Starting with polynomial:
P : t
Extension levels are: 1 2 6 10 18
-------------------------------------------------
Trying to find an order 2 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 6 Kronrod extension for:
P2 : t^3 - 3*t
Solvable: 1
-------------------------------------------------
Trying to find an order 10 Kronrod extension for:
P3 : t^9 - 117/4*t^7 + 945/4*t^5 - 2205/4*t^3 + 945/4*t
Solvable: 1
-------------------------------------------------
Trying to find an order 18 Kronrod extension for:
P4 : t^19 - 23713751/205892*t^17 + 2134183615/411784*t^15 - 48885080515/411784*t^13 + 623352876985/411784*t^11 - 4536269518165/411784*t^9 + 18427952550645/411784*t^7 - 38805894891225/411784*t^5 + 36681698574675/411784*t^3 - 11110847880825/411784*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^37 - 2866523542400994253836929184413188376368628899936493274794597330527311181985025656260490723674554611/6122139611368566484345411551199224025655026036309221039722779169101440508986888728096891216039042*t^35 + 4748704722524508474016000413552696348086879253107726532862701417559097003772550510490437472874946610455/48977116890948531874763292409593792205240208290473768317782233352811524071895109824775129728312336*t^33 - 1152158483373137211013565928808746431672248686614330121197187621375730417482191212876507163640384742033805/97954233781897063749526584819187584410480416580947536635564466705623048143790219649550259456624672*t^31 + 91452121262687374459126099790959544035485169237696837103964497851917947652318042599458453403240724830956145/97954233781897063749526584819187584410480416580947536635564466705623048143790219649550259456624672*t^29 - 5025020280819588216765994152512476889386333923391487982881788219269453584203219264220204465575559056972955495/97954233781897063749526584819187584410480416580947536635564466705623048143790219649550259456624672*t^27 + 197267806720891019128486393414880517673404163909547101819765336209181249098624497240090337844685332105456710135/97954233781897063749526584819187584410480416580947536635564466705623048143790219649550259456624672*t^25 - 5630775206349072298779825078261263813427657737986435996216175216471291171430342617313393367020426201439785947625/97954233781897063749526584819187584410480416580947536635564466705623048143790219649550259456624672*t^23 + 117827251880676519795356833890568978832753157614746877795854859727103670235262802817099891916721740998086050477125/97954233781897063749526584819187584410480416580947536635564466705623048143790219649550259456624672*t^21 - 1809399282816597579539677043320902614319267046148827542771804696941324276669521665932302879325879120449348452484875/97954233781897063749526584819187584410480416580947536635564466705623048143790219649550259456624672*t^19 + 20279540837768995742832549168121618543323743387871741122190758369918334792304926786272818500357553664363327797593375/97954233781897063749526584819187584410480416580947536635564466705623048143790219649550259456624672*t^17 - 163854704317572226565660429144981371079016061146111795493328319749736339739696351180546237273758636292945461890796375/97954233781897063749526584819187584410480416580947536635564466705623048143790219649550259456624672*t^15 + 934826895831672213617875418150155073511034356371058996826781316338428261150599585120616199740395717842743942118701875/97954233781897063749526584819187584410480416580947536635564466705623048143790219649550259456624672*t^13 - 3646072911592657438924826296658843377792232993334241535003041169410227240174245851275618697382292248549432865784633125/97954233781897063749526584819187584410480416580947536635564466705623048143790219649550259456624672*t^11 + 9246498376070694984101280222661815837983637074083024186759545471071402912169736142198118187821525303445848638271463125/97954233781897063749526584819187584410480416580947536635564466705623048143790219649550259456624672*t^9 - 14075162454890542561214993396182670539436769553388364727278752223859203913472759584421765867586855866074412261237221875/97954233781897063749526584819187584410480416580947536635564466705623048143790219649550259456624672*t^7 + 11223670470821662156664682589875885264407039996102127715344231731440924098308902639468784234646698023479273018219384375/97954233781897063749526584819187584410480416580947536635564466705623048143790219649550259456624672*t^5 - 3612597752089611750681961089938521768889926518371641578303796313820979622783857032689145772204954865076723960404165625/97954233781897063749526584819187584410480416580947536635564466705623048143790219649550259456624672*t^3 + 247911845247377686610893496015462280834169800553184099839536121747826533047532604715178862440935597412091623909134375/97954233781897063749526584819187584410480416580947536635564466705623048143790219649550259456624672*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
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:
| (-5.7388168577316743351 + 2.5522245346421726061e-254j)  +/-  (4.27e-119, 4.27e-119j)
| (7.8090966693919782139 - 2.5182651467675872997e-253j)  +/-  (7.7e-120, 7.7e-120j)
| (-8.6613903551384526743 - 2.7994268118217848292e-267j)  +/-  (1.87e-120, 1.87e-120j)
| (5.7388168577316743351 + 1.0405326339803352685e-263j)  +/-  (4.48e-119, 4.48e-119j)
| (8.6613903551384526743 - 1.0637559158377474484e-272j)  +/-  (1.89e-120, 1.89e-120j)
| (-7.8090966693919782139 - 1.9292080565087004821e-279j)  +/-  (7.04e-120, 7.04e-120j)
| (-7.0520486959312922337 + 2.0436996934425946023e-278j)  +/-  (1.95e-119, 1.95e-119j)
| (7.0520486959312922337 + 2.137676390481670587e-280j)  +/-  (1.77e-119, 1.77e-119j)
| (-2.2083700357554732038 - 3.806617507917928983e-292j)  +/-  (1.2e-121, 1.2e-121j)
| (4.6889447333960424908 + 2.3655972481230536099e-297j)  +/-  (3.9e-119, 3.9e-119j)
| (2.5960831150492021594 + 8.5226209255561735935e-307j)  +/-  (1.27e-120, 1.27e-120j)
| (2.2083700357554732038 + 1.3687766514504183946e-312j)  +/-  (1.28e-121, 1.28e-121j)
| (-9.6918884843073256026 + 7.7875944863212047493e-318j)  +/-  (2.05e-121, 2.05e-121j)
| (-5.187016039913656066 + 8.2913814000478070516e-314j)  +/-  (4.48e-119, 4.48e-119j)
| (6.3633944943363699876 - 7.0527435575627383085e-323j)  +/-  (3.73e-119, 3.73e-119j)
| (1.7320508075688772935 + 3.210918009012612336e-339j)  +/-  (7.92e-123, 7.92e-123j)
| (-4.1849560176727318607 + 2.7168758340580325981e-335j)  +/-  (2.18e-119, 2.18e-119j)
| (5.187016039913656066 - 8.0369183281032999514e-342j)  +/-  (4.68e-119, 4.68e-119j)
| (-0.74109534999454084186 - 7.5149365876213586933e-358j)  +/-  (2.19e-125, 2.19e-125j)
| (9.6918884843073256026 + 2.154736142292773265e-355j)  +/-  (2.05e-121, 2.05e-121j)
| (-6.3633944943363699876 + 6.4217844252787423768e-352j)  +/-  (3.29e-119, 3.29e-119j)
| (0.74109534999454084186 + 4.2010551183236513769e-358j)  +/-  (2.38e-125, 2.38e-125j)
| (4.1849560176727318607 - 2.122476773432301691e-352j)  +/-  (2.22e-119, 2.22e-119j)
| (-1.7320508075688772935 + 1.1056033177689164972e-360j)  +/-  (7.57e-123, 7.57e-123j)
| (3.6731208076240386012 + 1.0877595229846988001e-355j)  +/-  (1.17e-119, 1.17e-119j)
| (-6.1914662542704873722e-376 - 1.217377855564378331e-375j)  +/-  (5.05e-374, 5.05e-374j)
| (2.8612795760570581173 + 1.8048092104308861297e-357j)  +/-  (3.37e-120, 3.37e-120j)
| (-3.2053337944991945187 - 5.6575128935164210184e-358j)  +/-  (5.92e-120, 5.92e-120j)
| (-4.6889447333960424908 - 7.7562357510012658382e-359j)  +/-  (4.01e-119, 4.01e-119j)
| (-1.2304236340273060078 - 4.5467786483825581185e-363j)  +/-  (4.17e-124, 4.17e-124j)
| (-2.8612795760570581173 + 5.7804163672441879071e-359j)  +/-  (3.58e-120, 3.58e-120j)
| (1.2304236340273060078 - 6.4284413903472222661e-364j)  +/-  (4.19e-124, 4.19e-124j)
| (0.30351594171962896269 + 1.820798046840762215e-366j)  +/-  (1.9e-126, 1.9e-126j)
| (3.2053337944991945187 + 2.9402773828623262599e-360j)  +/-  (6.24e-120, 6.24e-120j)
| (-2.5960831150492021594 - 1.8485838745181578377e-360j)  +/-  (1.18e-120, 1.18e-120j)
| (-0.30351594171962896269 + 2.1811925860988282807e-367j)  +/-  (1.9e-126, 1.9e-126j)
| (-3.6731208076240386012 - 6.1297957925777677121e-365j)  +/-  (1.13e-119, 1.13e-119j)
-------------------------------------------------
The weights are:
| (1.6595448809389818959e-08 + 2.0032888377631390512e-261j)  +/-  (8.45e-29, 1.44e-88j)
| (1.8224275154912935628e-14 + 2.1814840323368951103e-266j)  +/-  (4.41e-34, 7.5e-94j)
| (1.8778189314372894734e-17 - 9.1562128970972846197e-269j)  +/-  (7.15e-36, 1.22e-95j)
| (1.6595448809389818959e-08 - 9.7716368207584881714e-264j)  +/-  (4.18e-30, 7.12e-90j)
| (1.8778189314372894734e-17 + 8.6702099910317316199e-269j)  +/-  (6.03e-36, 1.03e-95j)
| (1.8224275154912935628e-14 + 1.001069525687866461e-266j)  +/-  (1.26e-34, 2.14e-94j)
| (4.5661763676186858993e-12 - 6.4761660047814484887e-265j)  +/-  (2.73e-33, 4.64e-93j)
| (4.5661763676186858993e-12 - 1.8604971474403395663e-265j)  +/-  (1.47e-33, 2.5e-93j)
| (0.015513109874859354023 + 1.9820514389734764022e-257j)  +/-  (1.01e-20, 1.72e-80j)
| (3.3097587097920341861e-06 + 8.9668395538735716229e-262j)  +/-  (3.04e-29, 5.17e-89j)
| (0.0043334988122723492024 - 5.591803409029635063e-258j)  +/-  (3.01e-23, 5.13e-83j)
| (0.015513109874859354023 + 6.4753229603158362306e-258j)  +/-  (1.35e-21, 2.29e-81j)
| (1.9030350940130498048e-21 + 2.698044954988971799e-271j)  +/-  (5.48e-40, 9.32e-100j)
| (2.9590752023074404861e-07 - 9.1880546278956361273e-261j)  +/-  (8.48e-32, 1.44e-91j)
| (4.2252584396311104076e-10 + 1.6941648859897034533e-264j)  +/-  (2.94e-33, 5.01e-93j)
| (0.04421164421898454443 - 8.65179541847629125e-258j)  +/-  (6.4e-22, 1.09e-81j)
| (3.2265185983739747007e-05 - 1.5959760889447732933e-259j)  +/-  (9.24e-31, 1.57e-90j)
| (2.9590752023074404861e-07 - 2.3139430052164258653e-263j)  +/-  (2.97e-31, 5.06e-91j)
| (0.14309930289683338899 - 4.604964246689374012e-257j)  +/-  (3.76e-23, 6.39e-83j)
| (1.9030350940130498048e-21 - 1.8863322455625602719e-271j)  +/-  (7.01e-41, 1.19e-100j)
| (4.2252584396311104076e-10 + 3.6445389785750276483e-263j)  +/-  (9.07e-35, 1.54e-94j)
| (0.14309930289683338899 - 3.2409810566933277016e-257j)  +/-  (2.61e-24, 4.44e-84j)
| (3.2265185983739747007e-05 - 9.6643767105677399133e-261j)  +/-  (2.95e-30, 5.02e-90j)
| (0.04421164421898454443 - 2.0271789487181451871e-257j)  +/-  (8.38e-27, 1.43e-86j)
| (0.00023494036646597522213 + 8.8837501309620819624e-260j)  +/-  (8.31e-30, 1.41e-89j)
| (0.096882455292842549857 - 1.1923688930771872633e-256j)  +/-  (4.73e-26, 8.04e-86j)
| (0.0017680222581829544265 + 3.2448523750682890168e-258j)  +/-  (3.92e-28, 6.67e-88j)
| (0.00098582758299648382384 - 4.4765180970684460028e-258j)  +/-  (4.72e-32, 8.03e-92j)
| (3.3097587097920341861e-06 + 3.677386477440577341e-260j)  +/-  (4.6e-34, 7.84e-94j)
| (0.093720828065524590185 + 2.7142454834811224324e-257j)  +/-  (1.2e-28, 2.05e-88j)
| (0.0017680222581829544265 + 1.5081770833812705587e-257j)  +/-  (9.61e-32, 1.64e-91j)
| (0.093720828065524590185 + 1.5024369042377754605e-257j)  +/-  (1.88e-29, 3.2e-89j)
| (0.14765571040268624946 + 7.9689963885738113281e-257j)  +/-  (1.08e-28, 1.86e-88j)
| (0.00098582758299648382384 - 7.4509047144152629569e-259j)  +/-  (1.96e-31, 3.33e-91j)
| (0.0043334988122723492024 - 2.1737091105353059266e-257j)  +/-  (1.21e-31, 2.09e-91j)
| (0.14765571040268624946 + 9.1933873099933387037e-257j)  +/-  (1.78e-30, 4.27e-90j)
| (0.00023494036646597522213 + 8.0724318301760241293e-259j)  +/-  (2.07e-33, 3.47e-93j)
