Bisect method for solving
    x^6 - x - 1 = 0

bisect('fcn',1,2,1.0e-7)

    a            b            c            f(c)       b-c=c-a
1.0000e+000  2.0000e+000  1.5000e+000  8.8906e+000  5.0000e-001
1.0000e+000  1.5000e+000  1.2500e+000  1.5647e+000  2.5000e-001
1.0000e+000  1.2500e+000  1.1250e+000 -9.7713e-002  1.2500e-001
1.1250e+000  1.2500e+000  1.1875e+000  6.1665e-001  6.2500e-002
1.1250e+000  1.1875e+000  1.1563e+000  2.3327e-001  3.1250e-002
1.1250e+000  1.1563e+000  1.1406e+000  6.1578e-002  1.5625e-002
1.1250e+000  1.1406e+000  1.1328e+000 -1.9576e-002  7.8125e-003
1.1328e+000  1.1406e+000  1.1367e+000  2.0619e-002  3.9063e-003
1.1328e+000  1.1367e+000  1.1348e+000  4.2684e-004  1.9531e-003
1.1328e+000  1.1348e+000  1.1338e+000 -9.5980e-003  9.7656e-004
1.1338e+000  1.1348e+000  1.1343e+000 -4.5915e-003  4.8828e-004
1.1343e+000  1.1348e+000  1.1345e+000 -2.0838e-003  2.4414e-004
1.1345e+000  1.1348e+000  1.1346e+000 -8.2885e-004  1.2207e-004
1.1346e+000  1.1348e+000  1.1347e+000 -2.0110e-004  6.1035e-005
1.1347e+000  1.1348e+000  1.1347e+000  1.1285e-004  3.0518e-005
1.1347e+000  1.1347e+000  1.1347e+000 -4.4131e-005  1.5259e-005
1.1347e+000  1.1347e+000  1.1347e+000  3.4357e-005  7.6294e-006
1.1347e+000  1.1347e+000  1.1347e+000 -4.8874e-006  3.8147e-006
1.1347e+000  1.1347e+000  1.1347e+000  1.4735e-005  1.9073e-006
1.1347e+000  1.1347e+000  1.1347e+000  4.9237e-006  9.5367e-007
1.1347e+000  1.1347e+000  1.1347e+000  1.8165e-008  4.7684e-007
1.1347e+000  1.1347e+000  1.1347e+000 -2.4346e-006  2.3842e-007
1.1347e+000  1.1347e+000  1.1347e+000 -1.2082e-006  1.1921e-007

root = 1.13472408056259

Error_bound = 5.9605e-008