Have the energy savings for glass recycling been correctly calculated?

I have been researching the energy cost invloved with recycling of various products. I am of the belief that Aluminum is the only material that we save energy by recycling.

Many sources state that adding “cullet” or crushed glass to the ingredients, when making glass, allows the other ingredients to melt at lower temperature. Therefore this saves energy.

But is the energy used to haul the used glass to the plant, sort it, wash it and then go through one or maybe two crushing cycles deducted from the energy saved by the lower melting temperature? Glass isn’t exactly light by volume. So I am thinking we use a lot of energy getting the used bottles and jars to the “cullet” stage. How much energy are we really saving here? Answers from those with knowledge in this area would be appreciated. Please state sources if available.