This system was solved in May 2020, using solveSystem in Macaulay2 v1.15 with an Intel(R) Core(TM) i5-5250U CPU at 1.60GHz.
There were 9 solutions found in 0.141 seconds (with a Bezout bound of 36).
Reference: "Testing unconstrained optimization software" by J.J. More, B.S. Garbow and K.E. Hilstrom (pages 17-41).
See also: http://homepages.math.uic.edu/~jan/Demo/wood.html.
i1 : wood(RR_53)
3 2 3
o1 = {200x - 200x x + x - 1, - 100x + 110.1x + 9.9x - 20, 180x -
1 1 2 1 1 2 4 3
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2
180x x + x - 1, - 90x + 9.9x + 100.1x - 20}
3 4 3 3 2 4
o1 : List
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The object wood is a method function.