Starting with polynomial:
P : 1/720*t^6 - 1/20*t^5 + 5/8*t^4 - 10/3*t^3 + 15/2*t^2 - 6*t + 1
Extension levels are: 6 14
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Trying to find an order 14 Kronrod extension for:
P1 : 1/720*t^6 - 1/20*t^5 + 5/8*t^4 - 10/3*t^3 + 15/2*t^2 - 6*t + 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 1/720*t^20 - 1248200932605445697389168613/2801768277162142048455216000*t^19 + 180110040817296246590331445783/2801768277162142048455216000*t^18 - 161520545177251925729022296291/29185086220438979671408500*t^17 + 37112913218106893840690789438377/116740344881755918685634000*t^16 - 2009428005079893302232613639433059/155653793175674558247512000*t^15 + 2384932953270236628488159793031769/6226151727026982329900480*t^14 - 26354840649308347268596588773106887/3113075863513491164950240*t^13 + 438267170837918872691796366848300719/3113075863513491164950240*t^12 - 1375550888638304507085520928705403153/778268965878372791237560*t^11 + 13006840056232957821411581792224976487/778268965878372791237560*t^10 - 45959114290536922421519208077232417627/389134482939186395618780*t^9 + 239504253352572850465877858788931274327/389134482939186395618780*t^8 - 225546102742847460782168399406692350626/97283620734796598904695*t^7 + 597009656187141848784946143307604105478/97283620734796598904695*t^6 - 1067196402796560224013589948017406985412/97283620734796598904695*t^5 + 243407637536440330559263432931579611188/19456724146959319780939*t^4 - 162591625880239764328999540342904150928/19456724146959319780939*t^3 + 55379924793668198280713463433808778096/19456724146959319780939*t^2 - 7433590732731799520489217996941926368/19456724146959319780939*t + 209255692919127561731700741553199712/19456724146959319780939
-------------------------------------------------
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: 1
  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
-------------------------------------------------
The nodes are:
| (46.213804818747886135 + 4.5469851812018854957e-269j)  +/-  (5.8e-119, 5.8e-119j)
| (38.631490040687793524 - 1.7641536901547702151e-268j)  +/-  (2.4e-118, 2.4e-118j)
| (56.22926715292725482 - 3.0784274246659605006e-271j)  +/-  (5.91e-120, 5.91e-120j)
| (32.411854204094907194 - 1.0436900943450733474e-266j)  +/-  (7.08e-118, 7.08e-118j)
| (27.133818421750637223 + 7.7602376777878980044e-266j)  +/-  (1.31e-117, 1.31e-117j)
| (12.447744968912973737 + 4.2873976702364933766e-270j)  +/-  (5.53e-118, 5.53e-118j)
| (22.565358258538688247 + 1.8511594366526161661e-287j)  +/-  (2.2e-117, 2.2e-117j)
| (15.982873980601701783 + 6.2649193834553005215e-314j)  +/-  (4.11e-116, 4.11e-116j)
| (0.037567892900867128138 + 2.788074089055102575e-341j)  +/-  (2.24e-127, 2.24e-127j)
| (2.9927363260593140777 + 4.2875074311120210816e-336j)  +/-  (1.58e-121, 1.58e-121j)
| (0.60205280482845576985 - 2.043856528952892364e-342j)  +/-  (1.05e-124, 1.05e-124j)
| (1.9838679117582711043 - 1.8256696451322722376e-343j)  +/-  (2.05e-122, 2.05e-122j)
| (18.444897047984054928 + 3.8184537246406577258e-337j)  +/-  (6.78e-117, 6.78e-117j)
| (9.8374674183825899177 + 1.6369068541384541969e-351j)  +/-  (1.32e-118, 1.32e-118j)
| (0.22284660417926068946 - 2.426839187406307412e-369j)  +/-  (5.92e-126, 5.92e-126j)
| (1.1889321016726230307 + 5.3574124227089921052e-367j)  +/-  (1.63e-123, 1.63e-123j)
| (4.2425581174791486958 - 7.7160465666031748041e-363j)  +/-  (1.1e-120, 1.1e-120j)
| (7.6289617489780068676 + 5.8724621633321249814e-361j)  +/-  (2.72e-119, 2.72e-119j)
| (16.1901397929067247 - 9.0490130652766860279e-372j)  +/-  (4.4e-116, 4.4e-116j)
| (5.7751435691045105018 + 2.7896677483673220428e-387j)  +/-  (5.75e-120, 5.75e-120j)
-------------------------------------------------
The weights are:
| (7.2376914991630953543e-20 - 5.0462016335198579211e-283j)  +/-  (2.96e-46, 2.52e-104j)
| (1.1357747951380104604e-16 + 5.9071899929295246114e-281j)  +/-  (5.19e-45, 4.42e-103j)
| (4.6030431266132057334e-24 + 1.4608712084178800301e-285j)  +/-  (2.01e-48, 1.72e-106j)
| (4.7823746711035452433e-14 - 4.3248778682743625804e-279j)  +/-  (2.97e-44, 2.53e-102j)
| (8.0429009267862757433e-12 - 4.0905798535138082349e-277j)  +/-  (1.26e-43, 1.07e-101j)
| (1.1163039422474423817e-05 + 3.9582940171250545093e-274j)  +/-  (1.54e-40, 1.31e-98j)
| (6.7767477484273498067e-10 + 2.9754152596881075889e-276j)  +/-  (2.58e-43, 2.19e-101j)
| (1.8509206208367957062e-06 - 1.8269619667535945128e-273j)  +/-  (3.43e-42, 2.92e-100j)
| (0.096677606248162958252 + 1.9164256094139411472e-272j)  +/-  (1.37e-34, 1.17e-92j)
| (0.05631521789670798964 - 2.765768469970014724e-272j)  +/-  (7.75e-37, 6.59e-95j)
| (0.26424347209150592768 + 6.1592367929166713897e-272j)  +/-  (9.13e-35, 7.77e-93j)
| (0.12370607995280022654 + 4.3600816668067019248e-272j)  +/-  (2.34e-35, 1.99e-93j)
| (4.1760134675207042391e-08 - 5.7126011713819160823e-275j)  +/-  (3.01e-43, 2.56e-101j)
| (0.00012810696826422663347 - 9.7293798915439329719e-274j)  +/-  (9.22e-42, 7.84e-100j)
| (0.22234490120705116431 - 4.9445698160654362516e-272j)  +/-  (1.99e-35, 1.69e-93j)
| (0.21046021813764442872 - 5.721045714919283098e-272j)  +/-  (1.97e-36, 1.67e-94j)
| (0.019890344554346170813 + 1.4631764148451086731e-272j)  +/-  (9.56e-40, 8.13e-98j)
| (0.00098470439476359007581 + 2.6252084591075529893e-273j)  +/-  (1.09e-41, 9.26e-100j)
| (-1.2923065097864252088e-06 + 1.7439142749724399614e-273j)  +/-  (1.91e-42, 1.63e-100j)
| (0.0052375844493195041698 - 6.5858530894127911322e-273j)  +/-  (3.8e-41, 3.23e-99j)
