Finally, you are understanding something! There is almost no relationship between philosophy and science. The tangential you see is science breaking away from philosophy, leaving almost no philosophical arguments to make about science! While there is a common starting point for both disciplines, the target of both disciplines is currently different in almost every case. While a scientist looks for valid, repeatable predictions based on models, philosophy rarely searches for models and repeatability. While mathematics looks for axioms and theorems, philosophy rarely touches mathematical axioms.
I am quite simply at a loss. The bolded section says precisely what I have been saying all along, and how you can make that statement and at the same time claim that "there is almost no relationship between philosophy and science" is beyond me. What you are talking about is the empirical nature of science, and empiricism is a philosophical stance. To state that "philosophy rarely searches for models and repeatability" is a completely absurd statement, and shows that though all along you've been talking down to the rest of us (me especially), you in fact don't have the slightest clue what you're talking about.
Empiricism is all about models and repeatability, and empiricism is an epistemological (and hence philosophical) theory, and probably the most significant epistemological theory at that. You seem unwilling or unable to recognise that empiricism is a theory of knowledge, and conclude that science isn't philosophical because it is empirical, when in fact that's precisely why it is philosophical!
If science is empirical, then it is also philosophical. You've essentially just stated that science is empirical, so we can therefore conclude that science is philosophical, Q.E.D.