The book Kiki shared says "In formulating poultry diets, energy level is usually selected as the starting point. An appropriate energy level is one that most likely results in the lowest feed cost per unit of product (weight gain or eggs). The feed cost per unit of product, in turn, is determined by the cost per unit weight of diet and the amount of diet required to produce a unit of product. In areas of the world where high-energy grains and feed-grade fats are relatively inexpensive, high-energy diets are often most economical (i.e., the lowest feed cost per unit of product); however, if a leaner carcass is desired, it may be necessary to consider other levels of dietary energy. In areas where lower-energy grains and by-products are less expensive, low-energy diets are often most economical."
What if you don't start there? At a backyard level... like my five... it isn't about cost anyway. I'd been ruminating on how to use pumpkins because they are very abundant around here and easy to store for me. Carrots even more so. They don't fit well into  grain based formulations but might they if you started with protein from meat, energy from fat, and bulk from vegetables. roots, and greens? If you start with what jungle fowl living in a jungle might eat, you wouldn't start with grain. It doesn't solve the trace minerals issues, of course.
I think I better make a calculator spreadsheet, this is getting interesting.
		
		
	 
OK, two things.  'cause I've run across this myself.
One - its dang hard to get sources to offer general agreement on how much "energy" a bird needs, mostly, I can't get them to even agree on a unit of measure (something that was a problem even at the time of publication for Kiki's book link, getting most of a page of valued discussion.  Things haven't improved.
Two - whether feeding a high energy diet or low, getting to the target profile in protein, fat, aminos, trace in the appropriate ratios is our goal  Because raw cost is somewhat less concerning to us, the most "efficient" feed from an economics standpoint is often less important to backyard owners than the best feed profile from the available resources.  Whatever we mix, its going to cost "too much" - that's a given.  BUT! If you are taking advantage of the (relatively) ready availability in the US of things like dried soybean meal, fish meal, shrimp or crab meal, even "poultry by product meal", you are taking the nutrient dense approach.
Three - garden additions, if you can balance them, AND you have the right soils, hits most of those trace mineral issues pretty quick.   The high moisture content and seasonal nature contributes to production of a low energy diet however (for good or ill).
That's more than two...  Hmmm, puts down coffee cup.  I was going somewhere with this.
Oh yeah.  Ultimately, for most backyard owners, unless you are raising a "special case" like the CX eating itself to death (and quite happily, too!) by way of fatty liver disease and similar, chances are very good that you offer feed "ad libitum" or "free feeding", rather than my approach.  In such a case, if the feed itself is balanced, the bird will eat as much (or as little) as it needs over the course of the day to meet its net energy needs, so "high energy" or "low energy" diet becomes (largely) irrelevant due to your choice of flock feed management style.
Focus on deliberate low energy diets for avian health reasons (usually to slow early growth and allow more robust skeletal development in fast growth meat breeds) has its place - but most BYC owners largely avoid that concern by not purchasing CX and similar birds to keep long term as "pets", and by processing for table before diet-related health issues become profoundly impairing for more than some insignificant portion of the flock.
I think that's what I meant to say.  I NEED MORE COFFEE.  Very best to all, I've got a lot of work to get done today.  Won't be hanging out on forums much.
