If you've never played it, it's worth finishing once for the "story" and takes less than 10 hours if you grok exponential growth quick enough.

Does it have a branch where you hack your own utility function and gain +infinity utility?

Kinda!

There's an optimal path that can get you to the end in 3 to 4 hours.

Really, it's about getting to space then being able to configure your drones to survive fights and explore.

How many playthroughs did it take for you to find this?

One is enough.

Though technically it was too, I accidentally restarted the first through the in-game restart modes.

Second one I just blatantly gave myself enough money to get to the monstrous amounts of clippers so it takes only minutes to proceed to the second part.

But it's worth to see the both endings.

I replayed it last week and managed under 6 hours (2nd time). Probably some poor ordering of perks; plus I shut off the auto-bet thing to find I needed a lot more of the resource it provided. Otherwise I found this playthrough pretty straightforward, and could probably do it in a few hours now.

There's an app version if that floats your boat...