RP_slope = (sqrt(2)-0.5)/2 =  0.45710678118654757
  TA1_slope =  0.50000000000000000
  TA2_c0 = 3/8 =  0.37500000000000000
  TA2_c1 = 6/8 =  0.75000000000000000
  TA2_c2 = -1/8 = -0.12500000000000000
  LLSQ_c0 = K1 =  0.38190217717175579
  LLSQ_c1 = K2 =  0.71612039556246587
  LLSQ_c2 = K3 = -0.10126647163746012
  rank =  3.00000000000000000
  $1 = {rank,K1:K3} = llsq("poly",A1:A16,B1:B16) =  3.00000000000000000
  MinMax_c0 = N1 =  0.37400439361667709
  MinMax_c1 = N2 =  0.72884922588010814
  MinMax_c2 = N3 = -0.10560521828722065
  $2 = {N1:N3} = search(M20,K1:K3) =  0.00493159014508437
   A  B  C  D  E  F  G  H  I  J  K  L  M  N
0 x sqrt(x) RP1 |err| TA1 |err| TA2 |err| LLSQ |err| coef MinMax |err| coef
1 0.5000 0.7071 0.7286 0.0214 0.7500 0.0429 0.7188 0.0116 0.7146 0.0075 0.3819 0.7120 0.0049 0.3740
2 0.6000 0.7746 0.7743 0.0003 0.8000 0.0254 0.7800 0.0054 0.7751 0.0005 0.7161 0.7733 0.0013 0.7288
3 0.7000 0.8367 0.8200 0.0167 0.8500 0.0133 0.8387 0.0021 0.8336 0.0031 -0.1013 0.8325 0.0042 -0.1056
4 0.8000 0.8944 0.8657 0.0287 0.9000 0.0056 0.8950 0.0006 0.8900 0.0044 0.8895 0.0049
5 0.9000 0.9487 0.9114 0.0373 0.9500 0.0013 0.9487 0.0001 0.9444 0.0043 0.9444 0.0043
6 1.0000 1.0000 0.9571 0.0429 1.0000 0.0000 1.0000 0.0000 0.9968 0.0032 0.9972 0.0028
7 1.1000 1.0488 1.0028 0.0460 1.0500 0.0012 1.0488 0.0001 1.0471 0.0017 1.0480 0.0009
8 1.2000 1.0954 1.0485 0.0469 1.1000 0.0046 1.0950 0.0004 1.0954 0.0000 1.0966 0.0011
9 1.3000 1.1402 1.0942 0.0459 1.1500 0.0098 1.1387 0.0014 1.1417 0.0015 1.1430 0.0029
10 1.4000 1.1832 1.1399 0.0433 1.2000 0.0168 1.1800 0.0032 1.1860 0.0028 1.1874 0.0042
11 1.5000 1.2247 1.1857 0.0391 1.2500 0.0253 1.2188 0.0060 1.2282 0.0035 1.2297 0.0049
12 1.6000 1.2649 1.2314 0.0335 1.3000 0.0351 1.2550 0.0099 1.2685 0.0035 1.2698 0.0049
13 1.7000 1.3038 1.2771 0.0268 1.3500 0.0462 1.2888 0.0151 1.3066 0.0028 1.3078 0.0040
14 1.8000 1.3416 1.3228 0.0188 1.4000 0.0584 1.3200 0.0216 1.3428 0.0012 1.3438 0.0021
15 1.9000 1.3784 1.3685 0.0099 1.4500 0.0716 1.3487 0.0297 1.3770 0.0014 1.3776 0.0008
16 2.0000 1.4142 1.4142 0.0000 1.5000 0.0858 1.3750 0.0392 1.4091 0.0051 1.4093 0.0049
17
18 ||err|| 0.1301 0.1516 0.0586 0.0138 0.0147
19
20 max|err| 0.0469 0.0858 0.0392 0.0075 0.0049