I don't see how you got there. Numerical analysis is a whole branch of computer science which regularly deals with slight differences in computation. The usage of a constant (like pi) that is one bit different could cascade into massive differences in the results between the two programs.

Neither are completely wrong (as their results are similar) they just aren't exactly the same, especially when dealing with 7 day forecasts, this isn't to be entirely unexpected. We are trying to approximate massive systems we don't fully understand. A physics simulator is decent at getting a broad sense of things, but is not precise enough to get it exactly right, even though we use them to fly airplanes, same thing here.

"The usage of a constant (like pi) that is one bit different..."

That brings back memories of debugging a Fast Fourier Transform code that had a slightly miscoded version of pi. Someone typed it in from memory, to a dozen or so places (single precision), and got it slightly wrong.

Talk about weird and hard to track down. Like being transported to the parallel universe where the cars ride on hexagons.

We could do that here... More like a universe where you can tile a floor with pentagons.