Starting with polynomial:
P : 2*t
Extension levels are: 1 20 22
-------------------------------------------------
Trying to find an order 20 Kronrod extension for:
P1 : 2*t
Solvable: 1
-------------------------------------------------
Trying to find an order 22 Kronrod extension for:
P2 : 2*t^21 - 10*t^19 + 171/8*t^17 - 51/2*t^15 + 595/32*t^13 - 273/32*t^11 + 5005/2048*t^9 - 429/1024*t^7 + 1287/32768*t^5 - 55/32768*t^3 + 11/524288*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^43 - 21*t^41 + 205/2*t^39 - 1235/4*t^37 + 82251/128*t^35 - 250971/256*t^33 + 145299/128*t^31 - 260865/256*t^29 + 5883955/8192*t^27 - 6556407/16384*t^25 + 5785065/32768*t^23 - 4032015/65536*t^21 + 141120525/8388608*t^19 - 59879925/16777216*t^17 + 9694845/16777216*t^15 - 2340135/33554432*t^13 + 13037895/2147483648*t^11 - 1562275/4294967296*t^9 + 120175/8589934592*t^7 - 5313/17179869184*t^5 + 1771/549755813888*t^3 - 11/1099511627776*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:   43 out of 43
Indefinite weights: 0 out of 43
Negative weights:   0 out of 43
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-0.95949297361449738989 + 4.3319369184154583143e-866j)  +/-  (5.67e-241, 5.67e-241j)
| (0.98982144188093273238 + 4.9121097565106013812e-868j)  +/-  (3.45e-241, 3.45e-241j)
| (-0.84125353283118116886 + 4.9356473498102047178e-869j)  +/-  (4.23e-242, 4.23e-242j)
| (0.99745211461025354136 + 3.308564339239746523e-869j)  +/-  (1.07e-241, 1.07e-241j)
| (0.93694972499976173582 - 2.5755601518677160082e-868j)  +/-  (4.04e-241, 4.04e-241j)
| (0.90963199535451837141 + 1.8615096689933810281e-868j)  +/-  (2.14e-241, 2.14e-241j)
| (-0.98982144188093273238 - 1.0822355865654164252e-866j)  +/-  (3.86e-241, 3.86e-241j)
| (-0.90963199535451837141 + 1.9699115681182847666e-867j)  +/-  (2.22e-241, 2.22e-241j)
| (-0.87767898956725561521 - 5.2785560992668951325e-869j)  +/-  (1.32e-241, 1.32e-241j)
| (-0.99745211461025354136 + 3.9727557874481202128e-868j)  +/-  (1.08e-241, 1.08e-241j)
| (0.87767898956725561521 - 2.8207772553926152611e-869j)  +/-  (1.08e-241, 1.08e-241j)
| (0.95949297361449738989 + 5.3229863296255372316e-870j)  +/-  (5.18e-241, 5.18e-241j)
| (-0.97714686597115951949 - 2.0273913849235941588e-870j)  +/-  (5.1e-241, 5.1e-241j)
| (-0.75574957435425828377 - 2.2282227038283571271e-873j)  +/-  (3.62e-243, 3.62e-243j)
| (0.97714686597115951949 - 1.8810342502225095411e-873j)  +/-  (5.54e-241, 5.54e-241j)
| (0.84125353283118116886 + 9.7451019115092839794e-875j)  +/-  (4.11e-242, 4.11e-242j)
| (0.80054124092436040397 + 1.1818229989393269392e-875j)  +/-  (1.32e-242, 1.32e-242j)
| (-0.34946417959909833671 - 7.6031157296411118033e-877j)  +/-  (1.18e-249, 1.18e-249j)
| (-0.80054124092436040397 + 2.2016087397247838884e-873j)  +/-  (1.45e-242, 1.45e-242j)
| (-0.93694972499976173582 - 1.3676269680690445729e-875j)  +/-  (4.7e-241, 4.7e-241j)
| (0.75574957435425828377 + 3.5147962480050406022e-878j)  +/-  (3.02e-243, 3.02e-243j)
| (0.7071067811865475244 + 1.6559602215651532044e-882j)  +/-  (7.53e-244, 7.53e-244j)
| (0.14231483827328514044 - 1.6321570094252776757e-891j)  +/-  (2.37e-253, 2.37e-253j)
| (-0.7071067811865475244 - 7.8495402629825709683e-882j)  +/-  (7.68e-244, 7.68e-244j)
| (-0.65486073394528506406 + 1.0413447978738934608e-889j)  +/-  (1.18e-244, 1.18e-244j)
| (0.21256528955297667388 - 8.2418973680346673075e-904j)  +/-  (5.73e-252, 5.73e-252j)
| (0.65486073394528506406 - 5.427926164797237858e-901j)  +/-  (1.31e-244, 1.31e-244j)
| (0.4792489867200568312 - 7.7568465795130284682e-905j)  +/-  (2.41e-247, 2.41e-247j)
| (-0.14231483827328514044 + 5.4512915906356231113e-903j)  +/-  (2.64e-253, 2.64e-253j)
| (-0.59927766651134693453 - 1.1105042788318659445e-909j)  +/-  (1.85e-245, 1.85e-245j)
| (-0.28173255684142969771 + 1.9765638022957956507e-927j)  +/-  (7.73e-251, 7.73e-251j)
| (0.41541501300188642553 + 2.3051232729712681771e-932j)  +/-  (1.73e-248, 1.73e-248j)
| (0.59927766651134693453 + 4.4601481608039192307e-937j)  +/-  (1.8e-245, 1.8e-245j)
| (-1.0071013413545283457e-942 + 2.6051114903222853482e-942j)  +/-  (1.2e-940, 1.2e-940j)
| (-0.41541501300188642553 - 2.1302569222654619186e-955j)  +/-  (2.1e-248, 2.1e-248j)
| (-0.54064081745559758211 - 1.4946221125236918668e-984j)  +/-  (2.04e-246, 2.04e-246j)
| (0.071339183199232340327 + 1.419354562296346878e-997j)  +/-  (1.71e-254, 1.71e-254j)
| (0.54064081745559758211 - 2.3549773414995172378e-996j)  +/-  (2.05e-246, 2.05e-246j)
| (0.28173255684142969771 - 3.7090171759623835645e-1000j)  +/-  (8.82e-251, 8.82e-251j)
| (-0.21256528955297667388 + 3.1731622548075336044e-997j)  +/-  (4.73e-252, 4.73e-252j)
| (-0.4792489867200568312 - 2.0821398002390106049e-1003j)  +/-  (2.29e-247, 2.29e-247j)
| (-0.071339183199232340327 - 1.3956880732620855489e-1010j)  +/-  (1.71e-254, 1.71e-254j)
| (0.34946417959909833671 + 9.8631105137358227686e-1008j)  +/-  (1.25e-249, 1.25e-249j)
-------------------------------------------------
The weights are:
| (0.0018039371269183958084 + 6.8052137479209721539e-868j)  +/-  (1.36e-72, 2.24e-189j)
| (0.00046030711801707511488 - 2.9478578236119813692e-870j)  +/-  (5.7e-73, 9.43e-190j)
| (0.0066430112158876542553 + 2.1320567863478798126e-867j)  +/-  (2.16e-73, 3.58e-190j)
| (0.00011566543317121895027 - 1.1385252250342437621e-869j)  +/-  (4.09e-73, 6.77e-190j)
| (0.0027755730187016104117 - 3.7445841666645970347e-869j)  +/-  (9.11e-74, 1.51e-190j)
| (0.0039220371142581242721 + 9.9583559074652782478e-870j)  +/-  (5.81e-74, 9.61e-191j)
| (0.00046030711801707511488 - 1.0586011245968132233e-867j)  +/-  (1.93e-75, 3.19e-192j)
| (0.0039220371142581242721 + 2.910345412734624489e-867j)  +/-  (2.95e-75, 4.88e-192j)
| (0.0052199907107318456579 - 2.5566033051800433245e-867j)  +/-  (2.99e-75, 4.95e-192j)
| (0.00011566543317121895027 - 1.5788254447205642887e-869j)  +/-  (6.82e-76, 1.13e-192j)
| (0.0052199907107318456579 - 2.2093554156441480914e-869j)  +/-  (2.4e-76, 3.97e-193j)
| (0.0018039371269183958084 + 3.2492674722874189633e-869j)  +/-  (6.85e-76, 1.13e-192j)
| (0.0010269091436986548703 + 3.448085961083768942e-867j)  +/-  (5.42e-76, 8.96e-193j)
| (0.009746422292349032495 + 1.7349828612362533797e-867j)  +/-  (1.08e-78, 1.79e-195j)
| (0.0010269091436986548703 + 9.8695001017033655321e-870j)  +/-  (6.57e-76, 1.09e-192j)
| (0.0066430112158876542553 + 6.5024911148031113728e-869j)  +/-  (8.27e-78, 1.37e-194j)
| (0.0081621300358928443442 - 1.0725669176179958147e-868j)  +/-  (9.01e-79, 1.49e-195j)
| (0.019951699708571116861 - 1.1272961466025653459e-867j)  +/-  (2.48e-82, 4.09e-199j)
| (0.0081621300358928443442 - 1.8999030566338724791e-867j)  +/-  (1.21e-78, 2e-195j)
| (0.0027755730187016104117 - 4.5419285735780329976e-867j)  +/-  (1.84e-77, 3.05e-194j)
| (0.009746422292349032495 + 1.4839961735544067824e-868j)  +/-  (2.62e-80, 4.34e-197j)
| (0.011363636363636363636 - 1.9110335852074842057e-868j)  +/-  (2.86e-81, 4.72e-198j)
| (0.022266965609255652158 + 6.7319071473910539694e-868j)  +/-  (2.44e-84, 4.04e-201j)
| (0.011363636363636363636 - 1.6118127227903640126e-867j)  +/-  (1.18e-81, 1.96e-198j)
| (0.012980850434923694778 + 1.5108688496845398114e-867j)  +/-  (1.55e-82, 2.56e-199j)
| (0.021700363583574072402 - 6.1241510768671769279e-868j)  +/-  (2.95e-85, 4.88e-202j)
| (0.012980850434923694778 + 2.3603567877162781431e-868j)  +/-  (2.08e-83, 3.44e-200j)
| (0.017507282016540881615 - 3.8505547352306924949e-868j)  +/-  (3.41e-85, 5.64e-202j)
| (0.022266965609255652158 + 9.2710429417241528581e-868j)  +/-  (2.03e-86, 3.36e-203j)
| (0.014565142691379882929 - 1.4229446083475112639e-867j)  +/-  (8.04e-85, 1.33e-201j)
| (0.020923335600354331464 + 1.0594915777559684506e-867j)  +/-  (2.93e-86, 4.85e-203j)
| (0.018805235613014603001 + 4.3915992408965667781e-868j)  +/-  (2.1e-86, 3.47e-203j)
| (0.014565142691379882929 - 2.8336545155842226966e-868j)  +/-  (1.84e-85, 3.04e-202j)
| (0.022727272727272727273 + 7.9823716914894801498e-868j)  +/-  (1.81e-87, 3e-204j)
| (0.018805235613014603001 + 1.1966361374785023516e-867j)  +/-  (3.49e-87, 5.77e-204j)
| (0.016084261511385073017 + 1.3430247442425786287e-867j)  +/-  (6.69e-87, 1.11e-203j)
| (0.022611607294101508322 - 7.3518192641805163367e-868j)  +/-  (8.5e-88, 1.4e-204j)
| (0.016084261511385073017 + 3.3307386600270525857e-868j)  +/-  (1.88e-87, 3.1e-204j)
| (0.020923335600354331464 + 5.5302754685038827306e-868j)  +/-  (2.38e-88, 3.95e-205j)
| (0.021700363583574072402 - 9.928298573238858512e-868j)  +/-  (1.21e-88, 2.02e-205j)
| (0.017507282016540881615 - 1.268180776603754664e-867j)  +/-  (1.46e-88, 2.44e-205j)
| (0.022611607294101508322 - 8.6223629722790718477e-868j)  +/-  (8.08e-89, 1.37e-205j)
| (0.019951699708571116861 - 4.9521271966876772028e-868j)  +/-  (5.5e-89, 8.56e-206j)
