No it's not. Someone did the math with probabilities and all. In the end, you would only save like 5 crystals unless you're extremely lucky to always level it up on the first try.

Even if it worked as intended (I'm not confirming it isn't), it would be a waste to not use the 3x option as you lose the chance of double level ups or 25% bonus for nothing.

Expected cost = cost / probability of success

(Intuitively, if your probability of success is 100% then expected cost = cost)

Your cost is always a multiple of "x" where your options for every level up is 1x, 2x, or 3x.

As seen in the Forge wiki page, your chances of success vary with the star requirement of the weapon, and the level of the weapon itself.

So the easiest thing to solve for is the break even points: at what probabilities do your 1x and 2x expected costs equal the 3x cost?

1x = 30%
2x = 67%

Since 2x level up is generally between the 70-80% success range, you "should" be getting the most out of your crystals leveling this way. But you're not getting that much more out of them (5% savings for 70% rate, 17% for 80% though). However, there are many claims that the percentage isn't correct and people are getting numerous failures doing so.

This doesn't take into account chance of double level up or prize boxes, which I have no way of knowing what those chances are. I generally get one double level up per 2 fully heated 5 star weapons, but that in no way implies any evidence.

This means there's really no reason to ever forge under 100% chance unless you enjoy losing fire crystals for no benefit.

What they should have done is actually increase the reward with lower percentages. And actually charge more fire crystals for lower percentage.

1x = 100% forge, easy stuff
2x = 60% forge, chance of UV, chance of double level up
3x = 30% forge, higher chance of UV, higher chance of double level up, prize box

This leads to a lot of interesting situations--people who just want to level up their weapons can do so easily. But once you have 1000 fire crystals built up and nothing to heat up, why not reward people for dumping 3x into a weapon to try and get a UV (same chance as forging)? Not to mention it's only 30% chance to level up, and ONLY on level up do you get a chance at UV, making it a HUGE fire crystal sink for end game players who have too much fire crystal and nothing to do with it.