Herbie seems unable to improve on Rump's Example.

[inkydragon]

Wev version

input

(FPCore (x y)
  :name "Rump"
  :precision binary64
  :pre (and (== x 77617) (== y 33096))
  :spec -54767/66192
  (+ (+ (+ 
    (* 333.75 (pow y 6))
    (* (pow x 2) 
        (- (- (- (* (* 11 (pow x 2)) (pow y 2)) (pow y 6)) (* 121 (pow y 4))) 2))) 
      (* 5.5 (pow y 8))) (/ x (* 2 y))))

Percentage Accurate:
9.2% → 9.2%
Time:
1.5s
Alternatives:
1
Speedup:
1.0×

https://herbie.uwplse.org/demo/d2e0435359137cb982c33c73a281138505dfc7b9.f54ecc7459e2826747d647a0d98ec9e41c611ae9/graph.html

Docker version

Percentage Accurate:
9.2% → 9.2%
Time:
500.0ms
Alternatives:
1
Speedup:
1.4×

herbie/bench/numerics/rump.fpcore

Line 2 in 400891f

:name "Rump's expression from Stadtherr's award speech"

[pavpanchekha]

That's correct; there are a couple of versions of Rump's expression out there, but this one Herbie has basically no good ideas for. Speculating, I think that's because the important step (associating the y^8 and the x^2 y^6 terms together, and then factoring) are hard for Herbie to achieve; it's in general weak on polynomials.

Was there something in particular about this expression that makes it seem like Herbie should do better than it does?