Starting with polynomial:
P : t
Extension levels are: 1 4 32
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 32 Kronrod extension for:
P2 : t^5 - 10*t^3 + 15*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^37 - 58546143341873950838/95149754265757479*t^35 + 112260395072761551226535/666048279860302353*t^33 - 6041588996376158281810160/222016093286767451*t^31 + 22126443518343101053645100/7655727354716119*t^29 - 233444927202359348100319640/1093675336388017*t^27 + 12359203476763425032689489980/1093675336388017*t^25 - 476701297621021623491397342000/1093675336388017*t^23 + 13483104573553783305964847484750/1093675336388017*t^21 - 279379632492871529072263578697500/1093675336388017*t^19 + 4208094708709089552490460083295250/1093675336388017*t^17 - 45397637068760450063601423821838000/1093675336388017*t^15 + 342796885010052090778678199464282500/1093675336388017*t^13 - 1751652111867793967615518337938335000/1093675336388017*t^11 + 5767097095305731024594158541124487500/1093675336388017*t^9 - 11368877416795180857147075221248530000/1093675336388017*t^7 + 11942582162355816791843849902026575625/1093675336388017*t^5 - 5428910299205575575286200251150456250/1093675336388017*t^3 + 664838004747515679748392921831009375/1093675336388017*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:   37 out of 37
Indefinite weights: 0 out of 37
Negative weights:   0 out of 37
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (6.7989755889015816601 + 8.1211860142549376791e-570j)  +/-  (2.36e-246, 2.36e-246j)
| (-10.678571095673114377 - 1.9396074242401735718e-575j)  +/-  (1.58e-248, 1.58e-248j)
| (8.8654213429651079384 - 5.3848267116272742034e-590j)  +/-  (5.86e-247, 5.86e-247j)
| (-8.1274302762710404811 - 1.2041572884266058367e-589j)  +/-  (1.59e-246, 1.59e-246j)
| (-9.6887614191812044188 + 7.2453460787351115658e-603j)  +/-  (1.54e-247, 1.54e-247j)
| (10.678571095673114377 - 7.5608118655850048567e-615j)  +/-  (1.71e-248, 1.71e-248j)
| (7.4439014694436400744 + 5.876373221066639228e-612j)  +/-  (2.34e-246, 2.34e-246j)
| (5.5903582833160686495 - 3.7105038361350749464e-612j)  +/-  (1.49e-246, 1.49e-246j)
| (-3.3793404540389733114 - 2.0656748225359938247e-613j)  +/-  (2.14e-248, 2.14e-248j)
| (9.6887614191812044188 - 1.1223421989072627174e-622j)  +/-  (1.67e-247, 1.67e-247j)
| (1.844080007303313832 - 2.1047690897764977636e-623j)  +/-  (1.07e-250, 1.07e-250j)
| (3.3793404540389733114 - 6.0293201679538829524e-625j)  +/-  (2.17e-248, 2.17e-248j)
| (-5.5903582833160686495 + 6.3547018163278254311e-635j)  +/-  (1.55e-246, 1.55e-246j)
| (-1.3556261799742658658 - 2.7713368304245755446e-658j)  +/-  (1.32e-251, 1.32e-251j)
| (-6.1831883586146615348 - 8.7703966115969598586e-680j)  +/-  (2.15e-246, 2.15e-246j)
| (6.1831883586146615348 + 7.5222354897263689315e-702j)  +/-  (2.15e-246, 2.15e-246j)
| (-7.4439014694436400744 - 1.7727359803849023304e-725j)  +/-  (2.26e-246, 2.26e-246j)
| (-2.8569700138728056542 - 2.2895837305849185264e-744j)  +/-  (4.72e-249, 4.72e-249j)
| (1.3556261799742658658 - 2.7413914975682556996e-752j)  +/-  (1.28e-251, 1.28e-251j)
| (8.1274302762710404811 + 2.6164566999572364072e-747j)  +/-  (1.48e-246, 1.48e-246j)
| (3.9125840901482804969 + 6.8855795430359117627e-749j)  +/-  (8.29e-248, 8.29e-248j)
| (5.0162106082416870131 - 1.4202054309135134943e-747j)  +/-  (7.38e-247, 7.38e-247j)
| (4.457688579104722789 - 5.7562814372201198888e-749j)  +/-  (2.58e-247, 2.58e-247j)
| (-5.0162106082416870131 - 1.2811657725089974585e-746j)  +/-  (6.46e-247, 6.46e-247j)
| (-2.3450829237213079751 + 2.1850212696404627628e-758j)  +/-  (7.96e-250, 7.96e-250j)
| (-6.7989755889015816601 + 2.8796743929764086514e-763j)  +/-  (2.41e-246, 2.41e-246j)
| (2.3450829237213079751 - 1.6120178369219056091e-778j)  +/-  (9e-250, 9e-250j)
| (0.88337111686406204862 - 4.4506354574138891523e-781j)  +/-  (1.2e-252, 1.2e-252j)
| (-4.457688579104722789 + 1.0257262247588216652e-774j)  +/-  (2.65e-247, 2.65e-247j)
| (-0.88337111686406204862 + 3.6678044894751592442e-789j)  +/-  (1.16e-252, 1.16e-252j)
| (-3.9125840901482804969 + 3.9078488222816295322e-785j)  +/-  (7.94e-248, 7.94e-248j)
| (2.8569700138728056542 - 1.0094046599984804812e-795j)  +/-  (4.88e-249, 4.88e-249j)
| (0.43219082853027765133 + 3.3305281936354203646e-799j)  +/-  (1.15e-253, 1.15e-253j)
| (-8.8654213429651079384 - 2.7446700042763258693e-802j)  +/-  (6.34e-247, 6.34e-247j)
| (-0.43219082853027765133 + 6.2039378564475995039e-826j)  +/-  (1.02e-253, 1.02e-253j)
| (-1.844080007303313832 - 1.2993122197896170527e-820j)  +/-  (1.15e-250, 1.15e-250j)
| (1.7493156024566616486e-827 + 1.298210495889876414e-827j)  +/-  (8.06e-826, 8.06e-826j)
-------------------------------------------------
The weights are:
| (2.3002624493696673753e-11 - 6.8355406625682421237e-580j)  +/-  (7.22e-88, 2.79e-211j)
| (7.8773309820135630015e-26 + 2.7310326844985192518e-589j)  +/-  (2.3e-95, 8.88e-219j)
| (2.6453806545913565752e-18 - 1.8963385293741315299e-584j)  +/-  (1.28e-92, 4.95e-216j)
| (1.2788987657373754545e-15 - 6.7721659481964527014e-584j)  +/-  (8.02e-92, 3.1e-215j)
| (1.457397100652228159e-21 - 4.7288281205288205212e-587j)  +/-  (4.77e-94, 1.84e-217j)
| (7.8773309820135630015e-26 - 1.2303280369973118662e-588j)  +/-  (1.88e-96, 7.26e-220j)
| (2.4516168481765435741e-13 - 2.5445038728162321488e-581j)  +/-  (5.7e-91, 2.2e-214j)
| (3.8035676395521828403e-08 - 8.8098476088780447242e-579j)  +/-  (3.25e-88, 1.26e-211j)
| (0.00069739586801630010896 - 3.0853026788748518093e-577j)  +/-  (3.92e-84, 1.51e-207j)
| (1.457397100652228159e-21 + 2.6980433494817339384e-586j)  +/-  (7.7e-95, 2.98e-218j)
| (0.03607503156114633023 + 9.3832580459055577161e-576j)  +/-  (2.84e-77, 1.1e-200j)
| (0.00069739586801630010896 - 9.1831977726456018639e-577j)  +/-  (1.04e-83, 4.03e-207j)
| (3.8035676395521828403e-08 - 8.5942750348588365438e-580j)  +/-  (5.28e-91, 2.04e-214j)
| (0.076584258355598676076 - 1.088792557300905106e-575j)  +/-  (6.28e-77, 2.43e-200j)
| (1.2012415319038830317e-09 + 1.2274087617963717558e-580j)  +/-  (3.28e-92, 1.27e-215j)
| (1.2012415319038830317e-09 + 2.5876505702868283316e-579j)  +/-  (1.32e-90, 5.09e-214j)
| (2.4516168481765435741e-13 + 1.1521663734047653678e-582j)  +/-  (1.76e-94, 6.8e-218j)
| (0.0034840548902827873177 + 9.1037887236950812044e-577j)  +/-  (1.42e-85, 5.47e-209j)
| (0.076584258355598676076 - 1.6311041321625683329e-575j)  +/-  (7.28e-80, 2.81e-203j)
| (1.2788987657373754545e-15 + 7.6091490730056623771e-583j)  +/-  (7.26e-94, 2.8e-217j)
| (0.00010193207697849650373 + 3.3672070405464125338e-577j)  +/-  (2.65e-88, 1.03e-211j)
| (7.7573710539917525809e-07 + 3.2274718378227927505e-578j)  +/-  (3.33e-90, 1.29e-213j)
| (1.065439070232153041e-05 - 1.099747840984989486e-577j)  +/-  (1.68e-89, 6.5e-213j)
| (7.7573710539917525809e-07 + 4.8698545012553914893e-579j)  +/-  (1.12e-93, 4.34e-217j)
| (0.012923754709752242437 - 2.3546014726080713755e-576j)  +/-  (2.93e-89, 1.13e-212j)
| (2.3002624493696673753e-11 - 1.3737995517596646993e-581j)  +/-  (2.32e-96, 8.96e-220j)
| (0.012923754709752242437 - 4.8341114746127293632e-576j)  +/-  (2.16e-89, 8.35e-213j)
| (0.12488078397886620065 + 2.5121463675853499641e-575j)  +/-  (7.72e-88, 2.98e-211j)
| (1.065439070232153041e-05 - 2.2873786547413426422e-578j)  +/-  (2.17e-93, 8.37e-217j)
| (0.12488078397886620065 + 1.9344172888404332202e-575j)  +/-  (1.4e-89, 5.49e-213j)
| (0.00010193207697849650373 + 9.0734478148687494763e-578j)  +/-  (9.27e-93, 3.58e-216j)
| (0.0034840548902827873177 + 2.2299737283992911784e-576j)  +/-  (4.59e-91, 1.8e-214j)
| (0.15987828367513700302 - 3.3062542106733527452e-575j)  +/-  (1.9e-89, 7.4e-213j)
| (2.6453806545913565752e-18 + 2.501647985125652802e-585j)  +/-  (1.08e-100, 4.17e-224j)
| (0.15987828367513700302 - 2.9110392027049518665e-575j)  +/-  (2.73e-90, 1.1e-213j)
| (0.03607503156114633023 + 5.379239241855617386e-576j)  +/-  (3.71e-91, 1.4e-214j)
| (0.1707260709924944956 + 3.5094906175212877978e-575j)  +/-  (2.08e-90, 8.54e-214j)
