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Agreed. "Evidence" in this case is a weasel word that could be anything. Misconfigured LLVM? Old/unsupported GCC target? Doesn't matter, look at the evidence of great success! This 10kb assembly loop has a 44,000% speedup versus compiling with automatic vectorization disabled!

LLMs generating "assembly that runs a great deal more efficiently" is a ludicrous claim that cannot be substantiated outside PEBCAK situations.

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One simple thing that LLM's doesn't have to do is use a calling convention. Compilers need to use them, at least to some extent because it's not known at compile time who will link against this function in the future. Humans kinda need them because it's a lot of mental load when everything is custom. But for a sufficiently smart llm, noticing a register doesn't need to be preserved because there is only two callers and neither of them care about it might be doable.
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