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Check the specification at the top. The range for x is [-1, 1]. For the range you provided the accuracy of the 0.5x alternative is reported as only 33%: https://herbie.uwplse.org/demo/570b973df0f1f4a78fe791858038a...

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You're right I misread the graph. That said though I have played around with Herbie before, trying it out on a few of the more gnarly expressions I had in my code (analytical partial derivatives if equations of motion if launch vehicle in rotating spherical frame) and didn't see much appreciable improvement over the expected range of values, but then again I didn't check every single one.

What would be cool is if you could some how have this kind of analysis done automatically for your whole program where it finds the needle in the haystack expression that can be improved, assuming you gave expected ranges for your variables

Author here. I've got a few papers about this problem (including one in submission), but it is very very hard to do, especially with acceptable overhead. The state of the art is maybe 100x overhead.

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