The principle behind HHO is this:
Your engine normally takes gasoline, burns 98-100% of it, and turns it into mechanical energy to turn the tires.
HHO uses electrical energy (which is created at a loss with mechanical energy by the alternator, which drags on the engine and reduces power / fuel economy) to make hydrogen which is fed back into the engine and burned along with gasoline to give you the power back that you've taken from it through the alternator. Taking only the energy contained in the system into account, HHO will always be a loss because you're converting energy back and forth several times at a loss, resulting in a net loss. It's for this reason that HHO inevitably ends up in the unicorn corral.
It's possible you might save a few percent in fuel if you have a very poorly designed engine that just happened to come from the factory better designed to burn a hydrogen mix than pure gasoline (more likely you'd lose a few percent), but you'd need to break the laws of physics to get a 30-60% increase in fuel economy. There simply isn't much you can do to improve the combustion efficiency in something like, say, a Prius engine, and any real improvements in fuel economy will come from reducing weight, improving aerodynamics, or getting rid of other parasitic losses such as friction/rolling resistance. Claims that show improvement with HHO are either poorly collected data, or are exceptions to the rule.
Be very skeptical when reading about these products.
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