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Опыт №1: Определяем количество итераций вычисления значения корня квадратного по методу Ньютона.
Это количество прохода цикла while( firstEstimation - nextEstimation != 0 ) { <..> } 
error = std::fabs( sqrtLib - sqrtMy);
error = std::fabs( sqrtLib - sqrtMy);
error, % вычисляется как: 100 * error/ sqrtLib; 
 
<cmath> sqrt(100): 10	 my sqrt(0,10): 10	 perform in 1 iterations	 error: 0	 error, %: 0
<cmath> sqrt(98.02): 9.9005	 my sqrt(0.1,9.9): 9.90051	 perform in 26 iterations	 error: 6.67572e-006	 error, %: 6.74281e-005
<cmath> sqrt(96.08): 9.80204	 my sqrt(0.2,9.8): 9.80205	 perform in 26 iterations	 error: 1.14441e-005	 error, %: 0.000116752
<cmath> sqrt(94.18): 9.70464	 my sqrt(0.3,9.7): 9.70465	 perform in 26 iterations	 error: 1.71661e-005	 error, %: 0.000176886
<cmath> sqrt(92.32): 9.60833	 my sqrt(0.4,9.6): 9.60833	 perform in 34 iterations	 error: 1.90735e-006	 error, %: 1.9851e-005
<cmath> sqrt(90.5): 9.51315	 my sqrt(0.5,9.5): 9.51318	 perform in 26 iterations	 error: 2.86102e-005	 error, %: 0.000300744
<cmath> sqrt(88.72): 9.41913	 my sqrt(0.6,9.4): 9.41916	 perform in 26 iterations	 error: 3.33786e-005	 error, %: 0.00035437
<cmath> sqrt(86.98): 9.32631	 my sqrt(0.7,9.3): 9.32635	 perform in 26 iterations	 error: 3.8147e-005	 error, %: 0.000409025
<cmath> sqrt(85.28): 9.23472	 my sqrt(0.8,9.2): 9.23476	 perform in 26 iterations	 error: 4.29153e-005	 error, %: 0.000464717
<cmath> sqrt(83.62): 9.1444	 my sqrt(0.9,9.1): 9.14445	 perform in 26 iterations	 error: 4.76837e-005	 error, %: 0.000521453
<cmath> sqrt(82): 9.05539	 my sqrt(1,9): 9.05544	 perform in 26 iterations	 error: 5.14984e-005	 error, %: 0.000568705
<cmath> sqrt(80.42): 8.96772	 my sqrt(1.1,8.9): 8.96778	 perform in 26 iterations	 error: 5.62668e-005	 error, %: 0.000627437
<cmath> sqrt(78.88): 8.88144	 my sqrt(1.2,8.8): 8.8815	 perform in 26 iterations	 error: 6.00815e-005	 error, %: 0.000676483
<cmath> sqrt(77.38): 8.79659	 my sqrt(1.3,8.7): 8.79665	 perform in 26 iterations	 error: 6.38962e-005	 error, %: 0.000726374
<cmath> sqrt(75.92): 8.71321	 my sqrt(1.4,8.6): 8.71328	 perform in 26 iterations	 error: 6.67572e-005	 error, %: 0.000766161
<cmath> sqrt(74.5): 8.63134	 my sqrt(1.5,8.5): 8.63134	 perform in 40 iterations	 error: 0	 error, %: 0
<cmath> sqrt(73.12): 8.55102	 my sqrt(1.6,8.4): 8.55102	 perform in 39 iterations	 error: 1.90735e-006	 error, %: 2.23055e-005
<cmath> sqrt(71.78): 8.47231	 my sqrt(1.7,8.3): 8.47231	 perform in 39 iterations	 error: 9.53674e-007	 error, %: 1.12564e-005
<cmath> sqrt(70.48): 8.39524	 my sqrt(1.8,8.2): 8.39524	 perform in 39 iterations	 error: 9.53674e-007	 error, %: 1.13597e-005
<cmath> sqrt(69.22): 8.31986	 my sqrt(1.9,8.1): 8.31985	 perform in 39 iterations	 error: 1.90735e-006	 error, %: 2.29253e-005
<cmath> sqrt(68): 8.24621	 my sqrt(2,8): 8.24621	 perform in 39 iterations	 error: 9.53674e-007	 error, %: 1.1565e-005
<cmath> sqrt(66.82): 8.17435	 my sqrt(2.1,7.9): 8.17435	 perform in 39 iterations	 error: 9.53674e-007	 error, %: 1.16667e-005
<cmath> sqrt(65.68): 8.10432	 my sqrt(2.2,7.8): 8.10432	 perform in 41 iterations	 error: 9.53674e-007	 error, %: 1.17675e-005
<cmath> sqrt(64.58): 8.03617	 my sqrt(2.3,7.7): 8.03617	 perform in 39 iterations	 error: 9.53674e-007	 error, %: 1.18673e-005
<cmath> sqrt(63.52): 7.96994	 my sqrt(2.4,7.6): 7.96994	 perform in 39 iterations	 error: 1.43051e-006	 error, %: 1.79488e-005
<cmath> sqrt(62.5): 7.90569	 my sqrt(2.5,7.5): 7.90569	 perform in 39 iterations	 error: 9.53674e-007	 error, %: 1.20631e-005
<cmath> sqrt(61.52): 7.84347	 my sqrt(2.6,7.4): 7.84347	 perform in 39 iterations	 error: 9.53674e-007	 error, %: 1.21588e-005
<cmath> sqrt(60.58): 7.78332	 my sqrt(2.7,7.3): 7.78331	 perform in 39 iterations	 error: 9.53674e-007	 error, %: 1.22528e-005
<cmath> sqrt(59.68): 7.72528	 my sqrt(2.8,7.2): 7.72528	 perform in 39 iterations	 error: 1.43051e-006	 error, %: 1.85173e-005
<cmath> sqrt(58.82): 7.66942	 my sqrt(2.9,7.1): 7.66942	 perform in 39 iterations	 error: 1.43051e-006	 error, %: 1.86521e-005
<cmath> sqrt(58): 7.61577	 my sqrt(3,7): 7.61577	 perform in 39 iterations	 error: 9.53674e-007	 error, %: 1.25224e-005
<cmath> sqrt(57.22): 7.56439	 my sqrt(3.1,6.9): 7.56439	 perform in 39 iterations	 error: 9.53674e-007	 error, %: 1.26074e-005
<cmath> sqrt(56.48): 7.51532	 my sqrt(3.2,6.8): 7.51532	 perform in 39 iterations	 error: 9.53674e-007	 error, %: 1.26897e-005
<cmath> sqrt(55.78): 7.4686	 my sqrt(3.3,6.7): 7.4686	 perform in 39 iterations	 error: 1.43051e-006	 error, %: 1.91537e-005
<cmath> sqrt(55.12): 7.42428	 my sqrt(3.4,6.6): 7.42428	 perform in 42 iterations	 error: 4.76837e-007	 error, %: 6.42267e-006
<cmath> sqrt(54.5): 7.38241	 my sqrt(3.5,6.5): 7.38241	 perform in 42 iterations	 error: 4.76837e-007	 error, %: 6.4591e-006
<cmath> sqrt(53.92): 7.34302	 my sqrt(3.6,6.4): 7.34302	 perform in 39 iterations	 error: 9.53674e-007	 error, %: 1.29875e-005
<cmath> sqrt(53.38): 7.30616	 my sqrt(3.7,6.3): 7.30616	 perform in 39 iterations	 error: 9.53674e-007	 error, %: 1.3053e-005
<cmath> sqrt(52.88): 7.27186	 my sqrt(3.8,6.2): 7.27186	 perform in 42 iterations	 error: 4.76837e-007	 error, %: 6.55729e-006
<cmath> sqrt(52.42): 7.24017	 my sqrt(3.9,6.1): 7.24016	 perform in 39 iterations	 error: 9.53674e-007	 error, %: 1.3172e-005
<cmath> sqrt(52): 7.2111	 my sqrt(4,6): 7.2111	 perform in 39 iterations	 error: 9.53674e-007	 error, %: 1.32251e-005
<cmath> sqrt(51.62): 7.18471	 my sqrt(4.1,5.9): 7.18471	 perform in 41 iterations	 error: 9.53674e-007	 error, %: 1.32737e-005
<cmath> sqrt(51.28): 7.16101	 my sqrt(4.2,5.8): 7.16101	 perform in 41 iterations	 error: 4.76837e-007	 error, %: 6.6588e-006
<cmath> sqrt(50.98): 7.14003	 my sqrt(4.3,5.7): 7.14003	 perform in 39 iterations	 error: 9.53674e-007	 error, %: 1.33567e-005
<cmath> sqrt(50.72): 7.1218	 my sqrt(4.4,5.6): 7.1218	 perform in 39 iterations	 error: 9.53674e-007	 error, %: 1.33909e-005
<cmath> sqrt(50.5): 7.10634	 my sqrt(4.5,5.5): 7.10633	 perform in 39 iterations	 error: 4.76837e-007	 error, %: 6.71003e-006
<cmath> sqrt(50.32): 7.09366	 my sqrt(4.6,5.4): 7.09366	 perform in 39 iterations	 error: 4.76837e-007	 error, %: 6.72202e-006
<cmath> sqrt(50.18): 7.08378	 my sqrt(4.7,5.3): 7.08378	 perform in 39 iterations	 error: 9.53674e-007	 error, %: 1.34628e-005
<cmath> sqrt(50.08): 7.07672	 my sqrt(4.8,5.2): 7.07672	 perform in 39 iterations	 error: 0	 error, %: 0
<cmath> sqrt(50.02): 7.07248	 my sqrt(4.9,5.1): 7.07248	 perform in 39 iterations	 error: 9.53674e-007	 error, %: 1.34843e-005
<cmath> sqrt(50): 7.07107	 my sqrt(5,5): 7.07112	 perform in 26 iterations	 error: 4.95911e-005	 error, %: 0.000701324
<cmath> sqrt(50.02): 7.07248	 my sqrt(5.1,4.9): 7.07248	 perform in 39 iterations	 error: 9.53674e-007	 error, %: 1.34843e-005
<cmath> sqrt(50.08): 7.07672	 my sqrt(5.2,4.8): 7.07672	 perform in 39 iterations	 error: 0	 error, %: 0
<cmath> sqrt(50.18): 7.08378	 my sqrt(5.3,4.7): 7.08378	 perform in 39 iterations	 error: 9.53674e-007	 error, %: 1.34628e-005
<cmath> sqrt(50.32): 7.09366	 my sqrt(5.4,4.6): 7.09366	 perform in 39 iterations	 error: 4.76837e-007	 error, %: 6.72202e-006
<cmath> sqrt(50.5): 7.10634	 my sqrt(5.5,4.5): 7.10633	 perform in 39 iterations	 error: 4.76837e-007	 error, %: 6.71003e-006
<cmath> sqrt(50.72): 7.1218	 my sqrt(5.6,4.4): 7.1218	 perform in 39 iterations	 error: 9.53674e-007	 error, %: 1.33909e-005
<cmath> sqrt(50.98): 7.14003	 my sqrt(5.7,4.3): 7.14003	 perform in 39 iterations	 error: 9.53674e-007	 error, %: 1.33567e-005
<cmath> sqrt(51.28): 7.16101	 my sqrt(5.8,4.2): 7.16101	 perform in 41 iterations	 error: 4.76837e-007	 error, %: 6.6588e-006
<cmath> sqrt(51.62): 7.18471	 my sqrt(5.9,4.1): 7.18471	 perform in 41 iterations	 error: 9.53674e-007	 error, %: 1.32737e-005
<cmath> sqrt(52): 7.2111	 my sqrt(6,4): 7.2111	 perform in 39 iterations	 error: 9.53674e-007	 error, %: 1.32251e-005
<cmath> sqrt(52.42): 7.24017	 my sqrt(6.1,3.9): 7.24016	 perform in 39 iterations	 error: 9.53674e-007	 error, %: 1.3172e-005
<cmath> sqrt(52.88): 7.27186	 my sqrt(6.2,3.8): 7.27186	 perform in 42 iterations	 error: 4.76837e-007	 error, %: 6.55729e-006
<cmath> sqrt(53.38): 7.30616	 my sqrt(6.3,3.7): 7.30616	 perform in 39 iterations	 error: 9.53674e-007	 error, %: 1.3053e-005
<cmath> sqrt(53.92): 7.34302	 my sqrt(6.4,3.6): 7.34302	 perform in 39 iterations	 error: 9.53674e-007	 error, %: 1.29875e-005
<cmath> sqrt(54.5): 7.38241	 my sqrt(6.5,3.5): 7.38241	 perform in 42 iterations	 error: 4.76837e-007	 error, %: 6.4591e-006
<cmath> sqrt(55.12): 7.42428	 my sqrt(6.6,3.4): 7.42428	 perform in 42 iterations	 error: 4.76837e-007	 error, %: 6.42267e-006
<cmath> sqrt(55.78): 7.4686	 my sqrt(6.7,3.3): 7.4686	 perform in 39 iterations	 error: 1.43051e-006	 error, %: 1.91537e-005
<cmath> sqrt(56.48): 7.51532	 my sqrt(6.8,3.2): 7.51532	 perform in 39 iterations	 error: 9.53674e-007	 error, %: 1.26897e-005
<cmath> sqrt(57.22): 7.56439	 my sqrt(6.9,3.1): 7.56439	 perform in 39 iterations	 error: 9.53674e-007	 error, %: 1.26074e-005
<cmath> sqrt(58): 7.61577	 my sqrt(7,3): 7.61577	 perform in 39 iterations	 error: 9.53674e-007	 error, %: 1.25224e-005
<cmath> sqrt(58.82): 7.66942	 my sqrt(7.1,2.9): 7.66942	 perform in 39 iterations	 error: 1.43051e-006	 error, %: 1.86521e-005
<cmath> sqrt(59.68): 7.72528	 my sqrt(7.2,2.8): 7.72528	 perform in 39 iterations	 error: 1.43051e-006	 error, %: 1.85173e-005
<cmath> sqrt(60.58): 7.78332	 my sqrt(7.3,2.7): 7.78331	 perform in 39 iterations	 error: 9.53674e-007	 error, %: 1.22528e-005
<cmath> sqrt(61.52): 7.84347	 my sqrt(7.4,2.6): 7.84347	 perform in 39 iterations	 error: 9.53674e-007	 error, %: 1.21588e-005
<cmath> sqrt(62.5): 7.90569	 my sqrt(7.5,2.5): 7.90569	 perform in 39 iterations	 error: 9.53674e-007	 error, %: 1.20631e-005
<cmath> sqrt(63.52): 7.96994	 my sqrt(7.6,2.4): 7.96994	 perform in 39 iterations	 error: 1.43051e-006	 error, %: 1.79488e-005
<cmath> sqrt(64.58): 8.03617	 my sqrt(7.7,2.3): 8.03617	 perform in 39 iterations	 error: 9.53674e-007	 error, %: 1.18673e-005
<cmath> sqrt(65.68): 8.10432	 my sqrt(7.8,2.2): 8.10432	 perform in 41 iterations	 error: 9.53674e-007	 error, %: 1.17675e-005
<cmath> sqrt(66.82): 8.17435	 my sqrt(7.9,2.1): 8.17435	 perform in 39 iterations	 error: 9.53674e-007	 error, %: 1.16667e-005
<cmath> sqrt(68): 8.24621	 my sqrt(8,2): 8.24621	 perform in 39 iterations	 error: 9.53674e-007	 error, %: 1.1565e-005
<cmath> sqrt(69.22): 8.31986	 my sqrt(8.1,1.9): 8.31985	 perform in 39 iterations	 error: 1.90735e-006	 error, %: 2.29253e-005
<cmath> sqrt(70.48): 8.39524	 my sqrt(8.2,1.8): 8.39524	 perform in 39 iterations	 error: 9.53674e-007	 error, %: 1.13597e-005
<cmath> sqrt(71.78): 8.47231	 my sqrt(8.3,1.7): 8.47231	 perform in 39 iterations	 error: 9.53674e-007	 error, %: 1.12564e-005
<cmath> sqrt(73.12): 8.55102	 my sqrt(8.4,1.6): 8.55102	 perform in 39 iterations	 error: 1.90735e-006	 error, %: 2.23055e-005
<cmath> sqrt(74.5): 8.63134	 my sqrt(8.5,1.5): 8.63134	 perform in 40 iterations	 error: 0	 error, %: 0
<cmath> sqrt(75.92): 8.71321	 my sqrt(8.6,1.4): 8.71328	 perform in 26 iterations	 error: 6.67572e-005	 error, %: 0.000766161
<cmath> sqrt(77.38): 8.79659	 my sqrt(8.7,1.3): 8.79665	 perform in 26 iterations	 error: 6.38962e-005	 error, %: 0.000726374
<cmath> sqrt(78.88): 8.88144	 my sqrt(8.8,1.2): 8.8815	 perform in 26 iterations	 error: 6.00815e-005	 error, %: 0.000676483
<cmath> sqrt(80.42): 8.96772	 my sqrt(8.9,1.1): 8.96778	 perform in 26 iterations	 error: 5.62668e-005	 error, %: 0.000627437
<cmath> sqrt(82): 9.05539	 my sqrt(9,1): 9.05544	 perform in 26 iterations	 error: 5.14984e-005	 error, %: 0.000568705
<cmath> sqrt(83.62): 9.1444	 my sqrt(9.1,0.9): 9.14445	 perform in 26 iterations	 error: 4.76837e-005	 error, %: 0.000521453
<cmath> sqrt(85.28): 9.23472	 my sqrt(9.2,0.8): 9.23476	 perform in 26 iterations	 error: 4.29153e-005	 error, %: 0.000464717
<cmath> sqrt(86.98): 9.32631	 my sqrt(9.3,0.7): 9.32635	 perform in 26 iterations	 error: 3.8147e-005	 error, %: 0.000409025
<cmath> sqrt(88.72): 9.41913	 my sqrt(9.4,0.6): 9.41916	 perform in 26 iterations	 error: 3.33786e-005	 error, %: 0.00035437
<cmath> sqrt(90.5): 9.51315	 my sqrt(9.5,0.5): 9.51318	 perform in 26 iterations	 error: 2.86102e-005	 error, %: 0.000300744
<cmath> sqrt(92.32): 9.60833	 my sqrt(9.6,0.4): 9.60833	 perform in 34 iterations	 error: 1.90735e-006	 error, %: 1.9851e-005
<cmath> sqrt(94.18): 9.70464	 my sqrt(9.7,0.3): 9.70465	 perform in 26 iterations	 error: 1.71661e-005	 error, %: 0.000176886
<cmath> sqrt(96.08): 9.80204	 my sqrt(9.8,0.2): 9.80205	 perform in 26 iterations	 error: 1.14441e-005	 error, %: 0.000116752
<cmath> sqrt(98.02): 9.9005	 my sqrt(9.9,0.1): 9.90051	 perform in 26 iterations	 error: 6.67572e-006	 error, %: 6.74281e-005