```/* nag_roots_sys_func_aa (c05mbc) Example Program.
*
* Copyright 2019 Numerical Algorithms Group.
*
* Mark 27.0, 2019.
*/

#include <nag.h>
#include <stdio.h>
#include <math.h>

#ifdef __cplusplus
extern "C"
{
#endif
static void NAG_CALL f(Integer n, const double x[], double fvec[],
Nag_Comm *comm, Integer *iflag);
#ifdef __cplusplus
}
#endif

int main(void)
{
static double ruser[1] = { -1.0 };
Integer exit_status = 0, i, n = 4, m = 2, astart = 0;
double *fvec = 0, *x = 0, atol, rtol, cndtol = 0.0;
/* Nag Types */
NagError fail;
Nag_Comm comm;

INIT_FAIL(fail);

printf("nag_roots_sys_func_aa (c05mbc) Example Program Results\n");

/* For communication with user-supplied functions: */
comm.user = ruser;

if (n > 0) {
if (!(fvec = NAG_ALLOC(n, double)) || !(x = NAG_ALLOC(n, double)))
{
printf("Allocation failure\n");
exit_status = -1;
goto END;
}
}
else {
printf("Invalid n.\n");
exit_status = 1;
goto END;
}

/* The following starting values provide a rough solution. */
x[0] = 2.0;
x[1] = 0.5;
x[2] = 2.0;
x[3] = 0.5;

/* nag_machine_precision (x02ajc).
* The machine precision
*/
atol = sqrt(nag_machine_precision);
rtol = sqrt(nag_machine_precision);

/* nag_roots_sys_func_aa (c05mbc).
* Solution of a system of nonlinear equations using
* Anderson acceleration
*/
nag_roots_sys_func_aa(f, n, x, fvec, atol, rtol, m, cndtol, astart,
&comm, &fail);

if (fail.code != NE_NOERROR) {
printf("Error from nag_roots_sys_func_aa (c05mbc).\n%s\n",
fail.message);
exit_status = 1;
if (fail.code != NE_TOO_MANY_FEVALS &&
fail.code != NE_NO_IMPROVEMENT)
goto END;
}

printf(fail.code == NE_NOERROR ? "Final approximate" : "Approximate");
printf(" solution\n\n");
for (i = 0; i < n; i++)
printf("%12.4f  ", x[i]);

printf("\n");

if (fail.code != NE_NOERROR)
exit_status = 2;

END:
NAG_FREE(fvec);
NAG_FREE(x);
return exit_status;
}

static void NAG_CALL f(Integer n, const double x[], double fvec[],
Nag_Comm *comm, Integer *iflag)
{

if (comm->user[0] == -1.0) {
printf("(User-supplied callback f, first invocation.)\n");
comm->user[0] = 0.0;
}

fvec[0] = cos(x[2]) - x[0];
fvec[1] = sqrt(1.0 - x[3]*x[3])- x[1];
fvec[2] = sin(x[0]) - x[2];
fvec[3] = x[1]*x[1] - x[3];

/* Set iflag negative to terminate execution for any reason. */
*iflag = 0;
}
```