Starting with polynomial:
P : 16*t^4 - 12*t^2 + 1
Extension levels are: 4 15 20
-------------------------------------------------
Trying to find an order 15 Kronrod extension for:
P1 : 16*t^4 - 12*t^2 + 1
Solvable: 1
-------------------------------------------------
Trying to find an order 20 Kronrod extension for:
P2 : 16*t^19 - 72*t^17 + 136*t^15 - 140*t^13 + 1365/16*t^11 - 1001/32*t^9 + 429/64*t^7 - 99/128*t^5 + 165/4096*t^3 - 5/8192*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 16*t^39 - 152*t^37 + 666*t^35 - 1785*t^33 + 6545/2*t^31 - 17391/4*t^29 + 69223/16*t^27 - 105183/32*t^25 + 7888725/4096*t^23 - 7153575/8192*t^21 + 10015005/32768*t^19 - 5368545/65536*t^17 + 4345965/262144*t^15 - 1300075/524288*t^13 + 557175/2097152*t^11 - 81719/4194304*t^9 + 245157/268435456*t^7 - 13167/536870912*t^5 + 665/2147483648*t^3 - 5/4294967296*t
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
 current precision for weights: 53
Linear system for weights solvable: 0
  current precision for roots: 106
  current precision for roots: 212
 current precision for weights: 106
Linear system for weights solvable: 0
  current precision for roots: 212
  current precision for roots: 424
 current precision for weights: 212
Linear system for weights solvable: 1
  current precision for roots: 424
  current precision for roots: 848
 current precision for weights: 424
Linear system for weights solvable: 1
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (0.97236992039767660183 + 1.5265700329321654698e-948j)  +/-  (1.52e-242, 1.52e-242j)
| (-0.97236992039767660183 + 1.1707220002439708596e-958j)  +/-  (1.67e-242, 1.67e-242j)
| (-0.92387953251128675613 - 2.6885452195453620172e-960j)  +/-  (9.52e-243, 9.52e-243j)
| (-0.98768834059513772619 + 2.6388550506484704959e-959j)  +/-  (1.26e-242, 1.26e-242j)
| (0.89100652418836786236 - 8.7711880356779995172e-958j)  +/-  (6.06e-243, 6.06e-243j)
| (0.92387953251128675613 + 7.0090955420822364539e-968j)  +/-  (1.26e-242, 1.26e-242j)
| (-0.9969173337331279762 + 7.3418912551165654833e-974j)  +/-  (4.63e-243, 4.63e-243j)
| (-0.89100652418836786236 + 4.7838557549444806056e-978j)  +/-  (5.69e-243, 5.69e-243j)
| (-0.3090169943749474241 + 2.377366683964752593e-991j)  +/-  (8.02e-251, 8.02e-251j)
| (0.98768834059513772619 - 1.0982576652184876236e-1001j)  +/-  (1.13e-242, 1.13e-242j)
| (0.85264016435409222152 + 1.5098834330541872477e-1022j)  +/-  (2.62e-243, 2.62e-243j)
| (0.9969173337331279762 + 7.7092800750229589614e-1038j)  +/-  (3.26e-243, 3.26e-243j)
| (-0.8090169943749474241 - 2.8406180659232559881e-1052j)  +/-  (1.01e-243, 1.01e-243j)
| (-0.85264016435409222152 - 4.8233216323718160014e-1054j)  +/-  (3.15e-243, 3.15e-243j)
| (0.95105651629515357212 + 8.6707666376255471041e-1056j)  +/-  (1.75e-242, 1.75e-242j)
| (0.8090169943749474241 - 1.7666479813266464018e-1068j)  +/-  (8.98e-244, 8.98e-244j)
| (0.76040596560003093817 - 1.1914295477504421028e-1070j)  +/-  (2.52e-244, 2.52e-244j)
| (-0.95105651629515357212 + 6.3094960691197920008e-1069j)  +/-  (1.78e-242, 1.78e-242j)
| (-0.7071067811865475244 + 7.2383534529625659381e-1073j)  +/-  (4.72e-245, 4.72e-245j)
| (-0.76040596560003093817 - 1.4331085204602432941e-1074j)  +/-  (2.18e-244, 2.18e-244j)
| (0.45399049973954679156 + 4.2751229342886366373e-1080j)  +/-  (1.51e-248, 1.51e-248j)
| (0.7071067811865475244 + 2.7589871200564713674e-1078j)  +/-  (4.6e-245, 4.6e-245j)
| (0.078459095727844945033 - 4.0912151402935011309e-1083j)  +/-  (1.12e-254, 1.12e-254j)
| (-0.45399049973954679156 - 1.2240697036544851684e-1078j)  +/-  (1.31e-248, 1.31e-248j)
| (-0.52249856471594886499 + 4.9657989422015822501e-1078j)  +/-  (1.49e-247, 1.49e-247j)
| (-2.8595468728057473166e-1082 - 7.8447231626594243615e-1082j)  +/-  (3.26e-1080, 3.26e-1080j)
| (0.64944804833018365573 - 3.9311439319699328179e-1080j)  +/-  (9.13e-246, 9.13e-246j)
| (0.38268343236508977173 - 2.7435042994976669092e-1083j)  +/-  (1.14e-249, 1.14e-249j)
| (-0.23344536385590541177 - 1.8446036347787471704e-1079j)  +/-  (4.88e-252, 4.88e-252j)
| (-0.64944804833018365573 - 6.0930636933979950812e-1079j)  +/-  (1.01e-245, 1.01e-245j)
| (-0.078459095727844945033 + 9.3842615422892038516e-1085j)  +/-  (1.12e-254, 1.12e-254j)
| (0.3090169943749474241 - 2.370659254699230743e-1086j)  +/-  (6.85e-251, 6.85e-251j)
| (0.52249856471594886499 + 2.3502414500020865942e-1081j)  +/-  (1.61e-247, 1.61e-247j)
| (-0.15643446504023086901 + 9.5906324533735874754e-1084j)  +/-  (2.52e-253, 2.52e-253j)
| (-0.58778525229247312917 - 2.3947975054628579339e-1082j)  +/-  (1.35e-246, 1.35e-246j)
| (-0.38268343236508977173 + 2.2458842788090409909e-1086j)  +/-  (1.07e-249, 1.07e-249j)
| (0.15643446504023086901 - 6.4136768445626492791e-1090j)  +/-  (2.04e-253, 2.04e-253j)
| (0.58778525229247312917 + 3.6856331098583872469e-1084j)  +/-  (1.34e-246, 1.34e-246j)
| (0.23344536385590541177 - 2.9009658561258196267e-1091j)  +/-  (5.29e-252, 5.29e-252j)
-------------------------------------------------
The weights are:
| (0.0013624184476454017205 - 5.5664654287890838975e-950j)  +/-  (1.65e-78, 1.23e-195j)
| (0.0013624184476454017205 - 1.0694629318652157556e-951j)  +/-  (7.92e-79, 5.89e-196j)
| (0.003661165235168155945 - 2.9474102759467222604e-951j)  +/-  (3.75e-79, 2.79e-196j)
| (0.00061179354631058034854 + 4.7648874745979937849e-952j)  +/-  (2.86e-79, 2.13e-196j)
| (0.0051526843463440858854 + 9.6676563185943930106e-950j)  +/-  (2.68e-80, 1.99e-197j)
| (0.003661165235168155945 - 1.1526047475574670136e-949j)  +/-  (2.79e-80, 2.07e-197j)
| (0.00015389574256077842262 - 1.1929830399542017832e-952j)  +/-  (1.16e-79, 8.59e-197j)
| (0.0051526843463440858854 + 4.2213335525723505703e-951j)  +/-  (1.94e-80, 1.44e-197j)
| (0.022612712429686842801 + 2.6939473766919495178e-950j)  +/-  (1.74e-83, 1.3e-200j)
| (0.00061179354631058034854 - 6.0968799796944123572e-950j)  +/-  (3.67e-81, 2.73e-198j)
| (0.0068251187532556651055 - 8.7021156000460506092e-950j)  +/-  (1.07e-81, 7.93e-199j)
| (0.00015389574256077842262 + 9.5705655667309340641e-951j)  +/-  (1.17e-81, 8.67e-199j)
| (0.0086372875703131571987 + 7.4017745728667321172e-951j)  +/-  (1.16e-82, 8.64e-200j)
| (0.0068251187532556651055 - 5.7090214700544654091e-951j)  +/-  (5.02e-82, 3.73e-199j)
| (0.0023872875703131571987 + 1.7098918814449579201e-949j)  +/-  (2.12e-81, 1.58e-198j)
| (0.0086372875703131571987 + 8.0717405599744719201e-950j)  +/-  (2.03e-83, 1.51e-200j)
| (0.010544569186997114137 - 7.5942267454454893203e-950j)  +/-  (2.87e-84, 2.13e-201j)
| (0.0023872875703131571987 + 1.8947236947182309185e-951j)  +/-  (1.9e-83, 1.41e-200j)
| (0.0125 + 1.1361947086341746008e-950j)  +/-  (3.29e-86, 2.44e-203j)
| (0.010544569186997114137 - 9.2897318477028481854e-951j)  +/-  (1.63e-85, 1.21e-202j)
| (0.019847315653655914115 + 5.8448148448029858212e-950j)  +/-  (8.88e-89, 6.6e-206j)
| (0.0125 + 7.1936589018894704577e-950j)  +/-  (7.56e-87, 5.62e-204j)
| (0.024846104257439221577 - 4.2430762856724978866e-950j)  +/-  (1.06e-89, 7.9e-207j)
| (0.019847315653655914115 + 2.1241698028701284549e-950j)  +/-  (5.45e-89, 4.05e-206j)
| (0.018174881246744334895 - 1.8560314403031763741e-950j)  +/-  (7.54e-89, 5.6e-206j)
| (0.025 + 3.9248695423876972609e-950j)  +/-  (2.63e-90, 1.95e-207j)
| (0.014455430813002885863 - 6.8336119097991320238e-950j)  +/-  (1.63e-89, 1.21e-206j)
| (0.021338834764831844055 - 5.5241601040003515111e-950j)  +/-  (1.03e-90, 7.65e-208j)
| (0.023637581552354598279 - 2.9925332792557074438e-950j)  +/-  (7.77e-91, 5.77e-208j)
| (0.014455430813002885863 - 1.3606476142616610292e-950j)  +/-  (5.4e-90, 4.02e-207j)
| (0.024846104257439221577 - 3.6094662055875060048e-950j)  +/-  (2.91e-91, 2.16e-208j)
| (0.022612712429686842801 + 5.2038496893378009884e-950j)  +/-  (4.63e-92, 3.44e-209j)
| (0.018174881246744334895 - 6.1673695673099789949e-950j)  +/-  (8.19e-92, 6.09e-209j)
| (0.024388206453689419651 + 3.2982069904694245123e-950j)  +/-  (1.13e-91, 8.43e-209j)
| (0.016362712429686842801 + 1.601047568802744964e-950j)  +/-  (1.14e-91, 8.5e-209j)
| (0.021338834764831844055 - 2.4039810416943019059e-950j)  +/-  (6.04e-92, 4.49e-209j)
| (0.024388206453689419651 + 4.5628983159042425477e-950j)  +/-  (5.64e-93, 4.2e-210j)
| (0.016362712429686842801 + 6.4950135931214844391e-950j)  +/-  (2.46e-93, 1.88e-210j)
| (0.023637581552354598279 - 4.8833704809748657273e-950j)  +/-  (3.61e-93, 2.67e-210j)
