Which takes less energy?

All electric home – gas oven is not an option.

I want to get water in a 4-quart saucepan to a boil.

Time is not a factor.

Options:

1) take tap water (at room temp), fill the saucepan, put it on the stove top, turn the burner on high. (takes longer on stove top)

2) run tap water until it is hot (from the water heater), fill the saucepan, then put on stove top,turn the burner on high. (Shorter on stove top, but longer wait for tap water to get hot; wastes the cool water)

My gut feeling is that option 1 is more fuel efficient.

I imagine to prove the case I would need to calculate the power draw of the water heater for some period of time and compare that to the power draw of the electric element of the stove.

Any ideas?