Starting with polynomial:
P : 2*t
Extension levels are: 1 2 44
-------------------------------------------------
Trying to find an order 2 Kronrod extension for:
P1 : 2*t
Solvable: 1
-------------------------------------------------
Trying to find an order 44 Kronrod extension for:
P2 : 2*t^3 - 3*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^47 - 3514153654452277745561/3361510671905005977*t^45 + 560094854974915264947525/2241007114603337318*t^43 - 23235237349503802180731855/640287747029524948*t^41 + 4589211166692680833587627675/1280575494059049896*t^39 - 654332443892435585022558356115/2561150988118099792*t^37 + 69768361009792761626324762278245/5122301976236199584*t^35 - 5686994763539639731787371497356625/10244603952472399168*t^33 + 179641401761147525936125560635060025/10244603952472399168*t^31 - 8866618776816825270702172862629823625/20489207904944798336*t^29 + 343141664249892418409003718753397432575/40978415809889596672*t^27 - 10411891887501693410950202360790221192475/81956831619779193344*t^25 + 246861130393920491316691242397596289546875/163913663239558386688*t^23 - 4542808906990427521691210670860428728331875/327827326479116773376*t^21 + 64219806452410651454825299748976098863003125/655654652958233546752*t^19 - 687391264019599746960819809559521741531720625/1311309305916467093504*t^17 + 10925504486189207144722730433672171252428495625/5245237223665868374016*t^15 - 62786031519102820709806472412200567904462515625/10490474447331736748032*t^13 + 251727692309709392180155564004512495180539909375/20980948894663473496064*t^11 - 669791682913080396700696637662556444875218796875/41961897789326946992128*t^9 + 1099616293294393121499592062088006516136395509375/83923795578653893984256*t^7 - 993607557345241528937930176383411431497397184375/167847591157307787968512*t^5 + 403454009725495425625576495763098339481090390625/335695182314615575937024*t^3 - 46339333129265119198494450887799679578225328125/671390364629231151874048*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
Positive weights:   47 out of 47
Indefinite weights: 0 out of 47
Negative weights:   0 out of 47
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (2.8516210371571591626 + 1.635983788593735778e-856j)  +/-  (2.14e-246, 2.14e-246j)
| (8.1096707948033437738 - 5.5694060190388414329e-856j)  +/-  (6.06e-246, 6.06e-246j)
| (7.5548011102150838639 + 2.6124167076252963879e-856j)  +/-  (3.69e-245, 3.69e-245j)
| (-5.755211604757442286 - 7.9566698530988376429e-854j)  +/-  (6.37e-244, 6.37e-244j)
| (-4.6029126273780190163 + 3.4303956113948705551e-855j)  +/-  (3.25e-244, 3.25e-244j)
| (-7.5548011102150838639 - 1.0546796819137226315e-857j)  +/-  (3.28e-245, 3.28e-245j)
| (6.1673124746699056304 + 3.3100097030357116182e-854j)  +/-  (4.54e-244, 4.54e-244j)
| (-7.0584452770860247342 + 5.9555691992608865092e-865j)  +/-  (1.27e-244, 1.27e-244j)
| (6.5995595049548510874 - 3.652609585613785714e-863j)  +/-  (2.88e-244, 2.88e-244j)
| (5.755211604757442286 - 1.6802351607334024128e-880j)  +/-  (6.28e-244, 6.28e-244j)
| (-8.7782432951616818723 - 1.2706744868562453982e-899j)  +/-  (4.37e-247, 4.37e-247j)
| (8.7782432951616818723 + 3.5753734891492645864e-896j)  +/-  (4.6e-247, 4.6e-247j)
| (-1.2247448713915890491 - 4.6995638372626348604e-906j)  +/-  (1.63e-250, 1.63e-250j)
| (-2.5178185065002532258 - 4.3040343703295798523e-904j)  +/-  (4.63e-247, 4.63e-247j)
| (-1.541726944100363691 + 5.4335754761524637511e-909j)  +/-  (1.68e-249, 1.68e-249j)
| (4.9756173309565537224 - 3.7820196901671827268e-909j)  +/-  (4.33e-244, 4.33e-244j)
| (-5.3589808471965573741 + 1.6515152816801183957e-923j)  +/-  (5.13e-244, 5.13e-244j)
| (-1.8629738504950506515 + 1.6484296611043757013e-934j)  +/-  (1.18e-248, 1.18e-248j)
| (4.2391865246262135225 + 3.5394017916527217176e-941j)  +/-  (1.42e-244, 1.42e-244j)
| (5.3589808471965573741 - 4.0791965446313481867e-958j)  +/-  (5.43e-244, 5.43e-244j)
| (-6.5995595049548510874 + 6.9944152503881212177e-963j)  +/-  (2.93e-244, 2.93e-244j)
| (1.2247448713915890491 + 5.7548859147296676427e-972j)  +/-  (1.64e-250, 1.64e-250j)
| (7.0584452770860247342 - 6.4563294462196838554e-966j)  +/-  (1.14e-244, 1.14e-244j)
| (0.60450531534020979857 + 1.6147663420392363635e-974j)  +/-  (1.23e-252, 1.23e-252j)
| (-3.1900843244101086001 - 8.4768068727640972756e-968j)  +/-  (8.29e-246, 8.29e-246j)
| (-4.2391865246262135225 - 1.3541550887682252649e-965j)  +/-  (1.45e-244, 1.45e-244j)
| (-6.1673124746699056304 + 4.2220619832081932282e-967j)  +/-  (4.62e-244, 4.62e-244j)
| (-8.1096707948033437738 - 1.0542953021461985931e-969j)  +/-  (6.37e-246, 6.37e-246j)
| (4.6029126273780190163 - 3.2857559177290739592e-966j)  +/-  (2.83e-244, 2.83e-244j)
| (-3.8831291656386980172 + 3.7137766107978771706e-971j)  +/-  (6.53e-245, 6.53e-245j)
| (-4.9756173309565537224 - 1.1803369055475222191e-972j)  +/-  (4.65e-244, 4.65e-244j)
| (2.5178185065002532258 + 5.5740143335138838022e-975j)  +/-  (4.39e-247, 4.39e-247j)
| (3.5337035233113910384 - 1.1945405870341404859e-971j)  +/-  (2.31e-245, 2.31e-245j)
| (0.91228969228252829534 + 4.2342133405130456646e-980j)  +/-  (1.45e-251, 1.45e-251j)
| (-3.5337035233113910384 - 4.7081365814503088282e-974j)  +/-  (2.47e-245, 2.47e-245j)
| (-9.0608743385980754061e-997 + 1.2420915257978835312e-996j)  +/-  (7.23e-995, 7.23e-995j)
| (3.1900843244101086001 + 2.6964200745288548998e-975j)  +/-  (8.5e-246, 8.5e-246j)
| (0.30093763012467238823 + 5.0428346598500836292e-984j)  +/-  (8.89e-254, 8.89e-254j)
| (1.8629738504950506515 - 3.473462477255563255e-979j)  +/-  (1.22e-248, 1.22e-248j)
| (-2.8516210371571591626 + 1.6202703981935772105e-978j)  +/-  (2.08e-246, 2.08e-246j)
| (-0.60450531534020979857 - 7.3758972532170118276e-985j)  +/-  (1.24e-252, 1.24e-252j)
| (-0.30093763012467238823 - 1.9776664551511540818e-985j)  +/-  (8.89e-254, 8.89e-254j)
| (3.8831291656386980172 - 9.1113152197818729587e-982j)  +/-  (6.25e-245, 6.25e-245j)
| (2.1883319529349756662 + 1.7688440488696414707e-986j)  +/-  (7.98e-248, 7.98e-248j)
| (1.541726944100363691 + 6.1558285471549539405e-988j)  +/-  (1.57e-249, 1.57e-249j)
| (-2.1883319529349756662 + 7.796766713206742532e-987j)  +/-  (8.03e-248, 8.03e-248j)
| (-0.91228969228252829534 + 3.7471147859601293511e-990j)  +/-  (1.69e-251, 1.69e-251j)
-------------------------------------------------
The weights are:
| (5.5753825710999322004e-05 - 2.8727938878507052532e-860j)  +/-  (2.35e-62, 7.75e-185j)
| (9.2274878677981832982e-30 - 2.6308953650324461427e-874j)  +/-  (1.53e-83, 5.05e-206j)
| (4.7932546080586163274e-26 + 2.2743363871917452953e-872j)  +/-  (3.99e-82, 1.32e-204j)
| (9.3854077339941546112e-16 - 1.9048561252731026175e-867j)  +/-  (6.67e-79, 2.2e-201j)
| (1.3059466365691391564e-10 + 3.4082477187986480098e-864j)  +/-  (6.64e-75, 2.19e-197j)
| (4.7932546080586163274e-26 - 8.4540630660884102857e-873j)  +/-  (1.15e-84, 3.79e-207j)
| (7.1998510795274788695e-18 - 4.8471909936018432105e-868j)  +/-  (1.62e-80, 5.34e-203j)
| (6.1815837323676348784e-23 + 3.2704780264702377124e-871j)  +/-  (1.37e-83, 4.53e-206j)
| (3.0456916416867581478e-20 + 2.5981227654098148459e-869j)  +/-  (9.21e-82, 3.04e-204j)
| (9.3854077339941546112e-16 + 6.747133069407904828e-867j)  +/-  (6.71e-80, 2.22e-202j)
| (1.4895391117189483721e-34 - 3.8396263705590461162e-877j)  +/-  (8.45e-90, 2.79e-212j)
| (1.4895391117189483721e-34 + 8.6662658023155843172e-877j)  +/-  (3.43e-88, 1.13e-210j)
| (0.039624916678602944819 + 1.1146265565641823839e-859j)  +/-  (1.11e-59, 3.68e-182j)
| (0.00033026953191792548014 + 5.1791834144799668246e-861j)  +/-  (1.55e-70, 5.13e-193j)
| (0.016716292355742534739 - 6.0104284627266798153e-860j)  +/-  (1.94e-63, 6.4e-186j)
| (3.7745357599802455985e-12 + 6.7273406885828685067e-865j)  +/-  (2.7e-79, 8.92e-202j)
| (7.4033771751600412492e-14 + 1.2542926154007920684e-866j)  +/-  (2.19e-81, 7.22e-204j)
| (0.0056722656728298486271 + 2.9340761599302902812e-860j)  +/-  (1.63e-67, 5.39e-190j)
| (3.1826364133730327201e-09 + 3.4799738832226850216e-863j)  +/-  (3.57e-78, 1.18e-200j)
| (7.4033771751600412492e-14 - 7.4322792118104843691e-866j)  +/-  (5.26e-80, 1.74e-202j)
| (3.0456916416867581478e-20 - 7.6215570409313143761e-870j)  +/-  (3.26e-85, 1.08e-207j)
| (0.039624916678602944819 + 2.6668590523705288805e-859j)  +/-  (1.06e-66, 3.49e-189j)
| (6.1815837323676348784e-23 - 9.7648791356698170677e-871j)  +/-  (2.07e-84, 6.83e-207j)
| (0.11960825349211707601 + 4.2195109404846249603e-859j)  +/-  (5.98e-67, 1.98e-189j)
| (7.3190234591552841512e-06 + 6.0617484547671149069e-862j)  +/-  (5.2e-77, 1.72e-199j)
| (3.1826364133730327201e-09 - 1.3544801564659746968e-863j)  +/-  (4.09e-80, 1.35e-202j)
| (7.1998510795274788695e-18 + 1.1466857118189648408e-868j)  +/-  (1.61e-84, 5.31e-207j)
| (9.2274878677981832982e-30 + 1.0701041738230169221e-874j)  +/-  (1.94e-90, 6.42e-213j)
| (1.3059466365691391564e-10 - 5.1685516195121573848e-864j)  +/-  (3.14e-82, 1.04e-204j)
| (5.6247039057970043797e-08 + 4.8438657586213427558e-863j)  +/-  (2.36e-80, 7.79e-203j)
| (3.7745357599802455985e-12 - 1.5545069608887211396e-867j)  +/-  (4.7e-82, 1.55e-204j)
| (0.00033026953191792548014 + 7.3752540853090811887e-860j)  +/-  (1.1e-79, 3.64e-202j)
| (7.3780546909474101915e-07 + 1.2744199105841577373e-861j)  +/-  (4.41e-82, 1.45e-204j)
| (0.076119381586906109777 - 3.5032099443698002405e-859j)  +/-  (6.68e-76, 2.21e-198j)
| (7.3780546909474101915e-07 - 1.7820978797237445413e-862j)  +/-  (6.11e-81, 2.02e-203j)
| (0.16951288623579623009 + 4.4120640635064830785e-859j)  +/-  (1.41e-76, 4.66e-199j)
| (7.3190234591552841512e-06 - 8.8613338250922208801e-861j)  +/-  (1.77e-81, 5.85e-204j)
| (0.15557099489080675878 - 4.5792118925536025744e-859j)  +/-  (6.53e-77, 2.14e-199j)
| (0.0056722656728298486271 + 1.2952867274540068983e-859j)  +/-  (6.07e-80, 2.01e-202j)
| (5.5753825710999322004e-05 - 1.8662179913315703637e-861j)  +/-  (5.01e-81, 1.67e-203j)
| (0.11960825349211707601 + 2.8035403899937515753e-859j)  +/-  (2.26e-78, 7.38e-201j)
| (0.15557099489080675878 - 3.7446653142581956876e-859j)  +/-  (4.16e-78, 1.36e-200j)
| (5.6247039057970043797e-08 - 2.1349997843260645763e-862j)  +/-  (5.92e-83, 1.95e-205j)
| (0.0015373124544197870774 - 8.9410414983631469081e-860j)  +/-  (1.19e-80, 3.92e-203j)
| (0.016716292355742534739 - 1.8974784595687447801e-859j)  +/-  (7.13e-80, 2.33e-202j)
| (0.0015373124544197870774 - 1.2966315920308878013e-860j)  +/-  (2.92e-81, 1.12e-203j)
| (0.076119381586906109777 - 1.8662562377331481074e-859j)  +/-  (8.33e-80, 2.27e-202j)
