WarpMonkey doesn't get rid of the profiling stuff - the profiling is inherent in ICs - we keep hitcounts and other information for various paths taken through code (including ICs) and use that to guide compilation later.
Warp's uniqueness is in how it implements the ICs. The design goal when we built baseline JIT in SpiderMonkey was to split the code and data components of ICs. At the time, we were looking at V8 ICs which where basically compiled code blocks with the relevant parameter data (e.g. pointer to the hidden type to compare against) baked into the code.
We wanted to segregate the data from the code - e.g. so that all ShapedGetProp ICs can have a data stub with a pointer to their own shape, but share a pointer to the code. Effectively your ICs end up looking like small linked lists of C++ pure virtual objects (without the vtable indirection and just a single code pointer hanging off of the stub).
Originally the "shared code" was emitted by a bunch of statically defined methods that emitted a fixed bit of assembly (one for each kind of stub). That became unweildy as we added more stubs, so CacheIR was designed. CacheIR was a simple bytecode language that the stubs could express their logic in, which would get compiled down to machine code. The CacheIR bytecode would be a key to the compiled stubcode.
That let stubs generate arbitrary CacheIR for their logic, but still share code between stubs that emitted the same logic.
That led to the idea of Warp, where we noticed that one could build the input for an optimized method-jit compiler just by combining the profiling info that stubs produced, and the CacheIR bytecode for those stubs.
Normally you'd start from bytecode, build an SSA, then do a pass where you apply type information.
With Warp, the design simplifies into stitching together a bunch of CacheIR chunks which already embed the optimization information you care about, and then compiling that.
Ultimately it does the same thing as the other JITs, but it goes about it in a really nice and clean way. It kind of expresses some of the ideas that Maxime Boisvert-Chevalier was exploring in their work with basic block versioning.