R Under development (unstable) (2023-11-25 r85635 ucrt) -- "Unsuffered Consequences"
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> # R. Baker Kearfott, Some tests of Generalized Bisection,
> # ACM Transactions on Methematical Software, Vol. 13, No. 3, 1987, pp 197-220
> 
> # A high-degree polynomial system (section 4.3 Problem 12)
> # There are 12 real roots (and 126 complex roots to this system!)
> 
> library(nleqslv)
> 
> hdp <- function(x) {
+     f <- numeric(length(x))
+     f[1] <- 5 * x[1]^9 - 6 * x[1]^5 * x[2]^2 + x[1] * x[2]^4 + 2 * x[1] * x[3]
+     f[2] <- -2 * x[1]^6 * x[2] + 2 * x[1]^2 * x[2]^3 + 2 * x[2] * x[3]
+     f[3] <- x[1]^2 + x[2]^2 - 0.265625
+     f
+ }
> 
> 
> N <- 40
> set.seed(123)
> xstart <- matrix(runif(3*N,min=-1,max=1), N, 3)  # N starting values, each of length 3
> 
> ans <- searchZeros(xstart,hdp, method="Broyden",global="dbldog")
> nrow(ans$x) == 12
[1] TRUE
> all(ans$xfnorm <= 1e-10)
[1] TRUE
> 
> zans <- searchZeros(ans$xstart,hdp, method="Broyden",global="dbldog")
> length(zans$idxcvg) == 12
[1] TRUE
> 
> proc.time()
   user  system elapsed 
   0.18    0.03    0.20