Starting with polynomial:
P : t
Extension levels are: 1 4 42
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 42 Kronrod extension for:
P2 : t^5 - 10*t^3 + 15*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^47 - 6042082028238263961637701173651/6062989709009127413615092763*t^45 + 52223877439453078662870319733319555/115196804471173420858686762497*t^43 - 14398492116015867143560046342882102415/115196804471173420858686762497*t^41 + 207237263468932259836752648757147139475/8861292651628724681437443269*t^39 - 1469792988804031235541802727880437157345/466383823769932877970391751*t^37 + 147745609997502383846464291221740937595515/466383823769932877970391751*t^35 - 11323851931734135557003805728872894783589775/466383823769932877970391751*t^33 + 670818858283552010834995489733360209668562950/466383823769932877970391751*t^31 - 30957982830086420889173043112922729624563881750/466383823769932877970391751*t^29 + 1116961238066997391441598922201489460036484142450/466383823769932877970391751*t^27 - 31505624829557414791623352245407876144542439962650/466383823769932877970391751*t^25 + 692489240475627237406400743648427641225665386441250/466383823769932877970391751*t^23 - 11785446481001605849854289080450595393803895543661250/466383823769932877970391751*t^21 + 153814795713475619434473245377640143018041727681893750/466383823769932877970391751*t^19 - 1519082892546816319984743568448900918991471873869298750/466383823769932877970391751*t^17 + 11152799106172287692772797742601924263831764719252231875/466383823769932877970391751*t^15 - 59457406625701624494136965852498445155553264857578446875/466383823769932877970391751*t^13 + 223033480663511672359435075630979650790966480231473715625/466383823769932877970391751*t^11 - 563476573862874596760432912434651623236225866268436078125/466383823769932877970391751*t^9 + 898893692825998097097524089690322801623793677594473778125/466383823769932877970391751*t^7 - 816029399917821761606448883369480451411849857192597978125/466383823769932877970391751*t^5 + 348029524649384212588888010645384486904261408217071609375/466383823769932877970391751*t^3 - 44335989471845965337836263429333145906504114639289671875/466383823769932877970391751*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
-------------------------------------------------
The nodes are:
| (11.296663891940933347 + 3.7679978275392805401e-532j)  +/-  (6.07e-246, 6.07e-246j)
| (12.247164293312831172 + 2.646199227598319186e-533j)  +/-  (4.73e-247, 4.73e-247j)
| (6.8337840939876432471 + 1.3680891596779729285e-530j)  +/-  (3.66e-244, 3.66e-244j)
| (8.5324935609562350871 - 1.5381708604618659154e-530j)  +/-  (4.29e-244, 4.29e-244j)
| (10.507486647611075862 - 9.3856650802595400479e-532j)  +/-  (3.46e-245, 3.46e-245j)
| (6.301916166188586349 - 1.3272535224891031507e-530j)  +/-  (2.49e-244, 2.49e-244j)
| (7.9453566582339717018 - 8.0144380992597599717e-530j)  +/-  (5.21e-244, 5.21e-244j)
| (9.8012452678614038492 + 5.265656858956848678e-532j)  +/-  (1.12e-244, 1.12e-244j)
| (9.1480452614054474744 + 2.8173454015387818324e-530j)  +/-  (2.57e-244, 2.57e-244j)
| (5.2738150784007923498 + 7.7617796386603677346e-531j)  +/-  (5.72e-245, 5.72e-245j)
| (7.3805470153762160157 - 1.3937408955278902756e-530j)  +/-  (5.07e-244, 5.07e-244j)
| (4.7742845463355232769 + 3.0618188313154043736e-531j)  +/-  (2.06e-245, 2.06e-245j)
| (5.7825459961141707053 - 1.5047430741019743852e-530j)  +/-  (1.24e-244, 1.24e-244j)
| (-9.1480452614054474744 + 9.9794069406482926072e-529j)  +/-  (2.56e-244, 2.56e-244j)
| (-11.296663891940933347 + 2.4811090518030684315e-541j)  +/-  (6.18e-246, 6.18e-246j)
| (-5.7825459961141707053 - 7.467702119735408239e-561j)  +/-  (1.3e-244, 1.3e-244j)
| (-12.247164293312831172 + 2.1171888441492033717e-579j)  +/-  (4.62e-247, 4.62e-247j)
| (2.4129658388254360396 + 8.0470474953296447276e-597j)  +/-  (1.71e-248, 1.71e-248j)
| (-6.8337840939876432471 + 3.7342653875758115001e-590j)  +/-  (3.86e-244, 3.86e-244j)
| (-9.8012452678614038492 + 6.8181643303608828633e-602j)  +/-  (1.17e-244, 1.17e-244j)
| (-3.3229259298581947972 + 2.332118401826946208e-614j)  +/-  (3.49e-247, 3.49e-247j)
| (-10.507486647611075862 - 6.0550803404624216004e-610j)  +/-  (3.74e-245, 3.74e-245j)
| (3.3229259298581947972 + 5.7304336744453791421e-626j)  +/-  (3.54e-247, 3.54e-247j)
| (-1.3556261799742658658 - 1.7797852830527763045e-629j)  +/-  (5.83e-251, 5.83e-251j)
| (-2.8569700138728056542 + 2.0559886526550353467e-622j)  +/-  (7.83e-248, 7.83e-248j)
| (1.3556261799742658658 - 9.0802584391322314086e-635j)  +/-  (6e-251, 6e-251j)
| (-5.2738150784007923498 - 5.3744944013693694376e-637j)  +/-  (5.6e-245, 5.6e-245j)
| (-7.9453566582339717018 - 1.8594024664622406241e-693j)  +/-  (5.43e-244, 5.43e-244j)
| (3.799042534656610263 - 1.4602299382065300075e-727j)  +/-  (1.63e-246, 1.63e-246j)
| (-7.3805470153762160157 + 6.7646870840279105649e-734j)  +/-  (4.9e-244, 4.9e-244j)
| (2.0447814591468816666 + 2.7181170398496204663e-754j)  +/-  (4.12e-249, 4.12e-249j)
| (0.91210951430925429309 + 2.0005807853094434641e-757j)  +/-  (2.86e-252, 2.86e-252j)
| (-3.799042534656610263 + 5.1345527069193956128e-749j)  +/-  (1.51e-246, 1.51e-246j)
| (-6.301916166188586349 + 3.4711299115555002221e-753j)  +/-  (2.44e-244, 2.44e-244j)
| (-0.91210951430925429309 + 2.8960677474704839114e-771j)  +/-  (2.72e-252, 2.72e-252j)
| (2.8569700138728056542 - 6.6502661162214357228e-767j)  +/-  (7.51e-248, 7.51e-248j)
| (-4.2828956422855575255 + 1.4435447637808227402e-763j)  +/-  (5.97e-246, 5.97e-246j)
| (-2.4129658388254360396 + 7.1688738257521202398e-767j)  +/-  (1.65e-248, 1.65e-248j)
| (4.2828956422855575255 - 1.6684107808967117682e-764j)  +/-  (6.22e-246, 6.22e-246j)
| (-1.7489733978826258191 - 1.8863247121218300579e-768j)  +/-  (8.11e-250, 8.11e-250j)
| (-0.45744829953605723793 - 7.4184513495041107176e-791j)  +/-  (1.91e-253, 1.91e-253j)
| (-4.7742845463355232769 - 1.0918291862813242538e-762j)  +/-  (1.91e-245, 1.91e-245j)
| (0.45744829953605723793 + 1.1999976078194541956e-792j)  +/-  (1.5e-253, 1.5e-253j)
| (1.7489733978826258191 + 2.015331183966946836e-770j)  +/-  (8.91e-250, 8.91e-250j)
| (-8.5324935609562350871 - 7.8342605646236635213e-765j)  +/-  (4.11e-244, 4.11e-244j)
| (-7.6784287644832737835e-797 + 1.6214550034115907231e-796j)  +/-  (8.43e-795, 8.43e-795j)
| (-2.0447814591468816666 - 3.3739382530207418334e-781j)  +/-  (4.37e-249, 4.37e-249j)
-------------------------------------------------
The weights are:
| (6.5833349762053062922e-29 + 3.8581555078883581146e-550j)  +/-  (5.81e-64, 4.87e-186j)
| (1.1758416090148482335e-33 - 1.1588508829349096691e-552j)  +/-  (1.05e-65, 8.84e-188j)
| (1.5541046331493630956e-11 - 3.9690511425021757549e-540j)  +/-  (1.81e-55, 1.52e-177j)
| (3.7160972558973831821e-17 + 1.1248731648143638188e-543j)  +/-  (1.27e-59, 1.06e-181j)
| (3.1327039947964453807e-25 - 3.6653185169943112978e-548j)  +/-  (2.02e-63, 1.69e-185j)
| (4.9828166853307267506e-10 + 9.5586129931807131588e-539j)  +/-  (2.65e-55, 2.22e-177j)
| (4.4922260439109058812e-15 - 1.5607793928623898126e-542j)  +/-  (7.24e-59, 6.07e-181j)
| (3.7237601014019463774e-22 + 1.7450362935548899103e-546j)  +/-  (7.78e-63, 6.53e-185j)
| (1.6967060051581689336e-19 - 5.2288508995784680958e-545j)  +/-  (1.46e-61, 1.23e-183j)
| (1.8353984674361813653e-07 - 8.9219982905192445869e-537j)  +/-  (1.35e-55, 1.13e-177j)
| (3.2869926125040005956e-13 + 2.3992633846709613445e-541j)  +/-  (7.49e-59, 6.28e-181j)
| (2.2191319251198704206e-06 - 4.059946115351766026e-537j)  +/-  (2.79e-55, 2.34e-177j)
| (1.1239619716755752628e-08 + 2.1933640245938663386e-538j)  +/-  (1.69e-56, 1.42e-178j)
| (1.6967060051581689336e-19 + 9.2385330650535401097e-546j)  +/-  (1.37e-74, 1.15e-196j)
| (6.5833349762053062922e-29 - 9.4258659642504562822e-551j)  +/-  (1.27e-78, 1.06e-200j)
| (1.1239619716755752628e-08 + 7.2449047634738606918e-540j)  +/-  (1.53e-68, 1.28e-190j)
| (1.1758416090148482335e-33 + 3.2249667339233115107e-553j)  +/-  (1.76e-80, 1.48e-202j)
| (0.0091481797567925240216 - 7.5342950427123271451e-536j)  +/-  (2.91e-55, 2.44e-177j)
| (1.5541046331493630956e-11 + 1.7414698001159148881e-541j)  +/-  (1.58e-71, 1.33e-193j)
| (3.7237601014019463774e-22 - 3.1886642321568156063e-547j)  +/-  (1.34e-76, 1.12e-198j)
| (0.00075326600935467513981 - 8.9701043777471998755e-537j)  +/-  (3.41e-64, 2.86e-186j)
| (3.1327039947964453807e-25 + 7.8287824953070783929e-549j)  +/-  (7.98e-78, 6.69e-200j)
| (0.00075326600935467513981 + 1.4578471872546399116e-536j)  +/-  (7.84e-62, 6.58e-184j)
| (0.068505641787363872837 + 3.4647936163296546891e-535j)  +/-  (1.26e-55, 1.06e-177j)
| (0.0030899253554689836762 + 3.0370860202082380327e-536j)  +/-  (4.31e-63, 3.61e-185j)
| (0.068505641787363872837 + 3.7690776088277829085e-535j)  +/-  (7.17e-56, 6.01e-178j)
| (1.8353984674361813653e-07 - 3.7370166736079419153e-539j)  +/-  (9.6e-70, 8.05e-192j)
| (4.4922260439109058812e-15 + 2.0128753177717666486e-543j)  +/-  (7.89e-75, 6.62e-197j)
| (0.00014068118327174643177 - 1.7764597106322119962e-536j)  +/-  (3.05e-65, 2.56e-187j)
| (3.2869926125040005956e-13 - 2.0765744143872712707e-542j)  +/-  (7.85e-74, 6.58e-196j)
| (0.014938895126765334457 + 2.5956630743122303002e-535j)  +/-  (1.78e-62, 1.5e-184j)
| (0.11883187986015956987 - 3.5830425600889418985e-535j)  +/-  (7.41e-61, 6.22e-183j)
| (0.00014068118327174643177 + 2.5745076343463993933e-537j)  +/-  (1.57e-68, 1.32e-190j)
| (4.9828166853307267506e-10 - 1.21742995633312117e-540j)  +/-  (2.12e-72, 1.78e-194j)
| (0.11883187986015956987 - 3.3158198406775424938e-535j)  +/-  (2.81e-63, 2.36e-185j)
| (0.0030899253554689836762 + 2.6370976814099358925e-537j)  +/-  (1.07e-65, 8.96e-188j)
| (2.0219510304902156373e-05 - 6.9198438964154889116e-538j)  +/-  (5.98e-70, 5.02e-192j)
| (0.0091481797567925240216 - 1.0358185213127063008e-535j)  +/-  (2.18e-67, 1.83e-189j)
| (2.0219510304902156373e-05 + 2.1775289593237617426e-536j)  +/-  (9.64e-69, 8.1e-191j)
| (0.029155605598868900478 - 3.7156594735156033209e-535j)  +/-  (9.66e-67, 8.12e-189j)
| (0.1640950637155770124 + 3.3712335576608246088e-535j)  +/-  (7.8e-66, 6.5e-188j)
| (2.2191319251198704206e-06 + 1.6987412953443655722e-538j)  +/-  (6.61e-71, 5.54e-193j)
| (0.1640950637155770124 + 3.5238927485450233852e-535j)  +/-  (1.93e-66, 1.61e-188j)
| (0.029155605598868900478 - 3.8863687942255943793e-535j)  +/-  (8.89e-67, 7.5e-189j)
| (3.7160972558973831821e-17 - 1.5433815264807327638e-544j)  +/-  (3.79e-77, 3.16e-199j)
| (0.1826364553410499092 - 3.462035279214521225e-535j)  +/-  (2.81e-67, 2.12e-189j)
| (0.014938895126765334457 + 2.7077387449862920545e-535j)  +/-  (1.07e-67, 9.17e-190j)
