GPS satellites needs to correct their clocks based on General Relativity. It is a very very small correction, but quite important to the accuracy of the navigation system, so you see general relativity quite below galactic scale.
https://www.astronomy.ohio-state.edu/pogge.1/Ast162/Unit5/gp...
General relativity and Newtonian gravity give very similar answers in some cases (e.g. calculating space craft orbits), but different in others (e.g. the orbit of mercury or light passing near a black hole).
Consider the TSP problem from TFA, in this case two approximation algorithms were presented, one marginally better, meaning the answer would be different.
I believe channel capacity encoding was like this as well, but that is not in my wheelhouse.
Newton isn't causal and this is a root cause of a lot of the issues: it's used for convenience by people who usually don't understand the loss, and now that computers are many orders of magnitude better you lose little.
It's the cargo culting and fear of actually deciding what intractable means that's interesting to compare: numerical GR is only galactic for 1920s computers, not 1970s. Fuerer's multiplication algorithm is, in contrast, still crazy to consider and likely will be for decades to centuries, like other truly galactic algorithms
Doing software and basic embedded there are so many tools and techniques we just don't see in a world where the are are three main classes of algorithm, "very simple", "available on PyPi", and "Only one guy here knows how it works".
It also needs a kick in the pants with software. Very much behind the curve and tedious.
At the entry level jobs(As in, helping a company that has never made a PCB get a small run of IoT gadgets made) you might be working with stuff that's close to what hobbyists use.
The software and dev tools are amazing and a joy to use(PlatformIO, ESPHome, Arduino, ESP-IDF, Python), and the there's basically no math, just Ohm's law and simple stuff like that, not any algebra or calculus.
Unfortunately those jobs are harder to find and the 45k+ a year stuff everyone wants are jam packed with math, and from what I hear obnoxious vendor specific compilers for crappy ARM chips that don't have connectivity, even though it would only cost $2 more and make the product so much better...
What's really weird is that open source hardware uses the obscure chips too. Like... your whole selling point is that people can modify it... use something people already know how to use, with enough features that we can actually do something cool with it.
What do you mean by the "loss"?
It makes me wonder if you could you could classify General Relativity as a Galactic Algorithm for solving Newtonian Equations i.e. it's technically more accurate but the complexity outweighs the gains so rocket engineers default to newton instead of einstein.