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(4% productivity and -5% speed) & (+20% speed)
= 4% productivity + 15% speed
So I guess you could say that the speed module cancels the speed penalty of the productivity module. Let's say that they work together rather than cancel each other.
They also work together in making more pollution and draining more power.
1 AM3 with 4xPM3 has a crafting speed of 0.5 while using 1.57MW
1 AM3 with 4xPM3 and a 2xSM3 beacon has a crafting speed of 1.125 while using 1.84MW (+0.48MW for the beacon).
Even if you only use the beacon for a single assembler (very unlikely) it is still faster and uses less power than two assemblers without the beacon.
I think the OP is nowhere near beacons yet. Either they'll use mixed modules in the same assembler/miner/lab, or they'll use only one type of module in that machine, or no module at all.
As for your calculations, that's all very nice, but the lower electricity consumption is when using no modules at all (well, efficiency modules exist, so that statement is false).
A no module AM3 will produce, for example, 2.5 gears/sec, draining 0.375 MW
4x prod mod = 1.4 gears/sec, 1.57 MW (I'll use your calculations assuming they are right)
With a single beacon added we get 3.15 gears/sec, 2.32 MW when counting the beacon itself.
So to say that the beacon saves energy is some intense mental gymnastics. If you're able to do such gymnastics, then you can make any numbers say anything you want them to say. But I'm not willing to go there.
Not between a full-module build and a no-module build.
I understood that.
But if someone wants to talk about a) electricity consumption, then I'll talk about that.
If someone wants to talk about b) using energy efficiently, then i'll talk about that.
If someone wants to talk about c) using modules efficiently, then i'll talk about that.
If someone wants to talk about d) getting more gears with less iron, I'll talk about that.
The OP was about knowing if different types of modules can work together or cancel each other.
My answer is yes, their effects stack, but be warned about a), modules ramp it up real fast.
Then someones tells me I'm wrong because of b), not because of a). If you arrange modules in such or such way, then you get more or less production per MW. Yes, of course. What does that have to do with the fact that energy consumption ramps up when you use modules? It does not invalidate it. If you add speed modules to an existing build, the total energy consumption is higher than without them, in all cases.
And please, when someone builds an example and the purpose of that example is to prove that "speed modules save power" so that I would have been wrong when I said that modules increase power consumption and even that effect does stack, I think we can agree that one is trying to answer the OP, one is trying to show that they're skilled at juggling numbers without caring if it's relevant or not.
The per-item energy cost, however, is usually much more relevant to that concern. Because one is typically more interested in things like the power requirements to turn a belt of materials into finished product than they are things like the power requirements to run a set number of machines.
If me saying
"If you add speed modules to an existing build, the total energy consumption is higher than without them, in all cases."
is misleading, it would only be because the person reading it already thinks that saving energy is the most important thing in the game. And also thinks that the devs did put speed modules in the game despite them being an item they should never use. And sees no value in getting free items from prod modules because they also believe that the crafting speed penalty can't be countered by using speed modules.
The reply to my first post is
"Thanks! Who cares about pollution! xD"
Visibly, pollution and energy are not a problem. That person would not ask something about prod and speed modules interactions if energy consumption were that important to them. And visibly, me pointing out that modules ramp up pollution and energy consumption won't stop them either. Good. From the start, my hopes were that they would go on and experiment with all combinations of modules.
So I respectfully discard your "misleading" argument. The OP wasn't mislead, nobody reading what I said in the context of this thread will ever be mislead.
Also, I agree with you. Per item energy cost is something that can be considered once modules start being used in large amounts and used to compare different builds performances. As are the amount of modules required, total footprint, etc. The OP is likely not there yet. And even if they were there, it would not be the biggest thing to consider when using modules. If someone's considering using a lot of non-efficiency modules and beacons in any configuration, they reached a point where power is not an issue. Generating free items, with prod modules at every step of the production chain (when possible, with mining being one possible exception) is king, no matter the energy cost. Because producing more power is easy compared to building a 3 times bigger base. And we both know that.
If being energy efficient mattered, efficiency modules would be king.
If you are only going to rocket launch you don't need any modules but If you are going to play past the point in the game that you get them they are king. They cut down pollution which saves resources that you would use for ammunition. They cut down power draw so you don't have to mine another coal patch and drop another set of boilers and steam engines. If you don't want to use steel on another set of steel furnaces you can set out electric furnaces with 2 efficiency modules Is instead. The steel furnaces use 90 KJ worth of carbon fuel/sec. The electric furnaces with efficiency modules use 72 KJ of electric power plus a 2.4 KJ drain/sec and they only require belts for ore for infrastructure instead of both coal and ore. The extra boilers, steam engines, and steel furnaces go to waste once you have nuclear power. The efficiency modules in the electric furnaces get recycled into new miners that you set out as you grow the factory. They get replaced by productivity module IIIs when beacons and speed modules get added to the furnace arrays.
If you expand into a mega base, efficiency modules in your miners can save you having to mine another coal patch, lay out the infrastructure to move the coal, and build another set of boilers and steam engines. You can instead mine a uranium patch, process uranium, and set up nuclear power.
I still use them in the miners in my megabases. The miners has module slots and it isn't cost effective to use productivity and speed modules in them but the power they save keeps me from having to set 2 more nuclear plants which saves UPS when you are running a factory that's drawing 20 GW of power.
crickets chirping
But really, I only responded to push back for being so derogatory towards the idea that someone would dare bring up the point that adding speed modules to prod modules makes things more efficient.