Starting with polynomial:
P : 2*t
Extension levels are: 1 4 56
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Trying to find an order 4 Kronrod extension for:
P1 : 2*t
Solvable: 1
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Trying to find an order 56 Kronrod extension for:
P2 : 2*t^5 - 10*t^3 + 15/2*t
Solvable: 1
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Ending with final polynomial:
P : 2*t^61 - 1488698946934398188033760927573771790176396393566/869747000783558979970315732869543405757899861*t^59 + 15451323782868840253307478774649100978278280505809309/22613422020372533479228209054608128549705396386*t^57 - 637764541794905109587346243185576843305970796426316315/3768903670062088913204701509101354758284232731*t^55 + 1843875909873810047181407122422860823642772935906228635/63210124445485767936347195121196725505815224*t^53 - 18101850990628666941810309864986501435770194895611774475/4862317265037366764334399624707440423524248*t^51 + 7104524789780551725113958878990540526441162683011418771475/19449269060149467057337598498829761694096992*t^49 - 137347881935704000828805383558205225443770814301122881048975/4862317265037366764334399624707440423524248*t^47 + 136225030077824242056945151147516656506629406165660079899778375/77797076240597868229350393995319046776387968*t^45 - 6849464950283612590715736629139007614306416598201452469381974625/77797076240597868229350393995319046776387968*t^43 + 1126453347454579727886235855371893835374113352402793144211343692875/311188304962391472917401575981276187105551872*t^41 - 464292343665048217436617112180204604441578834430151844712443557125/3794979328809652108748799707088733989092096*t^39 + 103513522988254305850290077338888588004066961206115386106502186759875/30359834630477216869990397656709871912736768*t^37 - 2381460560036095679805441828518829360041754545334523307170372343731875/30359834630477216869990397656709871912736768*t^35 + 180824174189963282809991480176352741258971989798260184560678669785299375/121439338521908867479961590626839487650947072*t^33 - 353277913165937519375353473054859533910502658987081274180823233574330625/15179917315238608434995198828354935956368384*t^31 + 144953201275424224422236436449157293883796939085681345240525300414312630625/485757354087635469919846362507357950603788288*t^29 - 52302371534873876727587499446733047239951510278576517018488963951750324375/16750253589228809307580909051977860365647872*t^27 + 1774094695596567023909655387331844164806036522237100173451113743929573640625/67001014356915237230323636207911441462591488*t^25 - 6042175644137366255919063971747359754285032444364030281786917643997881265625/33500507178457618615161818103955720731295744*t^23 + 261567756972267595430364504113390202302167792060319371858439842308384210890625/268004057427660948921294544831645765850365952*t^21 - 1109265401154535010512145953177330298250942677182437688275847316045248115953125/268004057427660948921294544831645765850365952*t^19 + 14503136277338632222152035048984599922482415036399307940868990512953374522203125/1072016229710643795685178179326583063401463808*t^17 - 8949578006759614029767647715845808758609377886595710455874554713393671118671875/268004057427660948921294544831645765850365952*t^15 + 260231886104716472977789104310904195217620818212022764565102776326036103089765625/4288064918842575182740712717306332253605855232*t^13 - 337240483924836073225395744165901448003822272137708192914802713505153556330734375/4288064918842575182740712717306332253605855232*t^11 + 1195121162964850220699971417571689444132233699107239286990483146642295248356703125/17152259675370300730962850869225329014423420928*t^9 - 340844649636304612989817760199941778210212963206462399009543928191617321447234375/8576129837685150365481425434612664507211710464*t^7 + 909025020591112703069735275940144566896002107503670700138611240165627501661953125/68609038701481202923851403476901316057693683712*t^5 - 147343858277835657413934035102180541539366095303463757986279571278383079365078125/68609038701481202923851403476901316057693683712*t^3 + 29629035212755729957334471157149415749227676737539465019795262217994311734765625/274436154805924811695405613907605264230774734848*t
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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
Positive weights:   59 out of 61
Indefinite weights: 0 out of 61
Negative weights:   2 out of 61
Extension rule has valid weights: 0
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*** EXTENSION WITH INVALID WEIGHTS ***
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