Starting with polynomial:
P : 8*t^3 - 4*t
Extension levels are: 3 8 36
-------------------------------------------------
Trying to find an order 8 Kronrod extension for:
P1 : 8*t^3 - 4*t
Solvable: 1
-------------------------------------------------
Trying to find an order 36 Kronrod extension for:
P2 : 8*t^11 - 20*t^9 + 18*t^7 - 7*t^5 + 35/32*t^3 - 3/64*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 8*t^47 - 92*t^45 + 495*t^43 - 3311/2*t^41 + 61705/16*t^39 - 212667/32*t^37 + 1124097/128*t^35 - 2330445/256*t^33 + 15380937/2048*t^31 - 20376455/4096*t^29 + 43541267/16384*t^27 - 37550331/32768*t^25 + 104306475/262144*t^23 - 57998985/524288*t^21 + 51175575/2097152*t^19 - 17678835/4194304*t^17 + 300540195/536870912*t^15 - 59879925/1073741824*t^13 + 17298645/4294967296*t^11 - 1726725/8589934592*t^9 + 444015/68719476736*t^7 - 16445/137438953472*t^5 + 575/549755813888*t^3 - 3/1099511627776*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: 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:
| (0.98078528040323044913 + 1.6971045746336751303e-879j)  +/-  (1.51e-239, 1.51e-239j)
| (-0.99785892323860350674 - 1.3504376516740386223e-893j)  +/-  (2.99e-240, 2.99e-240j)
| (-0.89687274153268830389 - 5.8842621238879079575e-894j)  +/-  (4.23e-240, 4.23e-240j)
| (0.83146961230254523708 + 1.9002526429491816803e-894j)  +/-  (6.11e-241, 6.11e-241j)
| (0.96592582628906828675 - 2.5219989559816138725e-906j)  +/-  (1.63e-239, 1.63e-239j)
| (0.92387953251128675613 - 1.6065045908778393693e-920j)  +/-  (8.21e-240, 8.21e-240j)
| (-0.96592582628906828675 + 2.8013491883245232292e-922j)  +/-  (1.86e-239, 1.86e-239j)
| (-0.86602540378443864676 - 9.704537027190825875e-927j)  +/-  (1.65e-240, 1.65e-240j)
| (-0.98078528040323044913 - 3.5861858361415529973e-926j)  +/-  (1.5e-239, 1.5e-239j)
| (0.99785892323860350674 - 6.3751152164801611484e-937j)  +/-  (2.71e-240, 2.71e-240j)
| (0.86602540378443864676 + 2.5603096057159854958e-952j)  +/-  (1.79e-240, 1.79e-240j)
| (-0.99144486137381041114 - 5.2240278680767454469e-952j)  +/-  (1.17e-239, 1.17e-239j)
| (-0.92387953251128675613 + 9.2174262828949679981e-954j)  +/-  (8.51e-240, 8.51e-240j)
| (-0.83146961230254523708 + 1.7833873802440453376e-959j)  +/-  (6.14e-241, 6.14e-241j)
| (0.99144486137381041114 + 1.9906682801234673822e-956j)  +/-  (1.03e-239, 1.03e-239j)
| (0.75183980747897739641 + 1.0516674239429128827e-967j)  +/-  (4.6e-242, 4.6e-242j)
| (0.79335334029123516458 - 1.7782806032759956918e-966j)  +/-  (1.67e-241, 1.67e-241j)
| (-0.38268343236508977173 + 2.1968078069815509978e-975j)  +/-  (2.45e-248, 2.45e-248j)
| (-0.75183980747897739641 + 2.2955970012577575696e-968j)  +/-  (5.18e-242, 5.18e-242j)
| (-0.94693012949510566426 + 8.0632963799750940557e-966j)  +/-  (1.36e-239, 1.36e-239j)
| (0.89687274153268830389 - 4.6999735827976068786e-967j)  +/-  (3.62e-240, 3.62e-240j)
| (0.7071067811865475244 + 4.1703937108635939716e-980j)  +/-  (9.56e-243, 9.56e-243j)
| (0.94693012949510566426 - 1.1980655124653444546e-985j)  +/-  (1.72e-239, 1.72e-239j)
| (-0.79335334029123516458 - 2.1107551654084352565e-1001j)  +/-  (1.77e-241, 1.77e-241j)
| (-0.7071067811865475244 + 4.989765022655837198e-1007j)  +/-  (8.92e-243, 8.92e-243j)
| (0.065403129230143066815 + 1.359567161292693203e-1015j)  +/-  (1.61e-254, 1.61e-254j)
| (0.65934581510006886843 + 1.8324360453620204635e-1011j)  +/-  (1.88e-243, 1.88e-243j)
| (0.38268343236508977173 + 8.4919077242803032738e-1015j)  +/-  (2.44e-248, 2.44e-248j)
| (0.13052619222005159155 - 5.6125745143368094648e-1016j)  +/-  (2.55e-253, 2.55e-253j)
| (-0.65934581510006886843 - 6.802634931034938582e-1010j)  +/-  (1.63e-243, 1.63e-243j)
| (-0.19509032201612826785 + 8.5667286457321654942e-1020j)  +/-  (4.84e-252, 4.84e-252j)
| (0.442288690219001282 + 7.8751748869932249185e-1016j)  +/-  (2.64e-247, 2.64e-247j)
| (0.60876142900872063942 + 8.3496020293951541486e-1013j)  +/-  (2.3e-244, 2.3e-244j)
| (9.6156127094850341784e-1019 - 2.9848002443564127023e-1018j)  +/-  (1.47e-1016, 1.47e-1016j)
| (-0.60876142900872063942 + 3.0696413127766285961e-1013j)  +/-  (2.56e-244, 2.56e-244j)
| (-0.442288690219001282 - 1.142256567743833831e-1015j)  +/-  (2.58e-247, 2.58e-247j)
| (0.19509032201612826785 + 6.2516496855519795746e-1021j)  +/-  (4.59e-252, 4.59e-252j)
| (0.55557023301960222474 - 2.923560335687249093e-1016j)  +/-  (2.21e-245, 2.21e-245j)
| (0.25881904510252076235 - 4.2038793495022515733e-1021j)  +/-  (1.05e-250, 1.05e-250j)
| (-0.25881904510252076235 + 4.4903160050024112437e-1023j)  +/-  (1.11e-250, 1.11e-250j)
| (-0.55557023301960222474 + 4.2865973276602573219e-1015j)  +/-  (2.77e-245, 2.77e-245j)
| (-0.065403129230143066815 - 2.5148352326544114571e-1023j)  +/-  (1.61e-254, 1.61e-254j)
| (0.3214394653031615807 - 1.4380114572430679864e-1020j)  +/-  (1.58e-249, 1.58e-249j)
| (0.5 + 2.4702568339723513573e-1018j)  +/-  (3.1e-246, 3.1e-246j)
| (-0.13052619222005159155 - 2.64116326593382589e-1024j)  +/-  (2.56e-253, 2.56e-253j)
| (-0.5 + 1.7778456235299003775e-1018j)  +/-  (3.28e-246, 3.28e-246j)
| (-0.3214394653031615807 - 1.3303114483296369608e-1023j)  +/-  (1.47e-249, 1.47e-249j)
-------------------------------------------------
The weights are:
| (0.000792921536340762957 - 5.2015474565802941554e-881j)  +/-  (9.64e-66, 7.28e-182j)
| (8.9116027356141550578e-05 - 7.6435782351240443967e-884j)  +/-  (2.48e-66, 1.87e-182j)
| (0.0040754017811591600061 - 3.6835158082438208109e-882j)  +/-  (2.19e-66, 1.65e-182j)
| (0.0064303809128636482112 - 7.3086964031793411917e-881j)  +/-  (1.64e-66, 1.24e-182j)
| (0.0013955687105787640962 + 1.5938849602029149058e-880j)  +/-  (1.94e-66, 1.47e-182j)
| (0.0030509710293067966208 + 9.0989347872966157615e-881j)  +/-  (1.15e-66, 8.67e-183j)
| (0.0013955687105787640962 + 1.2166294396727447311e-882j)  +/-  (9.11e-68, 6.88e-184j)
| (0.0052083333333333333333 + 4.7861355805984059016e-882j)  +/-  (3.44e-68, 2.6e-184j)
| (0.000792921536340762957 - 6.8601700776817714074e-883j)  +/-  (6.1e-68, 4.61e-184j)
| (8.9116027356141550578e-05 + 8.858052095710423201e-882j)  +/-  (1.6e-69, 1.21e-185j)
| (0.0052083333333333333333 + 7.7022445358482032883e-881j)  +/-  (5e-69, 3.78e-185j)
| (0.00035493930948887201302 + 3.0542537257318264366e-883j)  +/-  (4.42e-68, 3.34e-184j)
| (0.0030509710293067966208 + 2.7184924380411506697e-882j)  +/-  (7.01e-69, 5.3e-185j)
| (0.0064303809128636482112 - 6.0217957792716146331e-882j)  +/-  (4.87e-70, 3.68e-186j)
| (0.00035493930948887201302 - 5.6509644001335361016e-881j)  +/-  (1.05e-69, 7.91e-186j)
| (0.0090570188310411292547 - 6.7136981982555888102e-881j)  +/-  (4.49e-72, 3.39e-188j)
| (0.0077206349468487420589 + 6.9906574512030888533e-881j)  +/-  (2.08e-71, 1.57e-187j)
| (0.017782362304026536713 + 2.2133642034722376334e-881j)  +/-  (4.41e-75, 3.33e-191j)
| (0.0090570188310411292547 - 8.8713410640338901129e-882j)  +/-  (2.83e-73, 2.14e-189j)
| (0.002152569371966300369 - 1.8950594624201408816e-882j)  +/-  (1.97e-70, 1.49e-186j)
| (0.0040754017811591600061 - 8.2423712824919156488e-881j)  +/-  (1.61e-71, 1.22e-187j)
| (0.010416666666666666667 + 6.459467113065988526e-881j)  +/-  (4.38e-74, 3.31e-190j)
| (0.002152569371966300369 - 1.0790486027647985377e-880j)  +/-  (2.27e-71, 1.72e-187j)
| (0.0077206349468487420589 + 7.3854008556819610682e-882j)  +/-  (1.33e-73, 1.01e-189j)
| (0.010416666666666666667 + 1.0473520822051219772e-881j)  +/-  (4.07e-75, 3.07e-191j)
| (0.020744217305977191783 - 3.845946312373803421e-881j)  +/-  (4.44e-79, 3.35e-195j)
| (0.011776314502292204079 - 6.2175430746550911966e-881j)  +/-  (2.57e-76, 1.94e-192j)
| (0.017782362304026536713 + 5.0457172993106321327e-881j)  +/-  (3.62e-79, 2.73e-195j)
| (0.02047839402384446132 + 4.0874571835838286638e-881j)  +/-  (1.42e-79, 1.07e-195j)
| (0.011776314502292204079 - 1.2185390100194012699e-881j)  +/-  (2.75e-78, 2.08e-194j)
| (0.020040411796992570376 - 2.892370117063623929e-881j)  +/-  (1.37e-80, 1.03e-196j)
| (0.016757931552174173327 - 5.2813634880887825166e-881j)  +/-  (1.79e-79, 1.35e-195j)
| (0.013112698386484591274 + 5.9817724949834017218e-881j)  +/-  (2.15e-78, 1.62e-194j)
| (0.020833333333333333333 + 3.6049017059404304912e-881j)  +/-  (1.22e-80, 9.22e-197j)
| (0.013112698386484591274 + 1.3999978915830953752e-881j)  +/-  (3.37e-80, 2.55e-196j)
| (0.016757931552174173327 - 1.9984879834572823524e-881j)  +/-  (2.28e-81, 1.72e-197j)
| (0.020040411796992570376 - 4.3287377849588329557e-881j)  +/-  (5.55e-81, 4.2e-197j)
| (0.014402952420469685122 - 5.7484598890400207858e-881j)  +/-  (1.79e-80, 1.35e-196j)
| (0.019437764622754569237 + 4.5691775666198158474e-881j)  +/-  (2.59e-81, 1.96e-197j)
| (0.019437764622754569237 + 2.6611652269341042417e-881j)  +/-  (8.07e-83, 6.09e-199j)
| (0.014402952420469685122 - 1.5909935055691835612e-881j)  +/-  (1.86e-82, 1.4e-198j)
| (0.020744217305977191783 - 3.3650827865228159906e-881j)  +/-  (7.65e-83, 5.78e-199j)
| (0.018680763961367032964 - 4.8082825810726536519e-881j)  +/-  (1.67e-82, 1.26e-198j)
| (0.015625 + 5.5154057454528393617e-881j)  +/-  (1.13e-82, 8.55e-199j)
| (0.02047839402384446132 + 3.1272939257056514946e-881j)  +/-  (3.43e-83, 2.59e-199j)
| (0.015625 + 1.7907565215283138154e-881j)  +/-  (7.67e-84, 5.83e-200j)
| (0.018680763961367032964 - 2.4345421234712637466e-881j)  +/-  (9.43e-84, 7.1e-200j)
