Starting with polynomial:
P : 2*t^2 - 1
Extension levels are: 2 8 40
-------------------------------------------------
Trying to find an order 8 Kronrod extension for:
P1 : 2*t^2 - 1
Solvable: 1
-------------------------------------------------
Trying to find an order 40 Kronrod extension for:
P2 : 2*t^10 - 5*t^8 + 35/8*t^6 - 25/16*t^4 + 25/128*t^2 - 1/256
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^50 - 25*t^48 + 1175/8*t^46 - 8625/16*t^44 + 177375/128*t^42 - 678755/256*t^40 + 4010825/1024*t^38 - 9367475/2048*t^36 + 140512125/32768*t^34 - 213624125/65536*t^32 + 264893915/131072*t^30 - 268598725/262144*t^28 + 890616825/2097152*t^26 - 601768125/4194304*t^24 + 659079375/16777216*t^22 - 289994925/33554432*t^20 + 1620559875/1073741824*t^18 - 441970875/2147483648*t^16 + 736618125/34359738368*t^14 - 113806875/68719476736*t^12 + 50075025/549755813888*t^10 - 3700125/1099511627776*t^8 + 336375/4398046511104*t^6 - 8125/8796093022208*t^4 + 625/140737488355328*t^2 - 1/281474976710656
-------------------------------------------------
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:
| (-0.999506560365731557 + 1.0993531426535570978e-849j)  +/-  (1.75e-238, 1.75e-238j)
| (0.97591676193874739896 - 6.7981919626688600781e-873j)  +/-  (6.07e-238, 6.07e-238j)
| (-0.94088076895422547232 - 1.1530805499227187887e-878j)  +/-  (2.31e-238, 2.31e-238j)
| (0.9955619646030800129 + 1.6788817323410536558e-889j)  +/-  (5.22e-238, 5.22e-238j)
| (0.96029368567694307175 + 1.548537429497245897e-894j)  +/-  (4.69e-238, 4.69e-238j)
| (0.89100652418836786236 - 9.5020805442536489777e-899j)  +/-  (5.79e-239, 5.79e-239j)
| (-0.98768834059513772619 - 1.0025333827491465775e-898j)  +/-  (5.75e-238, 5.75e-238j)
| (-0.89100652418836786236 + 1.3278227300204440757e-914j)  +/-  (6.2e-239, 6.2e-239j)
| (-0.39714789063478061375 + 1.1387897208698430727e-929j)  +/-  (9.58e-248, 9.58e-248j)
| (-0.9955619646030800129 + 3.3165745212355587789e-917j)  +/-  (4.85e-238, 4.85e-238j)
| (0.86074202700394363716 - 4.068833662597750697e-930j)  +/-  (1.65e-239, 1.65e-239j)
| (0.999506560365731557 + 1.5525508540058609398e-927j)  +/-  (2.22e-238, 2.22e-238j)
| (-0.91775462568398114115 + 4.651064628496267817e-929j)  +/-  (1.3e-238, 1.3e-238j)
| (-0.86074202700394363716 - 5.2941298426740244977e-931j)  +/-  (2.04e-239, 2.04e-239j)
| (0.98768834059513772619 + 7.9326873075875385781e-930j)  +/-  (6.75e-238, 6.75e-238j)
| (0.82708057427456182492 - 6.9099904135298937417e-934j)  +/-  (5.51e-240, 5.51e-240j)
| (0.33873792024529138122 - 2.9054479525920102366e-942j)  +/-  (8.1e-249, 8.1e-249j)
| (-0.96029368567694307175 - 5.1317469274183979769e-930j)  +/-  (4.61e-238, 4.61e-238j)
| (-0.75011106963045954151 + 1.5146922192526284311e-948j)  +/-  (3.56e-241, 3.56e-241j)
| (-0.97591676193874739896 - 1.6913735055148518632e-945j)  +/-  (6.16e-238, 6.16e-238j)
| (0.91775462568398114115 - 7.4306666126433080214e-963j)  +/-  (1.15e-238, 1.15e-238j)
| (0.7071067811865475244 - 1.2919570386651004256e-964j)  +/-  (7.26e-242, 7.26e-242j)
| (-0.21814324139654255202 - 1.4853237876522391041e-974j)  +/-  (2.08e-251, 2.08e-251j)
| (-0.79015501237569036516 - 5.157248463237171589e-962j)  +/-  (1.42e-240, 1.42e-240j)
| (-0.82708057427456182492 - 2.5261815137586516659e-962j)  +/-  (5.78e-240, 5.78e-240j)
| (0.21814324139654255202 - 9.6164381505690459786e-978j)  +/-  (2.16e-251, 2.16e-251j)
| (0.75011106963045954151 + 8.6164432468296474514e-970j)  +/-  (3.1e-241, 3.1e-241j)
| (0.79015501237569036516 - 3.1218340994352636521e-969j)  +/-  (1.54e-240, 1.54e-240j)
| (-0.33873792024529138122 - 9.4034300628487171549e-979j)  +/-  (7.1e-249, 7.1e-249j)
| (-0.61290705365297649336 - 9.8249649300532053623e-974j)  +/-  (1.62e-243, 1.62e-243j)
| (-0.7071067811865475244 - 9.6301897220444415913e-972j)  +/-  (5.45e-242, 5.45e-242j)
| (0.66131186532365187657 - 1.5591401108428088838e-972j)  +/-  (1.13e-242, 1.13e-242j)
| (0.61290705365297649336 - 4.92296069521859167e-973j)  +/-  (1.28e-243, 1.28e-243j)
| (0.27899110603922925185 + 3.2625904233288325826e-980j)  +/-  (4.43e-250, 4.43e-250j)
| (-0.66131186532365187657 + 1.0944664780949486005e-973j)  +/-  (1.06e-242, 1.06e-242j)
| (-0.45399049973954679156 + 4.5564876102184539105e-977j)  +/-  (1.43e-246, 1.43e-246j)
| (-0.031410759078128293839 + 7.3630331658522370595e-985j)  +/-  (3.13e-255, 3.13e-255j)
| (0.5620833778521306001 - 6.6649754986348080727e-975j)  +/-  (1.95e-244, 1.95e-244j)
| (0.94088076895422547232 + 2.01158879838505287e-980j)  +/-  (2.73e-238, 2.73e-238j)
| (-0.094108313318514318473 - 9.0458981773264445932e-996j)  +/-  (7.34e-254, 7.34e-254j)
| (-0.5620833778521306001 + 6.9787944191425499236e-987j)  +/-  (1.74e-244, 1.74e-244j)
| (-0.15643446504023086901 + 8.7125950920064280211e-997j)  +/-  (1.12e-252, 1.12e-252j)
| (0.39714789063478061375 - 2.1976138687675026518e-990j)  +/-  (9.57e-248, 9.57e-248j)
| (0.50904141575037130028 - 3.6825310701364723732e-990j)  +/-  (1.58e-245, 1.58e-245j)
| (0.031410759078128293839 - 1.0597541243963678674e-999j)  +/-  (3.13e-255, 3.13e-255j)
| (-0.50904141575037130028 + 2.0550965312055203655e-990j)  +/-  (1.86e-245, 1.86e-245j)
| (-0.27899110603922925185 - 2.1996423927112886267e-998j)  +/-  (4.11e-250, 4.11e-250j)
| (0.094108313318514318473 - 2.7064425130731810064e-998j)  +/-  (5.64e-254, 5.64e-254j)
| (0.45399049973954679156 - 1.7223533636388556021e-991j)  +/-  (1.49e-246, 1.49e-246j)
| (0.15643446504023086901 - 1.3816507006042794162e-997j)  +/-  (1.08e-252, 1.08e-252j)
-------------------------------------------------
The weights are:
| (0.02 + 1.1136943277183468856e-848j)  +/-  (6.49e-66, 3.27e-180j)
| (0.02 + 7.7298376290572652782e-851j)  +/-  (2.3e-66, 1.16e-180j)
| (0.02 - 4.044491103273370412e-849j)  +/-  (1.01e-66, 5.11e-181j)
| (0.02 + 3.3018623091202183941e-851j)  +/-  (6.19e-67, 3.12e-181j)
| (0.02 - 9.9647713270434735044e-851j)  +/-  (1.5e-66, 7.56e-181j)
| (0.02 + 1.6809541335582700151e-850j)  +/-  (6.85e-68, 3.46e-182j)
| (0.02 + 9.265506513091217703e-849j)  +/-  (3.18e-67, 1.6e-181j)
| (0.02 - 2.928907580115816692e-849j)  +/-  (2.78e-68, 1.4e-182j)
| (0.02 + 1.0664983865161453753e-849j)  +/-  (3.45e-70, 1.74e-184j)
| (0.02 - 1.6699915436400844348e-848j)  +/-  (5.15e-67, 2.6e-181j)
| (0.02 - 1.9154504453188571443e-850j)  +/-  (9.09e-69, 4.59e-183j)
| (0.02 - 1.0998958748717872016e-851j)  +/-  (3.92e-68, 1.98e-182j)
| (0.02 + 3.4005017855231218896e-849j)  +/-  (2.79e-68, 1.41e-182j)
| (0.02 + 2.567813185946427227e-849j)  +/-  (3.13e-69, 1.58e-183j)
| (0.02 - 5.5103700298663751154e-851j)  +/-  (4.04e-68, 2.04e-182j)
| (0.02 + 2.1540170374561150905e-850j)  +/-  (2.35e-70, 1.19e-184j)
| (0.02 + 4.9213915265066962382e-850j)  +/-  (7.87e-73, 3.97e-187j)
| (0.02 + 4.9802421917519846163e-849j)  +/-  (4.86e-69, 2.45e-183j)
| (0.02 - 1.8561219398221619154e-849j)  +/-  (2.42e-72, 1.22e-186j)
| (0.02 - 6.473010601311287801e-849j)  +/-  (4.39e-69, 2.22e-183j)
| (0.02 - 1.4499725018063017214e-850j)  +/-  (1.03e-70, 5.17e-185j)
| (0.02 - 2.9002714795040403123e-850j)  +/-  (8.38e-74, 4.23e-188j)
| (0.02 - 8.7427597464463709001e-850j)  +/-  (2.24e-75, 1.13e-189j)
| (0.02 + 2.0493079701077342151e-849j)  +/-  (3.53e-72, 1.78e-186j)
| (0.02 - 2.2818485180841497911e-849j)  +/-  (1.34e-71, 6.74e-186j)
| (0.02 + 5.6102105568832950857e-850j)  +/-  (1.96e-76, 9.91e-191j)
| (0.02 + 2.6457691904228288489e-850j)  +/-  (2.84e-74, 1.44e-188j)
| (0.02 - 2.3972453920055796512e-850j)  +/-  (8.69e-74, 4.39e-188j)
| (0.02 - 9.96721794495723882e-850j)  +/-  (8.43e-77, 4.26e-191j)
| (0.02 + 1.4306710527095238998e-849j)  +/-  (1.91e-76, 9.64e-191j)
| (0.02 + 1.6927653006235676398e-849j)  +/-  (2.32e-75, 1.17e-189j)
| (0.02 + 3.1614928668343273333e-850j)  +/-  (5.68e-77, 2.87e-191j)
| (0.02 - 3.4302409656986599116e-850j)  +/-  (7.43e-78, 3.75e-192j)
| (0.02 - 5.2576651060574378328e-850j)  +/-  (7.38e-79, 3.72e-193j)
| (0.02 - 1.5525570574874605934e-849j)  +/-  (1.52e-76, 7.69e-191j)
| (0.02 - 1.1433050689026386296e-849j)  +/-  (2.59e-78, 1.31e-192j)
| (0.02 + 7.2269674484925391141e-850j)  +/-  (1.13e-80, 5.71e-195j)
| (0.02 + 3.7074013583806497549e-850j)  +/-  (1.59e-79, 8.05e-194j)
| (0.02 + 1.2219802108752000217e-850j)  +/-  (2.38e-77, 1.2e-191j)
| (0.02 - 7.6969281569362509934e-850j)  +/-  (8.66e-81, 4.37e-195j)
| (0.02 - 1.3235331115543799328e-849j)  +/-  (1.79e-79, 9.06e-194j)
| (0.02 + 8.2005692106201418642e-850j)  +/-  (1.06e-80, 5.34e-195j)
| (0.02 - 4.5996670752158387343e-850j)  +/-  (1.27e-81, 6.44e-196j)
| (0.02 - 3.9939504092443960155e-850j)  +/-  (2.48e-81, 1.25e-195j)
| (0.02 - 6.7865741616428528757e-850j)  +/-  (2.13e-82, 1.08e-196j)
| (0.02 + 1.2284391404202187515e-849j)  +/-  (2.75e-81, 1.39e-195j)
| (0.02 + 9.329310743398966127e-850j)  +/-  (8.76e-82, 4.42e-196j)
| (0.02 + 6.3722480633987004838e-850j)  +/-  (3.83e-83, 1.93e-197j)
| (0.02 + 4.2909703390562175483e-850j)  +/-  (2.07e-83, 1.08e-197j)
| (0.02 - 5.9809894409027079796e-850j)  +/-  (2.56e-83, 1.28e-197j)
