At what point in history did Philosophy and Science start gettting considered as separate disciplines?

Part of what we think of as the "Scientific Revolution" is the gradual (not immediate) splitting of "philosophy" and "science" into separate domains of knowledge, method, and authority. This was originally gradual, with "mechanical philosophy" and "natural philosophy" being a subtle shading out of traditional philosophical questions. We traditionally think of Descartes as a philosopher, for example, but his work as a "mechanical philosopher" — basically a physicist — was what he was probably best known for in the century after his death. Since many of the "scientific" contributions of these earlier philosophers are today considered invalid, we tend to ignore that part of their work these days and see a stricter division between the "real scientists" and the "philosophers" than existed at the time.

A wonderful history that has this "split" (and its lack of firm demarcations) as its core is Shapin and Schaffer's Leviathan and the Air-Pump, which is about a late-17th century dispute over the nature of knowledge by Robert Boyle (the "scientist," who did a lot of philosophizing) and Thomas Hobbes (the "philosopher," who did a lot of writing on physics).

The Boyle v. Hobbes dispute, the authors argue in this seminal text in the history of science, was really about the political and epistemological status of "experiment" — can new "philosophy" be generated by an artificial apparatus (like the air-pump), much less one that only a small number of people had access to (there were no more than 7 in the world within the first decade of its invention)? Could such a device generate "matters of fact" that would stand up as authoritative as the deductive reasoning that one could get from classical philosophy? These are core questions about the nature of knowledge, and whether empirical induction was of the same character as derivations and deductions. In the end, Boyle was "victorious," and his approach became the basic philosophical assumption underlining British science. Variations on this sort of question played out differently in other contexts (e.g. the Galileo dispute was in part is whether mathematics and observations could be used to generate new philosophical knowledge or not).

To be sure, the split has never been absolute or entirely exclusive. Scientists tend to revisit philosophical questions when they hit apparent dead-ends or very difficult-to-intuit problems. Einstein's interventions in physics were in part a re-thinking of questions like "what is time? what is measurement?" which are philosophical at their core. Einstein's work did directly engage that work of people like Henri Bergson, and was directly influenced by the philosophical engagements of several other scientists, like that of the physicist Ernst Mach.