Chuck in baking powder and get more gas. In a nutshell use more energy in fuel creating o-hh than you get from using it in cylinders for improved combustion . Real gains only if energy for electrolysis from regeneration out of braking (or coasting) or using solar cell, wind etc. Do not dispute improved efficiency of having hydrogen to burn with the hydrocarbons but "The energy density per unit volume of both liquid hydrogen and compressed hydrogen gas at any practicable pressure is significantly less than that of traditional fuel sources" (
www.en.wikipedia.org/wiki/Hydrogen#Combustion ) points to these not being that significant.
Interesting work in Japan on using metal hydrides as retro-fit for any combustion engine. Spent batteries but perhaps CaH if can be produced at reasonable energy cost (was used to inflate weather balloons so is produced and available).
Water and baking powder are not cheaper than mineral hydrocarbons for the energy that is obtainable BUT ethanol , methanol, butanol , propanol can be made out home and these can also figure in a basic fuel cell or be combusted. The problem is the volumes required when alternatives to oil based fuels progress beyond diy tinkering. The inventor of the diesel engine had nothing until somebody tinkered with it to run on a waste product (just happened to be from oil refining) that's over a century ago and the truth persists in that given existing understanding vehicles propelled by fuel they carry need oil.
With that limited understanding (gravity and magnetism yet to be replicated by mankind ) and the "technology investment " in modern combustion engines diesel-electrics make sense. Making a hho cell is fun our engineering firm made one and he reckons diesels run smoother but the most fun is in launching pop bottles with it!
see
www.magpie.coop for some wild electric vehicles