Solve the nonlinear system:
    3x - cos((y-1)z) - 1/2 = 0
    x^2 - 81(y-0.9)^2 + sin(z) + 1.06 = 0
    exp(-x(y-1)) + 20z + (10 pi - 3)/3 = 0
Analytic solution:
    x = 0.5
    y = 1
    z = -0.523599
Solution method: Anderson accelerated fixed point iteration.
    tolerance    = 1.49012e-06
    max iters    = 30
    m_aa         = 0
    delay_aa     = 0
    damping_aa   = 1
    damping_fp   = 1
    orth routine = 0

Final Statistics:
Number of nonlinear iterations:      5
Number of function evaluations:      5
Computed solution:
    x = 0.5
    y = 1
    z = -0.523598
Solution error:
    ex = 6.91114e-12
    ey = 4.48202e-07
    ez = 3.07455e-07
PASS
