Starting with polynomial:
P : 16*t^4 - 12*t^2 + 1
Extension levels are: 4 5 30 40
-------------------------------------------------
Trying to find an order 5 Kronrod extension for:
P1 : 16*t^4 - 12*t^2 + 1
Solvable: 1
-------------------------------------------------
Trying to find an order 30 Kronrod extension for:
P2 : 16*t^9 - 32*t^7 + 21*t^5 - 5*t^3 + 5/16*t
Solvable: 1
-------------------------------------------------
Trying to find an order 40 Kronrod extension for:
P3 : 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
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 16*t^79 - 312*t^77 + 2926*t^75 - 17575*t^73 + 607725/8*t^71 - 4027191/16*t^69 + 42557613/64*t^67 - 184138713/128*t^65 + 1329890705/512*t^63 - 4064595535/1024*t^61 + 21252028083/4096*t^59 - 47908063307/8192*t^57 + 374810142343/65536*t^55 - 639027625005/131072*t^53 + 1906017461595/524288*t^51 - 2492484372855/1048576*t^49 + 366395202809685/268435456*t^47 - 369816259792035/536870912*t^45 + 656125622211675/2147483648*t^43 - 511200549488475/4294967296*t^41 + 1397281501935165/34359738368*t^39 - 835662302610135/68719476736*t^37 + 872337137207445/274877906944*t^35 - 395911973027025/549755813888*t^33 + 622147386185325/4398046511104*t^31 - 210398934237219/8796093022208*t^29 + 121683714103007/35184372088832*t^27 - 29846948742247/70368744177664*t^25 + 24599133578775/562949953421312*t^23 - 4207965378925/1125899906842624*t^21 + 1178230306099/4503599627370496*t^19 - 132638171391/9007199254740992*t^17 + 751616304549/1152921504606846976*t^15 - 50883115395/2305843009213693952*t^13 + 5075297955/9223372036854775808*t^11 - 177232627/18446744073709551616*t^9 + 16112057/147573952589676412928*t^7 - 212667/295147905179352825856*t^5 + 2665/1180591620717411303424*t^3 - 5/2361183241434822606848*t
-------------------------------------------------
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: 0
  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:
| (0.98768834059513772619 + 5.8129498845162588544e-822j)  +/-  (1.6e-227, 1.6e-227j)
| (-0.95105651629515357212 - 2.0341187688404069407e-820j)  +/-  (7.45e-228, 7.45e-228j)
| (-0.90814317382508129926 + 3.2488327387293934119e-826j)  +/-  (1.11e-228, 1.11e-228j)
| (-0.9969173337331279762 + 3.8613986127342008651e-824j)  +/-  (7.01e-228, 7.01e-228j)
| (0.89100652418836786236 - 2.7683020888975950111e-837j)  +/-  (4.97e-229, 4.97e-229j)
| (0.93819133592248413445 + 2.6173701268463589396e-835j)  +/-  (4.48e-228, 4.48e-228j)
| (0.9969173337331279762 + 1.1444875254609456786e-834j)  +/-  (6.83e-228, 6.83e-228j)
| (-0.92387953251128675613 + 3.32602428928510899e-835j)  +/-  (2.37e-228, 2.37e-228j)
| (-0.99922903624072293474 + 2.1328737768695132591e-832j)  +/-  (1.96e-228, 1.96e-228j)
| (-0.98768834059513772619 + 1.9319925778903488489e-837j)  +/-  (1.67e-227, 1.67e-227j)
| (0.87249600707279711453 - 4.4765996613033902259e-850j)  +/-  (1.76e-229, 1.76e-229j)
| (0.97236992039767660183 + 2.5437639917989056355e-847j)  +/-  (1.71e-227, 1.71e-227j)
| (-0.89100652418836786236 - 4.5483084105147503058e-849j)  +/-  (4.95e-229, 4.95e-229j)
| (-0.83146961230254523708 + 5.8684019705628837731e-852j)  +/-  (2.06e-230, 2.06e-230j)
| (0.98078528040323044913 - 4.1787378299327264363e-848j)  +/-  (1.72e-227, 1.72e-227j)
| (0.8090169943749474241 - 1.9979181338360166402e-853j)  +/-  (5.67e-231, 5.67e-231j)
| (0.83146961230254523708 - 1.5120681135017549681e-852j)  +/-  (1.9e-230, 1.9e-230j)
| (0.99306845695492629564 + 1.1515961879641300112e-849j)  +/-  (1.34e-227, 1.34e-227j)
| (-0.8090169943749474241 + 5.2252392144511384542e-852j)  +/-  (6.03e-231, 6.03e-231j)
| (-0.93819133592248413445 + 8.6070738802680345405e-848j)  +/-  (4.49e-228, 4.49e-228j)
| (0.92387953251128675613 - 2.2748030506608438835e-858j)  +/-  (2.36e-228, 2.36e-228j)
| (0.73432250943568553564 + 8.4572705318552501787e-864j)  +/-  (6.63e-233, 6.63e-233j)
| (0.99922903624072293474 + 8.0624656522318872991e-859j)  +/-  (2.01e-228, 2.01e-228j)
| (-0.85264016435409222152 - 2.3671101218822420055e-858j)  +/-  (6.22e-230, 6.22e-230j)
| (-0.78531693088074492747 + 3.6670191987996382172e-861j)  +/-  (1.44e-231, 1.44e-231j)
| (0.23344536385590541177 + 1.3028854314075423195e-878j)  +/-  (4.75e-248, 4.75e-248j)
| (0.7071067811865475244 - 1.0128635252252486319e-864j)  +/-  (1.3e-233, 1.3e-233j)
| (0.78531693088074492747 + 1.4666228479668166277e-862j)  +/-  (1.4e-231, 1.4e-231j)
| (0.96245523645364728763 + 2.9456240927321209974e-859j)  +/-  (1.11e-227, 1.11e-227j)
| (-0.64944804833018365573 + 2.9557941175226616027e-865j)  +/-  (3.05e-235, 3.05e-235j)
| (-0.87249600707279711453 + 3.220450054389773952e-857j)  +/-  (1.78e-229, 1.78e-229j)
| (0.76040596560003093817 + 1.3889869303005896502e-866j)  +/-  (3.46e-232, 3.46e-232j)
| (0.61909394930983398694 - 4.5230472709332836391e-871j)  +/-  (4.34e-236, 4.34e-236j)
| (-0.96245523645364728763 + 2.5943097492966333014e-860j)  +/-  (1.03e-227, 1.03e-227j)
| (-0.67880074553294174139 - 1.7666680304726900622e-889j)  +/-  (2.54e-234, 2.54e-234j)
| (-0.7071067811865475244 - 2.2326006256404625597e-888j)  +/-  (1.29e-233, 1.29e-233j)
| (0.85264016435409222152 + 1.7655584844527804765e-885j)  +/-  (6.14e-230, 6.14e-230j)
| (0.58778525229247312917 - 8.4372421975433892783e-892j)  +/-  (6.2e-237, 6.2e-237j)
| (0.90814317382508129926 + 7.5584841197908491487e-884j)  +/-  (1.35e-228, 1.35e-228j)
| (-0.97236992039767660183 - 2.4178323981609209848e-881j)  +/-  (1.56e-227, 1.56e-227j)
| (-0.55557023301960222474 - 9.6064645851743209156e-915j)  +/-  (6.49e-238, 6.49e-238j)
| (-0.99306845695492629564 + 4.4503831865638789296e-904j)  +/-  (1.13e-227, 1.13e-227j)
| (0.64944804833018365573 - 1.563529770481360121e-928j)  +/-  (3.19e-235, 3.19e-235j)
| (0.67880074553294174139 + 1.4501418552879447113e-927j)  +/-  (2.41e-234, 2.41e-234j)
| (-0.11753739745783764411 + 2.3204247821517880062e-946j)  +/-  (4.97e-252, 4.97e-252j)
| (-0.58778525229247312917 + 3.0429096549370439179e-930j)  +/-  (5.38e-237, 5.38e-237j)
| (-0.61909394930983398694 + 3.0091828669486036074e-931j)  +/-  (4.21e-236, 4.21e-236j)
| (0.95105651629515357212 - 6.9461813242123010161e-925j)  +/-  (7.39e-228, 7.39e-228j)
| (0.45399049973954679156 + 7.5207098804680126415e-939j)  +/-  (6.02e-241, 6.02e-241j)
| (0.55557023301960222474 + 1.3296017833959114152e-936j)  +/-  (6.24e-238, 6.24e-238j)
| (-0.73432250943568553564 - 7.858336630431490618e-928j)  +/-  (6.78e-233, 6.78e-233j)
| (-0.48862124149695494742 - 3.7726299328090621766e-936j)  +/-  (6.38e-240, 6.38e-240j)
| (-0.15643446504023086901 + 7.2887400713086376152e-948j)  +/-  (1.1e-250, 1.1e-250j)
| (0.52249856471594886499 - 2.0473709278491861649e-936j)  +/-  (8.11e-239, 8.11e-239j)
| (0.48862124149695494742 - 1.3662642972591306126e-937j)  +/-  (7.16e-240, 7.16e-240j)
| (0.078459095727844945033 - 1.578198348440487694e-950j)  +/-  (3.07e-253, 3.07e-253j)
| (-0.45399049973954679156 + 2.7736787196550045883e-937j)  +/-  (5.97e-241, 5.97e-241j)
| (-0.76040596560003093817 + 6.3475086742154116299e-930j)  +/-  (3.49e-232, 3.49e-232j)
| (0.19509032201612826785 + 1.0921776377651249123e-947j)  +/-  (2.57e-249, 2.57e-249j)
| (0.41865973753742808668 + 1.1306679475047564926e-941j)  +/-  (4.6e-242, 4.6e-242j)
| (-0.98078528040323044913 + 1.6554951625070476623e-947j)  +/-  (1.82e-227, 1.82e-227j)
| (-0.52249856471594886499 + 1.3963484397133442644e-963j)  +/-  (6.31e-239, 6.31e-239j)
| (-0.41865973753742808668 - 1.235528458522652106e-967j)  +/-  (5.06e-242, 5.06e-242j)
| (-0.078459095727844945033 + 7.6601530267092219214e-979j)  +/-  (3.07e-253, 3.07e-253j)
| (0.38268343236508977173 + 5.2060969862252785528e-969j)  +/-  (3.55e-243, 3.55e-243j)
| (0.27144044986507425334 + 1.2205144309670601856e-972j)  +/-  (9.8e-247, 9.8e-247j)
| (-0.19509032201612826785 + 1.2292068317791186878e-975j)  +/-  (2.35e-249, 2.35e-249j)
| (-0.38268343236508977173 + 2.8130630699082937954e-969j)  +/-  (2.94e-243, 2.94e-243j)
| (-0.23344536385590541177 - 1.7226264370555112939e-973j)  +/-  (4.52e-248, 4.52e-248j)
| (0.11753739745783764411 - 2.5278057841836209782e-977j)  +/-  (6.04e-252, 6.04e-252j)
| (0.34611705707749297647 + 1.9256492288050296247e-971j)  +/-  (2.34e-244, 2.34e-244j)
| (0.039259815759068609021 - 3.0060250129515087236e-980j)  +/-  (1.08e-254, 1.08e-254j)
| (-0.27144044986507425334 - 3.2597287894563398903e-972j)  +/-  (9e-247, 9e-247j)
| (-0.34611705707749297647 - 4.7042285893054700797e-970j)  +/-  (2.45e-244, 2.45e-244j)
| (-3.143930226552737792e-1018 + 3.4821809064362830949e-1018j)  +/-  (3.71e-1016, 3.71e-1016j)
| (0.3090169943749474241 + 4.8837048385517612226e-971j)  +/-  (1.46e-245, 1.46e-245j)
| (0.15643446504023086901 - 1.9201427814815760733e-976j)  +/-  (1.13e-250, 1.13e-250j)
| (-0.039259815759068609021 + 3.3429776328350977843e-980j)  +/-  (1.08e-254, 1.08e-254j)
| (-0.3090169943749474241 - 6.3280472010963318955e-972j)  +/-  (1.5e-245, 1.5e-245j)
-------------------------------------------------
The weights are:
| (0.00030589677315529017427 - 1.3973952345512260757e-823j)  +/-  (2.81e-19, 1.05e-125j)
| (0.0011936437851565785994 - 3.6298684269785102476e-822j)  +/-  (1.3e-19, 4.87e-126j)
| (0.0021909496979363521517 + 1.0391006397009855186e-821j)  +/-  (8.96e-20, 3.35e-126j)
| (7.6947871280389211312e-05 + 3.4179262276291996816e-823j)  +/-  (1.51e-20, 5.64e-127j)
| (0.0025763421731720429427 - 4.3934463638322174808e-823j)  +/-  (7.06e-21, 2.64e-127j)
| (0.0014974627149998066364 + 3.3706214330059836861e-823j)  +/-  (8.98e-21, 3.36e-127j)
| (7.6947871280389211312e-05 + 4.0432593027528276639e-824j)  +/-  (3.01e-21, 1.13e-127j)
| (0.0018305826175840779725 - 1.370594343795150126e-821j)  +/-  (2.13e-20, 7.98e-127j)
| (1.9266664167950148764e-05 - 8.0976731189156290778e-824j)  +/-  (2.99e-21, 1.12e-127j)
| (0.00030589677315529017427 + 1.698986959448608849e-822j)  +/-  (1.94e-21, 7.27e-128j)
| (0.0029843839705253195938 + 4.8343902932907941818e-823j)  +/-  (2.1e-22, 7.85e-129j)
| (0.00068120922382270086025 - 3.3052954285324284408e-823j)  +/-  (1.9e-22, 7.1e-129j)
| (0.0025763421731720429427 - 8.7341196706941266367e-822j)  +/-  (4.88e-22, 1.82e-128j)
| (0.0038582285477181889267 + 6.5741155125481574349e-822j)  +/-  (1.87e-23, 6.99e-130j)
| (0.0004757529218044577742 + 4.507083155858869114e-823j)  +/-  (2.33e-22, 8.71e-129j)
| (0.0043186437851565785994 - 6.395187019168330425e-823j)  +/-  (9.24e-25, 3.46e-131j)
| (0.0038582285477181889267 + 5.8376456849073979558e-823j)  +/-  (2.4e-24, 8.99e-131j)
| (0.00017268799751452123854 - 1.6851599509448348291e-823j)  +/-  (4.18e-23, 1.56e-129j)
| (0.0043186437851565785994 - 6.1977398453732619408e-822j)  +/-  (1.09e-26, 4.06e-133j)
| (0.0014974627149998066364 + 2.3679961380176383655e-821j)  +/-  (6.77e-25, 2.53e-131j)
| (0.0018305826175840779725 - 3.6532863899100954378e-823j)  +/-  (1.61e-24, 6.04e-131j)
| (0.0057596306517009690935 + 8.2715709607994462514e-823j)  +/-  (5.82e-28, 2.18e-134j)
| (1.9266664167950148764e-05 - 7.6953393353959408212e-825j)  +/-  (6.4e-24, 2.4e-130j)
| (0.0034125593766278325527 - 7.0631354501685343392e-822j)  +/-  (8.17e-27, 3.06e-133j)
| (0.0047909664759005911765 + 5.8947899983970402953e-822j)  +/-  (2.8e-28, 1.05e-134j)
| (0.01181879077617729914 - 2.1203345371139731934e-822j)  +/-  (1.76e-32, 6.61e-139j)
| (0.00625 - 8.960503262593494448e-823j)  +/-  (5.86e-29, 2.19e-135j)
| (0.0047909664759005911765 + 6.9876356638821866351e-823j)  +/-  (1.41e-27, 5.28e-134j)
| (0.0009209989727869236155 + 3.1005740670674344089e-823j)  +/-  (8.54e-26, 3.2e-132j)
| (0.0072277154065014429313 - 4.8994112210599202882e-822j)  +/-  (1.13e-32, 4.23e-139j)
| (0.0029843839705253195938 + 7.7357081821357408746e-822j)  +/-  (3.17e-28, 1.19e-134j)
| (0.0052722845934985570687 - 7.6135364267293568999e-823j)  +/-  (2.37e-28, 8.87e-135j)
| (0.0077090335240994088235 + 1.1200932327608780594e-822j)  +/-  (2.1e-32, 7.85e-139j)
| (0.0009209989727869236155 - 1.6433657463312645832e-821j)  +/-  (1.26e-29, 4.72e-136j)
| (0.0067403693482990309065 + 5.0586701218361538193e-822j)  +/-  (8.23e-33, 3.08e-139j)
| (0.00625 - 5.2320329087634418242e-822j)  +/-  (1.5e-32, 5.61e-139j)
| (0.0034125593766278325527 - 5.3166933041716980276e-823j)  +/-  (5.24e-28, 1.96e-134j)
| (0.0081813562148434214006 - 1.2001787552847511723e-822j)  +/-  (1.31e-33, 4.89e-140j)
| (0.0021909496979363521517 + 3.9977285926530973474e-823j)  +/-  (8.33e-28, 3.12e-134j)
| (0.00068120922382270086025 + 6.5004116464399447216e-822j)  +/-  (3.13e-31, 1.17e-137j)
| (0.0086417714522818110733 + 4.4765558781676357711e-822j)  +/-  (1.36e-37, 5.11e-144j)
| (0.00017268799751452123854 - 8.3734079626188062202e-823j)  +/-  (2.04e-31, 7.63e-138j)
| (0.0072277154065014429313 - 1.0426337777679862729e-822j)  +/-  (3.09e-33, 1.16e-139j)
| (0.0067403693482990309065 + 9.6791457333833240618e-823j)  +/-  (1.39e-32, 5.19e-139j)
| (0.012327312002485478761 + 3.0726547487284377674e-822j)  +/-  (1.96e-41, 7.35e-148j)
| (0.0081813562148434214006 - 4.6105308551952503263e-822j)  +/-  (1.44e-37, 5.41e-144j)
| (0.0077090335240994088235 + 4.7508626290890982236e-822j)  +/-  (6.36e-37, 2.38e-143j)
| (0.0011936437851565785994 - 3.1703906077481438933e-823j)  +/-  (2.18e-31, 8.14e-138j)
| (0.0099236578268279570573 - 1.5444958139606863945e-822j)  +/-  (3.63e-40, 1.36e-146j)
| (0.0086417714522818110733 + 1.2827762080969277302e-822j)  +/-  (9.03e-38, 3.38e-144j)
| (0.0057596306517009690935 + 5.4242061618656154714e-822j)  +/-  (2.09e-37, 7.82e-144j)
| (0.0095156160294746804062 + 4.2223958532578321397e-822j)  +/-  (6.5e-42, 2.43e-148j)
| (0.012194103226844709826 - 3.1829156477431574533e-822j)  +/-  (2.38e-44, 8.91e-151j)
| (0.0090874406233721674473 - 1.3677712680885818135e-822j)  +/-  (2.74e-39, 1.02e-145j)
| (0.0095156160294746804062 + 1.4550493744237369089e-822j)  +/-  (3.41e-40, 1.28e-146j)
| (0.012423052128719610789 - 2.5335308015822645306e-822j)  +/-  (4.41e-46, 1.65e-152j)
| (0.0099236578268279570573 - 4.1003237899233320902e-822j)  +/-  (5.13e-44, 1.92e-150j)
| (0.0052722845934985570687 - 5.641871380749460071e-822j)  +/-  (2.01e-39, 7.52e-146j)
| (0.012024247078195542226 + 2.2217980569465875089e-822j)  +/-  (1.47e-45, 5.51e-152j)
| (0.010309050302063647848 + 1.635995917023904384e-822j)  +/-  (5.55e-43, 2.08e-149j)
| (0.0004757529218044577742 - 3.2549602696914368115e-822j)  +/-  (1.44e-39, 5.38e-146j)
| (0.0090874406233721674473 - 4.3475338095634505517e-822j)  +/-  (5.32e-43, 1.99e-149j)
| (0.010309050302063647848 + 3.9806897607834948614e-822j)  +/-  (2.02e-45, 7.55e-152j)
| (0.012423052128719610789 - 2.9631642482458930998e-822j)  +/-  (1.18e-47, 4.4e-154j)
| (0.010669417382415922028 - 1.7294353470952051803e-822j)  +/-  (2.71e-45, 1.02e-151j)
| (0.011579001027213076384 + 2.020259669049193902e-822j)  +/-  (1.44e-46, 5.37e-153j)
| (0.012024247078195542226 + 3.2939500825132355486e-822j)  +/-  (2.23e-48, 8.36e-155j)
| (0.010669417382415922028 - 3.8630125807358866578e-822j)  +/-  (7.69e-48, 2.88e-154j)
| (0.01181879077617729914 - 3.4057873223992231782e-822j)  +/-  (7.02e-49, 2.63e-155j)
| (0.012327312002485478761 + 2.4284898801097196376e-822j)  +/-  (1.41e-49, 5.29e-156j)
| (0.011002537285000193364 + 1.8247004754059178248e-822j)  +/-  (2.65e-48, 9.92e-155j)
| (0.012480733335832049851 + 2.6395880021586383615e-822j)  +/-  (4.07e-50, 1.52e-156j)
| (0.011579001027213076384 + 3.5184882502170658733e-822j)  +/-  (3.54e-50, 1.32e-156j)
| (0.011002537285000193364 + 3.7469255209478762752e-822j)  +/-  (4.72e-50, 1.77e-156j)
| (0.0125 - 2.7465867237191313452e-822j)  +/-  (6.04e-51, 2.26e-157j)
| (0.011306356214843421401 - 1.921678836965765634e-822j)  +/-  (1.93e-50, 7.22e-157j)
| (0.012194103226844709826 - 2.3245487258395356544e-822j)  +/-  (7.01e-51, 2.62e-157j)
| (0.012480733335832049851 + 2.8544627009716522607e-822j)  +/-  (2.99e-51, 1.13e-157j)
| (0.011306356214843421401 - 3.6321521932131057052e-822j)  +/-  (2.37e-51, 8.65e-158j)
