You're starting from 6am on a 4.7" class phone. I consider that pretty decent, and we haven't even considered the exact amount of time you do each of these tasks as well as what brightness. I'm on the train to work by 6:30am and my old iPhone 5 would die before noon. If you were starting at 8am, that'd be one thing, but I don't think you would get any better if not worse from another smartphone in a similar size class.
Generally for the best battery life you need a ~3000 mah found in the 5.5" size class, which make up the top smartphones on the battery life chart. It may suck for your specific use case, but its perfectly in-line with the chart. There's no way any of the recent sub 5" android phones would last longer, especially the S6.
I stand by what said, the poor battery life (I guess in comparison to other phones) stereotype is inaccurate.
Apple could put a 25% larger battery in the 4.7 at the cost of 1mm, if it weren't OCD-like obsessed with thin. Sure it's "good enough" if you don't really use it to the max right now. Apple could set themselves ahead of everyone else in battery life and still be thinner than it's rivals. But stubbornly, function must follow form at all costs.
It's going to eventually bite Apple in the end.