
I'd be interested to know how well it holds for other people.

Well ok, it looks like opaque arbitrary values to me. Taking a sample of stuff I have easy access to I've come up some times (a lot of them based on the assumption that base prototype time = 10x base manufacture time, which seems to work.)

Assault mech 28,000s (8h)

Light bot 21,600s (6h)

14400s (4h)
Armor Hardener, Repair Tuning, Chassis Scanner, Range Extender, Signal Detector, S-Demob, ECM, Interference module, Weapon Tunings

7200s (2h)
LWF, Small Shield Generator, Accum Recharger, Coreactor, Evasive Mod, Remote Sensor Amp, Cargo Scanner, Coprocessor, Target Marker, ECCM, Small Lasers/Missile Launchers/Magnetic Weapons, Medium Firearms

3600s (1h)
Light Armor Plate, Small Armor Repairer, small neuts, small miners/harvesters/firearms

1440s (24m)
Industial Charges, Medium Ammo

720s (12m)
Small Ammo

I'm then getting actual manufacture times from:
base time / CT time efficiency / (1 + (factory time extensions * 0.01) / (1 + (relation * 0.01)
But I'm usually under the actual time by ~1%, so that's not correct

Reverse engineering time seems to follow entirely different rules, since it takes exactly the same amount of time to RE a light bot and a light gun, but the mech takes three times as long to manufacture.

Predicting the build time is really important for predicting potential profit from manufacture. The only way currently to discover it is to be able to prototype it, to make the CT, or to get someone else to tell you.

It would be really nice if base manufacture time was added to the item info component tab. Possibly as part of the forthcoming noob friendly industry patch?