Starting with polynomial:
P : 2*t^2 - 1
Extension levels are: 2 4 48
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P1 : 2*t^2 - 1
Solvable: 1
-------------------------------------------------
Trying to find an order 48 Kronrod extension for:
P2 : 2*t^6 - 3*t^4 + 9/8*t^2 - 1/16
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^54 - 27*t^52 + 1377/8*t^50 - 11025/16*t^48 + 62181/32*t^46 - 262683/64*t^44 + 13805451/2048*t^42 - 36129159/4096*t^40 + 306312435/32768*t^38 - 531697881/65536*t^36 + 3045178773/524288*t^34 - 3611723661/1048576*t^32 + 1777197357/1048576*t^30 - 1450433115/2097152*t^28 + 7832338821/33554432*t^26 - 4351299345/67108864*t^24 + 15802087095/1073741824*t^22 - 5803310205/2147483648*t^20 + 6806351475/17179869184*t^18 - 1565972595/34359738368*t^16 + 276348105/68719476736*t^14 - 36288135/137438953472*t^12 + 108864405/8796093022208*t^10 - 6870825/17592186044416*t^8 + 1068795/140737488355328*t^6 - 22113/281474976710656*t^4 + 729/2251799813685248*t^2 - 1/4503599627370496
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
  current precision for roots: 212
 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:
| (-0.98944163858094451897 + 2.7875356653556865339e-837j)  +/-  (2.12e-236, 2.12e-236j)
| (-0.99957695008220057696 + 2.0165821739330474257e-836j)  +/-  (7.15e-237, 7.15e-237j)
| (-0.94924264357303390826 + 9.6956050231988493881e-839j)  +/-  (1.06e-236, 1.06e-236j)
| (0.9961946980917455323 + 2.449252229125499882e-836j)  +/-  (1.68e-236, 1.68e-236j)
| (0.88020139118011113129 + 2.2242397494610503e-851j)  +/-  (9.72e-238, 9.72e-238j)
| (0.94924264357303390826 + 1.7977654285746932601e-875j)  +/-  (1.02e-236, 1.02e-236j)
| (-0.029084718743111406889 - 3.1101543246498558339e-903j)  +/-  (3.66e-255, 3.66e-255j)
| (-0.90630778703664996324 + 5.1062231583551488042e-889j)  +/-  (2.73e-237, 2.73e-237j)
| (-0.9961946980917455323 + 1.4244136719347673908e-888j)  +/-  (1.79e-236, 1.79e-236j)
| (0.97934062176555150151 - 3.0063832608984026576e-892j)  +/-  (2.07e-236, 2.07e-236j)
| (0.85111667243699972441 - 1.4106873283186355573e-905j)  +/-  (3.48e-238, 3.48e-238j)
| (0.98944163858094451897 - 1.503906870797768731e-905j)  +/-  (1.94e-236, 1.94e-236j)
| (-0.92934752422682245396 + 7.3825558825950272858e-916j)  +/-  (5.47e-237, 5.47e-237j)
| (-0.81915204428899178968 - 3.0574825551064068986e-918j)  +/-  (9.52e-239, 9.52e-239j)
| (0.96592582628906828675 + 1.225561939328862405e-914j)  +/-  (1.64e-236, 1.64e-236j)
| (0.81915204428899178968 - 1.2792842931268871154e-923j)  +/-  (8.12e-239, 8.12e-239j)
| (0.90630778703664996324 - 4.1276965080618132817e-921j)  +/-  (2.29e-237, 2.29e-237j)
| (-0.7071067811865475244 - 2.4063084674358667851e-928j)  +/-  (8.95e-241, 8.95e-241j)
| (-0.74702507124099597708 + 2.8057521469403531601e-927j)  +/-  (5.32e-240, 5.32e-240j)
| (-0.88020139118011113129 + 5.2408974485084383848e-924j)  +/-  (7.82e-238, 7.82e-238j)
| (0.92934752422682245396 + 5.5711177581866168579e-924j)  +/-  (5.72e-237, 5.72e-237j)
| (0.78441566491957571641 + 9.1204426977611788817e-933j)  +/-  (2.48e-239, 2.48e-239j)
| (0.99957695008220057696 + 9.7809185366423812951e-933j)  +/-  (6.73e-237, 6.73e-237j)
| (-0.85111667243699972441 + 1.1836238062504604477e-949j)  +/-  (3.23e-238, 3.23e-238j)
| (-0.78441566491957571641 + 4.829208143010522627e-951j)  +/-  (2.44e-239, 2.44e-239j)
| (-0.25881904510252076235 + 3.8681320623406498375e-962j)  +/-  (5.53e-250, 5.53e-250j)
| (0.66479586561393782871 + 2.5703236579000971913e-954j)  +/-  (1.31e-241, 1.31e-241j)
| (0.7071067811865475244 + 1.0251951045085780534e-953j)  +/-  (8.31e-241, 8.31e-241j)
| (-0.96592582628906828675 + 2.61772616619909855e-947j)  +/-  (1.55e-236, 1.55e-236j)
| (-0.66479586561393782871 - 3.6175085715869408055e-956j)  +/-  (1.3e-241, 1.3e-241j)
| (-0.97934062176555150151 + 2.4053588269172185221e-959j)  +/-  (1.99e-236, 1.99e-236j)
| (0.74702507124099597708 - 2.4557082036374260354e-966j)  +/-  (5.25e-240, 5.25e-240j)
| (0.62023549126826006777 - 5.2940055596643042171e-969j)  +/-  (1.82e-242, 1.82e-242j)
| (0.087155742747658173558 - 9.142433254635064271e-982j)  +/-  (4.81e-254, 4.81e-254j)
| (-0.57357643635104609611 + 1.104672188372331723e-967j)  +/-  (2.44e-243, 2.44e-243j)
| (-0.62023549126826006777 + 2.2232562712524947239e-970j)  +/-  (1.93e-242, 1.93e-242j)
| (0.14493185930724673754 - 1.7231039698356917917e-982j)  +/-  (1.1e-252, 1.1e-252j)
| (0.57357643635104609611 + 2.5452243488503010134e-971j)  +/-  (2.16e-243, 2.16e-243j)
| (0.3692061473126844512 + 9.3316810912198217682e-977j)  +/-  (1.26e-247, 1.26e-247j)
| (-0.3692061473126844512 - 4.9165052161933398299e-979j)  +/-  (1.43e-247, 1.43e-247j)
| (-0.52497658033456017552 + 1.5440229239522373742e-976j)  +/-  (2.76e-244, 2.76e-244j)
| (0.029084718743111406889 - 9.4075066957850664365e-986j)  +/-  (4.19e-255, 4.19e-255j)
| (0.52497658033456017552 + 2.0298491253981605614e-974j)  +/-  (3.15e-244, 3.15e-244j)
| (0.47460036974764040144 - 2.9733749069974526286e-976j)  +/-  (2.71e-245, 2.71e-245j)
| (-0.14493185930724673754 + 2.2660814106008933326e-984j)  +/-  (1.18e-252, 1.18e-252j)
| (-0.47460036974764040144 - 1.012660683406098485e-977j)  +/-  (3.1e-245, 3.1e-245j)
| (-0.3145447561516136728 - 1.3865279695764236252e-980j)  +/-  (7.59e-249, 7.59e-249j)
| (0.20221757233203793118 + 4.7121266173620770031e-984j)  +/-  (2.87e-251, 2.87e-251j)
| (0.3145447561516136728 - 4.7132188232454048012e-981j)  +/-  (8.44e-249, 8.44e-249j)
| (0.25881904510252076235 - 6.4936277845324064938e-982j)  +/-  (5.32e-250, 5.32e-250j)
| (-0.20221757233203793118 + 3.8541441027172525297e-983j)  +/-  (2.47e-251, 2.47e-251j)
| (-0.42261826174069943619 - 4.5303194416546230665e-978j)  +/-  (1.86e-246, 1.86e-246j)
| (-0.087155742747658173558 + 5.751410782795805304e-986j)  +/-  (5.1e-254, 5.1e-254j)
| (0.42261826174069943619 + 1.8019122579334281784e-978j)  +/-  (1.55e-246, 1.55e-246j)
-------------------------------------------------
The weights are:
| (0.018518518518518518519 + 1.8446133702756307821e-835j)  +/-  (3.27e-54, 9.67e-167j)
| (0.018518518518518518519 + 2.1954252796986604432e-835j)  +/-  (1.8e-54, 5.31e-167j)
| (0.018518518518518518519 - 8.217410982348464352e-836j)  +/-  (6.53e-55, 1.93e-167j)
| (0.018518518518518518519 - 2.9165344966451800031e-836j)  +/-  (9.92e-56, 2.93e-168j)
| (0.018518518518518518519 + 1.796242310497586886e-836j)  +/-  (5.26e-56, 1.55e-168j)
| (0.018518518518518518519 - 3.2734332612451589833e-836j)  +/-  (4.99e-56, 1.47e-168j)
| (0.018518518518518518519 + 8.515468875900354466e-837j)  +/-  (4e-57, 1.18e-169j)
| (0.018518518518518518519 - 5.8777597335846431249e-836j)  +/-  (4.52e-56, 1.33e-168j)
| (0.018518518518518518519 - 3.2604846373827364862e-835j)  +/-  (5.16e-55, 1.52e-167j)
| (0.018518518518518518519 - 6.1091221151268833455e-836j)  +/-  (2.12e-56, 6.26e-169j)
| (0.018518518518518518519 - 1.5089258350291342913e-836j)  +/-  (4.05e-57, 1.2e-169j)
| (0.018518518518518518519 + 1.1072689064551728935e-835j)  +/-  (1.63e-56, 4.82e-169j)
| (0.018518518518518518519 + 6.8585014131102952703e-836j)  +/-  (4.39e-57, 1.3e-169j)
| (0.018518518518518518519 + 4.0348271584395828255e-836j)  +/-  (8.16e-59, 2.41e-171j)
| (0.018518518518518518519 + 4.2761207997196212611e-836j)  +/-  (8.52e-57, 2.52e-169j)
| (0.018518518518518518519 + 1.2699571443276214985e-836j)  +/-  (6.06e-59, 1.79e-171j)
| (0.018518518518518518519 - 2.1542592891773391892e-836j)  +/-  (7.46e-58, 2.2e-170j)
| (0.018518518518518518519 - 2.9757741345434372926e-836j)  +/-  (1.66e-61, 4.9e-174j)
| (0.018518518518518518519 + 3.277167596220250191e-836j)  +/-  (2.89e-61, 8.53e-174j)
| (0.018518518518518518519 + 5.1238871759600546303e-836j)  +/-  (2.69e-60, 7.93e-173j)
| (0.018518518518518518519 + 2.621782520634674793e-836j)  +/-  (6.09e-59, 1.8e-171j)
| (0.018518518518518518519 - 1.0654676749086661489e-836j)  +/-  (1.03e-61, 3.04e-174j)
| (0.018518518518518518519 - 4.4942913013059360355e-836j)  +/-  (3.04e-59, 8.98e-172j)
| (0.018518518518518518519 - 4.5245564447044423404e-836j)  +/-  (1.54e-61, 4.55e-174j)
| (0.018518518518518518519 - 3.6255896430479666054e-836j)  +/-  (3.51e-62, 1.04e-174j)
| (0.018518518518518518519 + 1.3200233143355793495e-836j)  +/-  (7.4e-67, 2.19e-179j)
| (0.018518518518518518519 + 5.8096979428118089098e-837j)  +/-  (1.72e-65, 5.07e-178j)
| (0.018518518518518518519 - 7.2633930607591313297e-837j)  +/-  (8.35e-65, 2.47e-177j)
| (0.018518518518518518519 + 1.0207604566376288036e-835j)  +/-  (4.99e-63, 1.47e-175j)
| (0.018518518518518518519 + 2.7114523775017957516e-836j)  +/-  (1.61e-66, 4.75e-179j)
| (0.018518518518518518519 - 1.3494136477437022856e-835j)  +/-  (4.76e-63, 1.41e-175j)
| (0.018518518518518518519 + 8.8634875575217248366e-837j)  +/-  (1.78e-65, 5.25e-178j)
| (0.018518518518518518519 - 4.46944095868510589e-837j)  +/-  (9.27e-68, 2.74e-180j)
| (0.018518518518518518519 + 6.3911232466141357901e-837j)  +/-  (4.19e-71, 1.24e-183j)
| (0.018518518518518518519 + 2.2662956579267440389e-836j)  +/-  (3.13e-69, 9.25e-182j)
| (0.018518518518518518519 - 2.4768235446197795704e-836j)  +/-  (2.47e-68, 7.31e-181j)
| (0.018518518518518518519 - 5.356829163477070949e-837j)  +/-  (4.85e-72, 1.43e-184j)
| (0.018518518518518518519 + 3.2175990789265503132e-837j)  +/-  (3.95e-70, 1.17e-182j)
| (0.018518518518518518519 - 1.2435942079444288235e-837j)  +/-  (2.16e-72, 6.38e-185j)
| (0.018518518518518518519 + 1.591194015792107752e-836j)  +/-  (1.75e-72, 5.17e-185j)
| (0.018518518518518518519 - 2.0755462879114245521e-836j)  +/-  (5.38e-71, 1.59e-183j)
| (0.018518518518518518519 - 7.4416672755113106241e-837j)  +/-  (1.56e-72, 4.62e-185j)
| (0.018518518518518518519 - 2.0346601013755877155e-837j)  +/-  (6.01e-72, 1.78e-184j)
| (0.018518518518518518519 + 9.0501457342233548364e-838j)  +/-  (1.25e-72, 3.7e-185j)
| (0.018518518518518518519 + 1.076284473197803458e-836j)  +/-  (2.23e-74, 6.58e-187j)
| (0.018518518518518518519 + 1.9011744116565769417e-836j)  +/-  (2.01e-73, 5.93e-186j)
| (0.018518518518518518519 - 1.4515559414812373546e-836j)  +/-  (5.14e-74, 1.52e-186j)
| (0.018518518518518518519 + 4.331939299491221244e-837j)  +/-  (4.25e-75, 1.25e-187j)
| (0.018518518518518518519 + 2.282649541883658528e-837j)  +/-  (1.29e-75, 3.81e-188j)
| (0.018518518518518518519 - 3.3095800039552589537e-837j)  +/-  (1.36e-75, 4.02e-188j)
| (0.018518518518518518519 - 1.1953040366384381622e-836j)  +/-  (2.73e-76, 8.06e-189j)
| (0.018518518518518518519 - 1.7404599829472616033e-836j)  +/-  (3.64e-76, 1.08e-188j)
| (0.018518518518518518519 - 9.6198887750065331786e-837j)  +/-  (1.99e-76, 5.88e-189j)
| (0.018518518518518518519 + 1.841439955282059053e-838j)  +/-  (1.47e-76, 4.27e-189j)
