Shorter is shorter, and quicker is quicker, but that doesn't necessarily mean it is cheaper. It can be. It might be. But it might not. You typically use up the majority of fuel during acceleration. This is why city milage is worse than highway milage. Waze will definitely tell you the faster way in terms of time spent, but it might not be the cheaper way in terms of money spent on fuel. I think I remember looking at an iPhone app that used the accelerometers to track a trip and tell you which one likely used more fuel. Or something like that, not sure actually. At any rate, time is money, too.

Could be more than one reason for that. First being there are commonly routing mistakes near me, even though the map is correct, so unfortunately the same may hold true for you in your area. They're still trying to work bugs out in their routing algorithms. Turn restrictions not correctly set in the map as a portion of one of the trips and consequently it would route you strangely compared to what you can actually drive, which could be corrected by editing the map. Average speeds drastically different in one of the directions, perhaps simply by low Waze usage on any street involved, which could be corrected by more trips/drivers simply using Waze over time. And, of course, you could have been routed around traffic during the longer trip out there, which at that time may well have been the faster route, and perhaps at a different time it would have routed you along the mirror of the trip home.

This is why you see a message every time you request a route about it possibly not being optimal yet. It's possible that all streets/turns involved in your trip have been correctly set and travelled enough times to have good average speeds, and it's possible they haven't yet. But as Waze gets used more and more, and by more and more people, the data it uses to make decisions will get better and better and its performance will get better and better. It seems to slip a lot of peoples' minds that Waze will not route you like a dumb GPS unit will. It won't simply route you by the shortest route, regardless of anything else. If everything is working properly, and it has enough data to work with, it will route you by the most optimal route at that given moment. If you use it to get to and from work, Monday to Friday, every single day of every week of the year, 52 weeks * 5 workdays = 260 days, 260 trips, it is entirely possible that you might not drive the same route twice. Why? Because it could route you around slow traffic to keep your trip shorter/quicker. And slow traffic can occur anywhere. And its goal is to optimize your trip according to current conditions. So why on earth is it telling you to turn left here when you know you should go straight? Probably because if you go straight you'll run into traffic that'll make your trip shorter.

Waze can see more than you. You should trust Waze, even when you think it is wrong about what will be faster. In the short term, it may not be faster. Probably mainly due to a lack of good data for average speeds on all segments. But as Waze users drive on more and more segments it has more data to work with, giving it more data to use, better average speeds, more accurate turn restriction data, making it better in the long term. And that short term where it isn't very accurate or useful probably won't be very long. Once I had a good portion of my area mapped it didn't take long for it to stop changing its mind every day or two about routes and start routing me along the same optimal route every time, barring traffic. There definitely was a period where it would take me all sorts of ways to any given destination, since it didn't have very good average speeds yet. But that didn't last long. I trusted it and followed it several times no matter where I was going. Once I knew I had driven a given route maybe three times I would ignore it and take my own maybe three times, and another maybe three times, and then it would start picking and choosing better on its own. When it's green, it's not really, really useful. But once it has a ton of good data for average speeds it starts getting really good.

Yeah, it's not routing very well lately. They need more staff, methinks.

Average speed per segment will take care of long red lights.

Takes some time to get those average speeds that it uses to determine routes. Waze will always suck until it gets enough of that data. After it has that, it is awesome.

I find Waze at least in my area of Canada, sends me on the slowest routes possible.

Whilst I had a pretty good idea what the shortest way for me to get to work was (due to the UK's infamous "one-way-systems" in town centres there's often not much choice, there are a few slightly different ways to drive them.

Having Waze is a little like having someone time all the possible different ways to drive, recording each route and letting you know. I've never been nerdy enough to do that myself, but I do like knowing that the way I'm now going is one minute shorter than all the others.