Question about caster items (artifacts and wands)

I have a rago's flame wand right now (20% chance of half recharge Fire skills). If I get an artifact that has the same mod, do they stack (so it becomes 20% + 20% = 40% chance to half recharge fire skills)

If one item (eg wand) says "halves casting time of (all) spells 10%" and the artifact says "halves casting time of blood spells 20%", then when u use the blood spells u get 30% total chance of halving casting time?

I am not new in this game This my third char (E/Me) and its the first caster I make (the other two where W and R)

A last thing. They should really include artifact and wand upgrades. They should probably be lower than the staves bonuses.

You multiply the percentages together.

20% - 80%
SSSSSSSSDD 2
SSSSSSSSDD 0
NNNNNNNNSS %
NNNNNNNNSS -
NNNNNNNNSS
NNNNNNNNSS 8
NNNNNNNNSS 0
NNNNNNNNSS %
NNNNNNNNSS
NNNNNNNNSS

In this case, we're using two 20% modifiers. Each letter stands for 1%; you have a 4% chance to get an extra fast recharge (D), a 32% chance to get a fast recharge (S), and 64% chance to get a regular recharge (N).

For a 20% recharge and 10% recharge, you'd have 2% extra fast, 26% fast, and 72% chance none.

The formula is (First xx%) * (Second xx%) for double fast recharge, (100%-First xx%) * (100%-Second xx%) for the regular recharge rate, and subtract those two from 100% to get the fast recharge rate.

I feel the need to thank you man. Your knowledge on this is awesome. One more question. When u say extra fast recharge I suppose u mean instant recharge? (50% decrease from the first and 50% from the second probability - both applied on the original recharge). Or it is 75% recharge (50% from the first - applied to the original recharge and then the 50% decrease on the halved recharge time)?