Starting with polynomial:
P : 2*t^2 - 1
Extension levels are: 2 11 24
-------------------------------------------------
Trying to find an order 11 Kronrod extension for:
P1 : 2*t^2 - 1
Solvable: 1
-------------------------------------------------
Trying to find an order 24 Kronrod extension for:
P2 : 2*t^13 - 7*t^11 + 19/2*t^9 - 25/4*t^7 + 259/128*t^5 - 73/256*t^3 + 3/256*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^37 - 19*t^35 + 83*t^33 - 221*t^31 + 51305/128*t^29 - 134183/256*t^27 + 261261/512*t^25 - 385515/1024*t^23 + 6956235/32768*t^21 - 6002425/65536*t^19 + 985435/32768*t^17 - 973199/131072*t^15 + 5668327/4194304*t^13 - 1476433/8388608*t^11 + 263245/16777216*t^9 - 30039/33554432*t^7 + 62985/2147483648*t^5 - 1947/4294967296*t^3 + 9/4294967296*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:
| (-1 + 1.0257388287987615068e-937j)  +/-  (2.2e-242, 2.2e-242j)
| (-0.9961946980917455323 + 3.8638739552499205907e-967j)  +/-  (3.93e-242, 3.93e-242j)
| (-0.93969262078590838405 - 5.4841642974015237502e-978j)  +/-  (8.16e-243, 8.16e-243j)
| (0.9961946980917455323 - 1.2728696500297745197e-981j)  +/-  (4.01e-242, 4.01e-242j)
| (0.90630778703664996324 - 6.8343989421311713717e-987j)  +/-  (3.63e-243, 3.63e-243j)
| (0.86602540378443864676 - 1.470160533472709842e-986j)  +/-  (1.19e-243, 1.19e-243j)
| (-0.087155742747658173558 - 9.5172949568068736205e-1001j)  +/-  (1.46e-254, 1.46e-254j)
| (-0.90630778703664996324 - 3.8759035558373266623e-984j)  +/-  (4.11e-243, 4.11e-243j)
| (-0.98480775301220805937 + 4.1209386385352098276e-994j)  +/-  (2.45e-242, 2.45e-242j)
| (1 + 1.2153236286568026131e-1001j)  +/-  (2.23e-242, 2.23e-242j)
| (0.81915204428899178968 + 3.0376256776195675463e-1009j)  +/-  (3.43e-244, 3.43e-244j)
| (0.98480775301220805937 - 3.3416468816913349621e-1006j)  +/-  (3.43e-242, 3.43e-242j)
| (-0.42261826174069943619 - 1.143976081316139567e-1015j)  +/-  (1.49e-249, 1.49e-249j)
| (-0.86602540378443864676 - 4.9969664653786159905e-1013j)  +/-  (1.3e-243, 1.3e-243j)
| (0.57357643635104609611 + 2.0731553343171463525e-1021j)  +/-  (1.95e-247, 1.95e-247j)
| (0.64278760968653932632 + 1.5035525683401025682e-1022j)  +/-  (1.48e-246, 1.48e-246j)
| (0.7071067811865475244 - 8.1571563489643245081e-1023j)  +/-  (1.14e-245, 1.14e-245j)
| (-0.96592582628906828675 - 3.9195912203584856792e-1025j)  +/-  (1.88e-242, 1.88e-242j)
| (-0.7071067811865475244 + 9.1636696299362370049e-1036j)  +/-  (1.11e-245, 1.11e-245j)
| (-0.7660444431189780352 - 2.3260592269130256286e-1038j)  +/-  (5.91e-245, 5.91e-245j)
| (0.42261826174069943619 - 2.3273763310503437131e-1046j)  +/-  (1.5e-249, 1.5e-249j)
| (0.7660444431189780352 + 4.1835640337895341435e-1045j)  +/-  (6.37e-245, 6.37e-245j)
| (0.17364817766693034885 - 1.1417760112046700999e-1049j)  +/-  (2.49e-253, 2.49e-253j)
| (-0.81915204428899178968 + 1.2237756949951679515e-1044j)  +/-  (2.72e-244, 2.72e-244j)
| (-0.57357643635104609611 + 9.7816030559860237832e-1050j)  +/-  (1.82e-247, 1.82e-247j)
| (-2.2978818903779046178e-1054 - 4.3450930435622044626e-1053j)  +/-  (1.61e-1051, 1.61e-1051j)
| (0.93969262078590838405 - 1.8488938991856512999e-1048j)  +/-  (9.75e-243, 9.75e-243j)
| (0.34202014332566873304 + 2.9658262032912838654e-1057j)  +/-  (8.97e-251, 8.97e-251j)
| (-0.25881904510252076235 - 7.1231025330783801574e-1060j)  +/-  (6.16e-252, 6.16e-252j)
| (-0.64278760968653932632 - 1.328380521951201085e-1056j)  +/-  (1.52e-246, 1.52e-246j)
| (-0.17364817766693034885 + 9.196712307530530553e-1064j)  +/-  (2.31e-253, 2.31e-253j)
| (0.25881904510252076235 + 2.9447979271142493491e-1059j)  +/-  (4.38e-252, 4.38e-252j)
| (0.5 + 3.085312839510834386e-1058j)  +/-  (2.11e-248, 2.11e-248j)
| (0.087155742747658173558 - 7.0483118483315457542e-1061j)  +/-  (1.45e-254, 1.45e-254j)
| (-0.5 - 1.1874870900418747622e-1061j)  +/-  (1.81e-248, 1.81e-248j)
| (-0.34202014332566873304 - 1.1884681611356590298e-1066j)  +/-  (1.05e-250, 1.05e-250j)
| (0.96592582628906828675 - 1.4207033396103012689e-1069j)  +/-  (1.65e-242, 1.65e-242j)
-------------------------------------------------
The weights are:
| (0.013888888888888888889 + 6.1568073682296032108e-937j)  +/-  (4.8e-80, 4.96e-198j)
| (0.027777777777777777778 - 7.4876438010354783973e-937j)  +/-  (4.03e-80, 4.16e-198j)
| (0.027777777777777777778 + 4.7245868773803945168e-938j)  +/-  (3.32e-81, 3.44e-199j)
| (0.027777777777777777778 - 1.4273530167997926038e-939j)  +/-  (1.06e-82, 1.09e-200j)
| (0.027777777777777777778 - 1.4946560801024651614e-939j)  +/-  (1.26e-82, 1.3e-200j)
| (0.027777777777777777778 + 1.5269216156770765352e-939j)  +/-  (8.24e-83, 8.52e-201j)
| (0.027777777777777777778 - 3.12131505654350175e-939j)  +/-  (1.89e-83, 1.96e-201j)
| (0.027777777777777777778 - 3.041100678831832552e-938j)  +/-  (4.55e-82, 4.7e-200j)
| (0.027777777777777777778 + 1.8754793328008690808e-937j)  +/-  (3.54e-81, 3.66e-199j)
| (0.013888888888888888889 + 7.1231863111025104637e-940j)  +/-  (4.38e-83, 4.53e-201j)
| (0.027777777777777777778 - 1.5662651911839681306e-939j)  +/-  (4.06e-84, 4.2e-202j)
| (0.027777777777777777778 + 1.4355418151288725875e-939j)  +/-  (2.08e-83, 2.15e-201j)
| (0.027777777777777777778 - 4.934819263648762594e-939j)  +/-  (4.09e-86, 4.23e-204j)
| (0.027777777777777777778 + 2.1267274579850956948e-938j)  +/-  (2.08e-84, 2.15e-202j)
| (0.027777777777777777778 - 1.8106997910112102699e-939j)  +/-  (4.27e-86, 4.42e-204j)
| (0.027777777777777777778 + 1.7344144231673837003e-939j)  +/-  (5.38e-86, 5.57e-204j)
| (0.027777777777777777778 - 1.6690663734933895652e-939j)  +/-  (6.58e-86, 6.81e-204j)
| (0.027777777777777777778 - 8.3619768702619980245e-938j)  +/-  (5.55e-85, 5.74e-203j)
| (0.027777777777777777778 - 9.7280317242706271767e-939j)  +/-  (4.81e-88, 4.97e-206j)
| (0.027777777777777777778 + 1.2178699930987328395e-938j)  +/-  (1.27e-87, 1.31e-205j)
| (0.027777777777777777778 - 2.0028384290207722072e-939j)  +/-  (1.49e-89, 1.54e-207j)
| (0.027777777777777777778 + 1.6133651310659848282e-939j)  +/-  (1.05e-87, 1.09e-205j)
| (0.027777777777777777778 + 2.4277075350681453427e-939j)  +/-  (1.58e-90, 1.63e-208j)
| (0.027777777777777777778 - 1.5755082844254506107e-938j)  +/-  (3.22e-88, 3.33e-206j)
| (0.027777777777777777778 - 6.6817942706060727431e-939j)  +/-  (2.58e-90, 2.67e-208j)
| (0.027777777777777777778 + 2.8492745244410041855e-939j)  +/-  (3.86e-91, 3.99e-209j)
| (0.027777777777777777778 + 1.4689309501453684121e-939j)  +/-  (4.21e-90, 4.35e-208j)
| (0.027777777777777777778 + 2.1231235154043207533e-939j)  +/-  (3.37e-91, 3.48e-209j)
| (0.027777777777777777778 - 3.8442360203860313612e-939j)  +/-  (3.26e-92, 3.37e-210j)
| (0.027777777777777777778 + 7.9764157171051976704e-939j)  +/-  (3.08e-91, 3.19e-209j)
| (0.027777777777777777778 + 3.4480162655133283058e-939j)  +/-  (3.88e-92, 4.02e-210j)
| (0.027777777777777777778 - 2.2634504423222747798e-939j)  +/-  (1.89e-92, 1.96e-210j)
| (0.027777777777777777778 + 1.8995163496273361236e-939j)  +/-  (2.16e-92, 2.23e-210j)
| (0.027777777777777777778 - 2.6208522039719885998e-939j)  +/-  (1.09e-92, 1.13e-210j)
| (0.027777777777777777778 + 5.6985490488820083709e-939j)  +/-  (2.37e-93, 2.45e-211j)
| (0.027777777777777777778 + 4.3303370088596185594e-939j)  +/-  (2.18e-93, 2.25e-211j)
| (0.027777777777777777778 - 1.449329616783847549e-939j)  +/-  (1.04e-93, 1.04e-211j)
