```/* nag_zero_nonlin_eqns_aa_rcomm (c05mdc) Example Program.
*
* Copyright 2017 Numerical Algorithms Group.
*
* Mark 26.1, 2017.
*/

#include <nag.h>
#include <stdio.h>
#include <nag_stdlib.h>
#include <math.h>
#include <nagc05.h>
#include <nagx02.h>

int main(void)
{
Integer  exit_status = 0, i, n = 4, irevcm = 0, m = 2, astart = 0, icount =
0, imax = 50, exit_loop = 0;
double   *fvec = 0, *x = 0, *rwsav = 0;
Integer  *iwsav = 0;
double   cndtol = 0.0, rtol, atol;
/* Nag Types */
NagError fail;

INIT_FAIL(fail);

printf("nag_zero_nonlin_eqns_aa_rcomm (c05mdc) Example Program Results\n");

if (!(fvec = NAG_ALLOC(n, double)) ||
!(x = NAG_ALLOC(n, double)) ||
!(iwsav = NAG_ALLOC(14+m, Integer)) ||
!(rwsav = NAG_ALLOC(2*m*n+m*m+m+2*n+1+MIN(m, 1)*MAX(n, 3*m), double)))
{
printf("Allocation failure\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_zero_nonlin_eqns_aa_rcomm (c05mdc).
* Solution of a system of nonlinear equations using Anderson acceleration
* (reverse communication)
*/

do
{
nag_zero_nonlin_eqns_aa_rcomm(&irevcm, n, x, fvec, atol, rtol, m,
cndtol, astart, iwsav, rwsav, &fail);

switch (irevcm)
{
case 1:
if (icount == imax)
{
printf("Exiting after the maximum number of iterations\n\n");
exit_loop = 1;
}
else
{
icount++;
}
/* x and fvec are available for printing */
break;
case 2:
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];
break;
}
} while (irevcm != 0 && exit_loop == 0);

if (fail.code != NE_NOERROR)
{
printf("Error from nag_zero_nonlin_eqns_aa_rcomm (c05mdc).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}

printf("Final approximate solution after %ld iterations\n\n", icount);
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);
NAG_FREE(iwsav);
NAG_FREE(rwsav);
return exit_status;
}
```