Starting with polynomial:
P : 2*t
Extension levels are: 1 2 6 10 18
-------------------------------------------------
Trying to find an order 2 Kronrod extension for:
P1 : 2*t
Solvable: 1
-------------------------------------------------
Trying to find an order 6 Kronrod extension for:
P2 : 2*t^3 - 3*t
Solvable: 1
-------------------------------------------------
Trying to find an order 10 Kronrod extension for:
P3 : 2*t^9 - 117/4*t^7 + 945/8*t^5 - 2205/16*t^3 + 945/32*t
Solvable: 1
-------------------------------------------------
Trying to find an order 18 Kronrod extension for:
P4 : 2*t^19 - 23713751/205892*t^17 + 2134183615/823568*t^15 - 48885080515/1647136*t^13 + 623352876985/3294272*t^11 - 4536269518165/6588544*t^9 + 18427952550645/13177088*t^7 - 38805894891225/26354176*t^5 + 36681698574675/52708352*t^3 - 11110847880825/105416704*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^37 - 2866523542400994253836929184413188376368628899936493274794597330527311181985025656260490723674554611/6122139611368566484345411551199224025655026036309221039722779169101440508986888728096891216039042*t^35 + 4748704722524508474016000413552696348086879253107726532862701417559097003772550510490437472874946610455/97954233781897063749526584819187584410480416580947536635564466705623048143790219649550259456624672*t^33 - 1152158483373137211013565928808746431672248686614330121197187621375730417482191212876507163640384742033805/391816935127588254998106339276750337641921666323790146542257866822492192575160878598201037826498688*t^31 + 91452121262687374459126099790959544035485169237696837103964497851917947652318042599458453403240724830956145/783633870255176509996212678553500675283843332647580293084515733644984385150321757196402075652997376*t^29 - 5025020280819588216765994152512476889386333923391487982881788219269453584203219264220204465575559056972955495/1567267740510353019992425357107001350567686665295160586169031467289968770300643514392804151305994752*t^27 + 197267806720891019128486393414880517673404163909547101819765336209181249098624497240090337844685332105456710135/3134535481020706039984850714214002701135373330590321172338062934579937540601287028785608302611989504*t^25 - 5630775206349072298779825078261263813427657737986435996216175216471291171430342617313393367020426201439785947625/6269070962041412079969701428428005402270746661180642344676125869159875081202574057571216605223979008*t^23 + 117827251880676519795356833890568978832753157614746877795854859727103670235262802817099891916721740998086050477125/12538141924082824159939402856856010804541493322361284689352251738319750162405148115142433210447958016*t^21 - 1809399282816597579539677043320902614319267046148827542771804696941324276669521665932302879325879120449348452484875/25076283848165648319878805713712021609082986644722569378704503476639500324810296230284866420895916032*t^19 + 20279540837768995742832549168121618543323743387871741122190758369918334792304926786272818500357553664363327797593375/50152567696331296639757611427424043218165973289445138757409006953279000649620592460569732841791832064*t^17 - 163854704317572226565660429144981371079016061146111795493328319749736339739696351180546237273758636292945461890796375/100305135392662593279515222854848086436331946578890277514818013906558001299241184921139465683583664128*t^15 + 934826895831672213617875418150155073511034356371058996826781316338428261150599585120616199740395717842743942118701875/200610270785325186559030445709696172872663893157780555029636027813116002598482369842278931367167328256*t^13 - 3646072911592657438924826296658843377792232993334241535003041169410227240174245851275618697382292248549432865784633125/401220541570650373118060891419392345745327786315561110059272055626232005196964739684557862734334656512*t^11 + 9246498376070694984101280222661815837983637074083024186759545471071402912169736142198118187821525303445848638271463125/802441083141300746236121782838784691490655572631122220118544111252464010393929479369115725468669313024*t^9 - 14075162454890542561214993396182670539436769553388364727278752223859203913472759584421765867586855866074412261237221875/1604882166282601492472243565677569382981311145262244440237088222504928020787858958738231450937338626048*t^7 + 11223670470821662156664682589875885264407039996102127715344231731440924098308902639468784234646698023479273018219384375/3209764332565202984944487131355138765962622290524488880474176445009856041575717917476462901874677252096*t^5 - 3612597752089611750681961089938521768889926518371641578303796313820979622783857032689145772204954865076723960404165625/6419528665130405969888974262710277531925244581048977760948352890019712083151435834952925803749354504192*t^3 + 247911845247377686610893496015462280834169800553184099839536121747826533047532604715178862440935597412091623909134375/12839057330260811939777948525420555063850489162097955521896705780039424166302871669905851607498709008384*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:
| (-6.1245278546221590085 - 3.9662714933033664027e-467j)  +/-  (1.35e-120, 1.35e-120j)
| (3.66777421594633786 + 3.666816344341978704e-465j)  +/-  (3.53e-119, 3.53e-119j)
| (6.1245278546221590085 + 1.5624316198795220446e-468j)  +/-  (1.33e-120, 1.33e-120j)
| (5.5218652098683505936 - 1.0431131009330881093e-470j)  +/-  (5.46e-120, 5.46e-120j)
| (-3.66777421594633786 - 4.0152570940352128597e-470j)  +/-  (3.51e-119, 3.51e-119j)
| (-6.8532000697575198251 + 2.6463226545641429239e-475j)  +/-  (1.63e-121, 1.63e-121j)
| (6.8532000697575198251 + 3.8383310112692736545e-474j)  +/-  (1.54e-121, 1.54e-121j)
| (2.597288631188365787 - 1.646964965966825173e-471j)  +/-  (7.2e-120, 7.2e-120j)
| (2.9592107790638377223 + 6.6612013631913411904e-471j)  +/-  (1.46e-119, 1.46e-119j)
| (-5.5218652098683505936 - 5.4149837790313393521e-474j)  +/-  (5.46e-120, 5.46e-120j)
| (4.4995993983103888029 + 8.0030681684455437182e-477j)  +/-  (2.27e-119, 2.27e-119j)
| (-4.9865514541507660747 - 5.4508597966634843449e-481j)  +/-  (1.4e-119, 1.4e-119j)
| (0.87004089535290290013 + 4.8626417599448270014e-487j)  +/-  (2.98e-124, 2.98e-124j)
| (-2.597288631188365787 + 2.4456311411940601912e-481j)  +/-  (7.38e-120, 7.38e-120j)
| (1.5615534276518735234 - 1.6758936402625625859e-485j)  +/-  (8.69e-122, 8.69e-122j)
| (-2.0232301911005156592 + 3.4941550433866797924e-482j)  +/-  (2.41e-120, 2.41e-120j)
| (2.2665132620567880275 - 9.368316729285322772e-483j)  +/-  (4.31e-120, 4.31e-120j)
| (-3.3155846175932898359 + 5.5657440659247835805e-481j)  +/-  (2.62e-119, 2.62e-119j)
| (-1.5615534276518735234 - 1.6199253554639748031e-488j)  +/-  (8.35e-122, 8.35e-122j)
| (-4.0579563160897412786 - 3.6635727753664400233e-485j)  +/-  (3.01e-119, 3.01e-119j)
| (4.9865514541507660747 + 1.7017069044784450412e-490j)  +/-  (1.36e-119, 1.36e-119j)
| (3.3155846175932898359 + 1.2590859511978954938e-499j)  +/-  (2.71e-119, 2.71e-119j)
| (-4.4995993983103888029 + 6.115685263288237252e-506j)  +/-  (2.23e-119, 2.23e-119j)
| (-1.2247448713915890491 - 1.6764689356362042748e-514j)  +/-  (5.21e-123, 5.21e-123j)
| (1.8357079751751868738 + 5.6210295865157030295e-511j)  +/-  (8.32e-121, 8.32e-121j)
| (4.0579563160897412786 - 9.2883529916567245669e-517j)  +/-  (2.88e-119, 2.88e-119j)
| (1.2247448713915890491 + 7.0017437303082624042e-531j)  +/-  (5.46e-123, 5.46e-123j)
| (0.52403354748695764515 + 4.1154257174219013223e-532j)  +/-  (1.82e-125, 1.82e-125j)
| (-2.2665132620567880275 - 2.0831163023364837059e-526j)  +/-  (4.08e-120, 4.08e-120j)
| (-0.52403354748695764515 - 2.4968233801571805652e-533j)  +/-  (1.61e-125, 1.61e-125j)
| (-1.8357079751751868738 - 1.2770083503692304826e-527j)  +/-  (8.54e-121, 8.54e-121j)
| (2.0232301911005156592 + 3.4229666763588783821e-527j)  +/-  (2.41e-120, 2.41e-120j)
| (-0.21461818058817058787 - 2.495149398849249353e-534j)  +/-  (1.36e-126, 1.36e-126j)
| (-2.9592107790638377223 + 7.0372669895376103425e-531j)  +/-  (1.55e-119, 1.55e-119j)
| (-0.87004089535290290013 + 1.1675847190563261407e-536j)  +/-  (2.93e-124, 2.93e-124j)
| (4.0726548377601257571e-548 - 3.3179948271405314338e-548j)  +/-  (1.94e-546, 1.94e-546j)
| (0.21461818058817058787 - 2.6475528828612842696e-539j)  +/-  (1.36e-126, 1.36e-126j)
-------------------------------------------------
The weights are:
| (1.8778189314372894734e-17 + 5.5605708638217921842e-480j)  +/-  (1.06e-36, 1.39e-96j)
| (2.9590752023074404861e-07 - 6.8271471632374275724e-471j)  +/-  (4.68e-29, 6.14e-89j)
| (1.8778189314372894734e-17 - 2.2187237175134459808e-479j)  +/-  (2.89e-37, 3.79e-97j)
| (1.8224275154912935628e-14 + 2.2995237064812250888e-477j)  +/-  (9.31e-36, 1.22e-95j)
| (2.9590752023074404861e-07 - 1.4798461166756916645e-472j)  +/-  (1.27e-31, 1.66e-91j)
| (1.9030350940130498048e-21 - 2.0435716082974138368e-482j)  +/-  (2.51e-40, 3.28e-100j)
| (1.9030350940130498048e-21 + 6.7484945418400062088e-482j)  +/-  (1.36e-39, 1.78e-99j)
| (0.00023494036646597522213 + 3.4427906397050580507e-469j)  +/-  (2.65e-27, 3.47e-87j)
| (3.2265185983739747007e-05 - 7.6437511107697894488e-470j)  +/-  (9.94e-29, 1.3e-88j)
| (1.8224275154912935628e-14 - 4.638270551243635832e-478j)  +/-  (3.18e-38, 4.16e-98j)
| (4.2252584396311104076e-10 + 5.7420317802534131093e-474j)  +/-  (8.95e-35, 1.17e-94j)
| (4.5661763676186858993e-12 + 2.041247885704910211e-476j)  +/-  (3.01e-37, 3.94e-97j)
| (0.093720828065524590185 + 1.0460187492209582238e-467j)  +/-  (4.27e-26, 5.59e-86j)
| (0.00023494036646597522213 + 5.8827142023562731617e-470j)  +/-  (3.57e-31, 4.68e-91j)
| (0.015513109874859354023 + 7.6569978653993991575e-468j)  +/-  (4.22e-26, 5.53e-86j)
| (0.0017680222581829544265 + 1.7221990233348675006e-468j)  +/-  (2.87e-29, 3.75e-89j)
| (0.00098582758299648382384 - 1.8103648541210551066e-468j)  +/-  (6.13e-29, 8.03e-89j)
| (3.3097587097920341861e-06 + 1.1948373643019966326e-471j)  +/-  (1.56e-33, 2.05e-93j)
| (0.015513109874859354023 + 3.0840419163848017804e-468j)  +/-  (3.47e-28, 4.54e-88j)
| (1.6595448809389818959e-08 + 1.1616255499628914254e-473j)  +/-  (1.02e-35, 1.34e-95j)
| (4.5661763676186858993e-12 - 1.3397795820114918231e-475j)  +/-  (1.79e-38, 2.34e-98j)
| (3.3097587097920341861e-06 + 2.3687153989028348189e-470j)  +/-  (5.47e-34, 7.17e-94j)
| (4.2252584396311104076e-10 - 5.8470886262134441367e-475j)  +/-  (1.55e-37, 2.02e-97j)
| (0.04421164421898454443 - 3.8914341803036616115e-468j)  +/-  (1.61e-29, 2.11e-89j)
| (0.0043334988122723492024 - 8.487702629269641089e-468j)  +/-  (4.21e-31, 5.51e-91j)
| (1.6595448809389818959e-08 - 2.3006643828320550011e-472j)  +/-  (2.78e-36, 3.64e-96j)
| (0.04421164421898454443 - 7.7931138356700576192e-468j)  +/-  (1.92e-30, 2.52e-90j)
| (0.14309930289683338899 - 1.7902901215971918881e-467j)  +/-  (1.06e-30, 1.39e-90j)
| (0.00098582758299648382384 - 4.2748850156262296765e-469j)  +/-  (6.34e-33, 8.3e-93j)
| (0.14309930289683338899 - 1.3426711659407264064e-467j)  +/-  (4.51e-31, 5.91e-91j)
| (0.0043334988122723492024 - 2.8255226038947584001e-468j)  +/-  (6.04e-32, 7.91e-92j)
| (0.0017680222581829544265 + 5.9596477278957519585e-468j)  +/-  (6.02e-32, 7.89e-92j)
| (0.14765571040268624946 + 3.2199893243544646507e-467j)  +/-  (1.84e-31, 2.42e-91j)
| (3.2265185983739747007e-05 - 8.1733155750260991969e-471j)  +/-  (5.21e-35, 6.82e-95j)
| (0.093720828065524590185 + 6.4491218229045401495e-468j)  +/-  (6.32e-32, 8.26e-92j)
| (0.096882455292842549857 - 4.7505433564790784842e-467j)  +/-  (7.3e-32, 9.79e-92j)
| (0.14765571040268624946 + 3.6202395119034633651e-467j)  +/-  (4.66e-32, 5.81e-92j)
