As we know, if more energy is used to produce the gases than is produced then there is no point. However, I was thinking that if someone were to use a small solar panel instead of the car to produce the energy for the reaction, then there is some promise. I guess the first question is, can a small panel produce enough juice to make a difference. Or could this be attached to a separate battery that is recharged by connecting it to the grid. Of course still less energy produced than used, but the cost of said energy would be less than the same energy from just the gasoline.
There would have to be a few safety features built in to cut the electrical flow when the car was not in operation so that you do not have a buildup of gas, and possible a relief valve that would open at a set pressure.
Otherwise, using the engine to produce gases that will help the engine be more efficient does not compute....
Solar panels are expensive, breakable, provide very low power per square yard (less than 0.5 Amps) yes, that is 1/2 amp. If you use a very efficient HHO generator, you will need about 10 Amps or something like 20 square yards of solar panels to keep up.
On the reverse, an automobile alternator can produce an extra 10 amps for next to nothing - less than 1.5 horsepower. The HHO can provide about 75% of additional energy. So you should MAKE power from the "cracking" of water.