And here you go, I made it 50x faster (100 ns)
using NonlinearSolve, StaticArrays, BenchmarkTools
function fun(x, p)
SA[x[1] + 0.5 * (x[1] - x[2])^3 - 1.0,
0.5 * (x[2] - x[1])^3 + x[2]]
end
function test_nr()
prob = NonlinearProblem{false}(fun,SA[ 0.0; 0.0])
sol = solve(prob, NewtonRaphson())
sol.u
end
@btime test_nr() # 106.760 ns (0 allocations: 0 bytes)