using brent method
 iter [    lower,     upper]       min        err  err(est)
    0 [0.0000000, 6.0000000] 2.0000000 -1.1415927 6.0000000
    1 [2.0000000, 6.0000000] 3.5278640 +0.3862713 4.0000000
    2 [2.0000000, 3.5278640] 3.1748217 +0.0332290 1.5278640
    3 [2.0000000, 3.1748217] 3.1264576 -0.0151351 1.1748217
    4 [3.1264576, 3.1748217] 3.1414743 -0.0001183 0.0483641
    5 [3.1414743, 3.1748217] 3.1415930 +0.0000004 0.0333474
Converged:
    6 [3.1414743, 3.1415930] 3.1415927 +0.0000000 0.0001187