Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 3 4 24
-------------------------------------------------
Trying to find an order 3 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P2 : 4*t^5 - 14*t^3 + 6*t
Solvable: 1
-------------------------------------------------
Trying to find an order 24 Kronrod extension for:
P3 : 4*t^9 - 142/3*t^7 + 1399/9*t^5 - 2965/18*t^3 + 295/6*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^33 - 55228743238444850054839965670281091790733211659266/63182519542706008820545556987124360511709738529*t^31 + 79119328926466581326024603194966773667069687784151007/947737793140590132308183354806865407675646077935*t^29 - 8728445323345597808774140034898917207923223062417069429/1895475586281180264616366709613730815351292155870*t^27 + 68824339226732729335379092422906046985908141630553946573/421216796951373392136970379914162403411398256860*t^25 - 662652947579923606478401819707486712947341870037008133855/168486718780549356854788151965664961364559302744*t^23 + 454060196471565716921218623827113497118909337137050216135/6877008929818341096113802121047549443451400112*t^21 - 75401507282798797245389025505980062418103463107926570376035/96278125017456775345593229694665692208319601568*t^19 + 1267274454439789951824494544368244661134284220011865762100845/192556250034913550691186459389331384416639203136*t^17 - 2143152701684930850243636579529532963913761881878808777536705/55016071438546728768910416968380395547611200896*t^15 + 123301210512180682745375842388068255610914139813300760103739175/770225000139654202764745837557325537666556812544*t^13 - 686388472182978158320047396885397376264801351242077212677422525/1540450000279308405529491675114651075333113625088*t^11 + 2487879770623122924450370460500087200056392599124616175535775925/3080900000558616811058983350229302150666227250176*t^9 - 787431751846006787000850141789215588517281665393234723598867925/880257143016747660302566671494086328761779214336*t^7 + 958912810758155454685458845297971376371982748508452052413420525/1760514286033495320605133342988172657523558428672*t^5 - 526768892923732411179482267280038984784449260418646917353278375/3521028572066990641210266685976345315047116857344*t^3 + 41144959956984255291896461630401263429453382571132069953885375/3521028572066990641210266685976345315047116857344*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: 1
  current precision for roots: 212
  current precision for roots: 424
 current precision for weights: 212
Linear system for weights solvable: 1
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (6.8054951111182930648 - 2.6282678458544182886e-418j)  +/-  (7.73e-122, 7.73e-122j)
| (-6.8054951111182930648 - 6.0220729219923331591e-419j)  +/-  (7.83e-122, 7.83e-122j)
| (5.4838671693862639081 + 1.0340485484081854112e-415j)  +/-  (2.14e-120, 2.14e-120j)
| (-3.9751787627153273556 + 3.8844031070882154989e-423j)  +/-  (4.83e-120, 4.83e-120j)
| (3.9751787627153273556 + 6.244947216651187085e-424j)  +/-  (4.77e-120, 4.77e-120j)
| (-4.9451444114825361688 + 2.4642432430616793574e-434j)  +/-  (3.77e-120, 3.77e-120j)
| (4.9451444114825361688 - 1.5794048134235521641e-432j)  +/-  (4.17e-120, 4.17e-120j)
| (-5.4838671693862639081 - 2.138179318493567302e-439j)  +/-  (2.03e-120, 2.03e-120j)
| (-4.4459975376246611282 + 2.2882286263543087376e-440j)  +/-  (5.34e-120, 5.34e-120j)
| (6.0844051862733113591 + 8.3879713181464856436e-438j)  +/-  (6.36e-121, 6.36e-121j)
| (1.0672470719421885588 + 4.1400361190308573983e-444j)  +/-  (6.56e-124, 6.56e-124j)
| (3.5262593245251277251 + 4.9687585002324450413e-441j)  +/-  (3.08e-120, 3.08e-120j)
| (4.4459975376246611282 - 7.2499629276358333298e-448j)  +/-  (4.64e-120, 4.64e-120j)
| (-6.0844051862733113591 + 1.5800557593543755617e-453j)  +/-  (5.53e-121, 5.53e-121j)
| (-3.5262593245251277251 - 1.3950430629506781942e-451j)  +/-  (3.41e-120, 3.41e-120j)
| (1.7320508075688772935 + 1.8920156256363223639e-452j)  +/-  (7.45e-122, 7.45e-122j)
| (2.2912475080966007558 + 7.6812983818410907814e-451j)  +/-  (4.15e-121, 4.15e-121j)
| (-3.0956103472654601185 + 3.4873487379133804311e-458j)  +/-  (1.8e-120, 1.8e-120j)
| (-1.7320508075688772935 + 1.6287307637602851941e-459j)  +/-  (7.68e-122, 7.68e-122j)
| (-1.9605577397422489216 - 1.3344120720933307735e-458j)  +/-  (2.18e-121, 2.18e-121j)
| (1.9605577397422489216 - 1.6125776710885045295e-456j)  +/-  (2.1e-121, 2.1e-121j)
| (0.7071067811865475244 + 3.8922846562338657113e-466j)  +/-  (5.6e-125, 5.6e-125j)
| (1.4246904100481888474 + 4.1204152317282781552e-463j)  +/-  (9.05e-123, 9.05e-123j)
| (-0.35162993686431019231 + 1.2856381471162722348e-467j)  +/-  (2.77e-126, 2.77e-126j)
| (-1.4246904100481888474 - 1.5005564442908621253e-466j)  +/-  (8.96e-123, 8.96e-123j)
| (-2.6822224032999497583 + 5.17359100996476134e-462j)  +/-  (9.21e-121, 9.21e-121j)
| (0.35162993686431019231 - 3.2541834144841898121e-467j)  +/-  (3.95e-126, 3.95e-126j)
| (3.0956103472654601185 + 7.0727348122783744249e-463j)  +/-  (1.95e-120, 1.95e-120j)
| (-2.2912475080966007558 - 1.9951142341914771462e-476j)  +/-  (4.45e-121, 4.45e-121j)
| (-1.0672470719421885588 + 9.3880201656390306861e-480j)  +/-  (6.15e-124, 6.15e-124j)
| (-0.7071067811865475244 - 1.9238070296756506246e-481j)  +/-  (4.96e-125, 4.96e-125j)
| (2.6822224032999497583 + 8.5437711011518737318e-482j)  +/-  (8.59e-121, 8.59e-121j)
| (4.835339462963805584e-549 + 5.6635652296182142192e-550j)  +/-  (1.61e-547, 1.61e-547j)
-------------------------------------------------
The weights are:
| (3.6015197569257242615e-21 + 3.3020308376021733149e-433j)  +/-  (1.05e-42, 4.69e-102j)
| (3.6015197569257242615e-21 - 3.5509845079559252084e-434j)  +/-  (2.53e-43, 1.13e-102j)
| (2.7705125884558277957e-14 - 1.7800027139559850001e-428j)  +/-  (5.35e-40, 2.39e-99j)
| (3.552690311451739055e-08 + 1.2593203810799659707e-426j)  +/-  (1.25e-36, 5.6e-96j)
| (3.552690311451739055e-08 + 7.8911625305838865672e-426j)  +/-  (9.17e-37, 4.1e-96j)
| (6.982908399039081586e-12 + 6.6000351524919826753e-429j)  +/-  (1.17e-39, 5.21e-99j)
| (6.982908399039081586e-12 + 1.2778482085540875304e-427j)  +/-  (1.69e-39, 7.56e-99j)
| (2.7705125884558277957e-14 - 2.6118458948129964948e-430j)  +/-  (2.92e-41, 1.31e-100j)
| (7.1002163806943008581e-10 - 1.0734883513692146946e-427j)  +/-  (1.4e-38, 6.25e-98j)
| (3.0431306826563765944e-17 - 1.0439431431523351723e-430j)  +/-  (1.19e-42, 5.34e-102j)
| (0.065258581664804101401 + 8.1074544445016762229e-422j)  +/-  (5.61e-28, 2.51e-87j)
| (9.8633121575157149857e-07 - 5.2750766844344252173e-425j)  +/-  (1.1e-37, 4.93e-97j)
| (7.1002163806943008581e-10 - 1.0273228201817194146e-426j)  +/-  (4.01e-39, 1.79e-98j)
| (3.0431306826563765944e-17 + 5.4190440229383482676e-432j)  +/-  (4.05e-44, 1.81e-103j)
| (9.8633121575157149857e-07 - 1.1463735269465831809e-425j)  +/-  (4.17e-39, 1.87e-98j)
| (0.0069158210646804893695 + 6.3367886088579316041e-422j)  +/-  (8.17e-35, 3.66e-94j)
| (0.0011055237196887973011 + 8.5367881720946311654e-423j)  +/-  (1.42e-36, 6.33e-96j)
| (1.6410031680570402352e-05 + 8.6123332574372394847e-425j)  +/-  (6.03e-39, 2.69e-98j)
| (0.0069158210646804893695 + 3.2948263626542364105e-422j)  +/-  (1.48e-36, 6.61e-96j)
| (0.0032234803455836095835 - 1.694808530733758661e-422j)  +/-  (2.53e-37, 1.13e-96j)
| (0.0032234803455836095835 - 3.5808395778874454822e-422j)  +/-  (5.93e-37, 2.69e-96j)
| (0.12252971860201025046 - 9.5098726664690949433e-422j)  +/-  (2.28e-35, 1.03e-94j)
| (0.025764933047617364995 - 7.1803324114364187852e-422j)  +/-  (6.77e-36, 3.05e-95j)
| (0.17603205236374696963 + 9.2673927613092580208e-422j)  +/-  (3.18e-36, 1.44e-95j)
| (0.025764933047617364995 - 4.2189592120315989913e-422j)  +/-  (6.19e-37, 2.76e-96j)
| (0.00017116329603379650867 - 5.6731540293982404372e-424j)  +/-  (1.56e-39, 6.98e-99j)
| (0.17603205236374696963 + 1.0537230789748109342e-421j)  +/-  (1.73e-36, 8.2e-96j)
| (1.6410031680570402352e-05 + 3.0935118715439733487e-424j)  +/-  (5.54e-41, 2.65e-100j)
| (0.0011055237196887973011 + 3.5055506894928190799e-423j)  +/-  (8.88e-39, 3.91e-98j)
| (0.065258581664804101401 + 5.4659614488029665658e-422j)  +/-  (5.89e-38, 2.57e-97j)
| (0.12252971860201025046 - 7.3375950332877018823e-422j)  +/-  (5.25e-38, 2.33e-97j)
| (0.00017116329603379650867 - 1.6534650423329362384e-423j)  +/-  (1.07e-40, 6.39e-100j)
| (0.19796258657800580447 - 1.0503342031043129083e-421j)  +/-  (5.29e-38, 1.99e-97j)
