diff --git a/src/tableaus/rkc_tableaus.jl b/src/tableaus/rkc_tableaus.jl
deleted file mode 100644
index 5142663360..0000000000
--- a/src/tableaus/rkc_tableaus.jl
+++ /dev/null
@@ -1,37731 +0,0 @@
-function ROCK2ConstantCache(T, T2, zprev)
-    ms = SVector{46, Int}(
-        1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19,
-        20,
-        22, 24, 26, 28, 30, 33, 36, 39, 43, 47, 51, 56, 61, 66, 72, 78,
-        85, 93,
-        102, 112, 123, 135, 148, 163, 180, 198)
-    fp1 = SVector{46, T}(0.4102693550421609e+00, 0.3889624104727243e+00,
-        0.3804692420283886e+00,
-        0.3760815680865637e+00, 0.3735177579729938e+00,
-        0.3719340231904236e+00,
-        0.3708571145968057e+00, 0.3700947006022557e+00,
-        0.3695328931459086e+00,
-        0.3691085831661758e+00, 0.3687813249652330e+00,
-        0.3685244707068931e+00,
-        0.3683185599507446e+00, 0.3681542178682514e+00,
-        0.3680181997765286e+00,
-        0.3679084456991284e+00, 0.3678181571053212e+00,
-        0.3678314333608541e+00,
-        0.3677897070402892e+00, 0.3681800192470787e+00,
-        0.3681272993461229e+00,
-        0.3680840569645587e+00, 0.3680522380648169e+00,
-        0.3680263578626069e+00,
-        0.3680061275157194e+00, 0.3679837719607466e+00,
-        0.3679668653311732e+00,
-        0.3679542340323301e+00, 0.3679429332584250e+00,
-        0.3679349432021754e+00,
-        0.3679290943359695e+00, 0.3679242023884676e+00,
-        0.3679207541681089e+00,
-        0.3679185472223537e+00, 0.3679168690130640e+00,
-        0.3679158588043139e+00,
-        0.3679154592969145e+00, 0.3679154025286917e+00,
-        0.3679157536198652e+00,
-        0.3679163676763697e+00, 0.3679171904021983e+00,
-        0.3679181786833088e+00,
-        0.3679192462983425e+00, 0.3679204323079710e+00,
-        0.3679216942157868e+00,
-        0.3679229127010114e+00)
-    fp2 = SVector{46, T}(0.4495196112243335e+00, 0.4219428123056774e+00,
-        0.4084335547255627e+00,
-        0.4009301129475925e+00, 0.3963598727888637e+00,
-        0.3934034185789226e+00,
-        0.3913676516238603e+00, 0.3899091428928617e+00,
-        0.3888276962996660e+00,
-        0.3880048656683555e+00, 0.3873650613539532e+00,
-        0.3868583585730354e+00,
-        0.3864499054795832e+00, 0.3861178821587815e+00,
-        0.3858426294881124e+00,
-        0.3856144554520791e+00, 0.3854228843194507e+00,
-        0.3853156085078759e+00,
-        0.3851902798680153e+00, 0.3853705093720269e+00,
-        0.3851957294861824e+00,
-        0.3850587241670235e+00, 0.3849515900397918e+00,
-        0.3848648995575697e+00,
-        0.3847945082231300e+00, 0.3847117224407400e+00,
-        0.3846478726309070e+00,
-        0.3845979020112835e+00, 0.3845472492329918e+00,
-        0.3845088319509754e+00,
-        0.3844789634065264e+00, 0.3844504092359686e+00,
-        0.3844285235163634e+00,
-        0.3844115660464609e+00, 0.3843957877945634e+00,
-        0.3843835767106759e+00,
-        0.3843727001444428e+00, 0.3843632394180673e+00,
-        0.3843553120908175e+00,
-        0.3843487746818896e+00, 0.3843434800804404e+00,
-        0.3843392605995229e+00,
-        0.3843359163858929e+00, 0.3843331309176606e+00,
-        0.3843309056586355e+00,
-        0.3843292556220249e+00)
-    recf = [
-        0.1794612899156781, 0.09326607661089206,
-        0.1268473641290642, 0.02103378190528467,
-        0.0578662712551911, 0.07776456841673993,
-        0.02157791817707098, 0.09528922876588625,
-        0.08723622960881584, 0.03957407527591189,
-        0.05338681630900877, 0.02247986572029358,
-        0.06393794866013652, 0.0861675960246663,
-        0.07433164225960258, 0.1608966052260327,
-        0.02881884349012583, 0.03903194468364506,
-        0.02315538732440072, 0.04666180548151659,
-        0.08821448969005685, 0.05288869100008489,
-        0.1558852247558841, 0.05955157767537859,
-        0.2309801425356076, 0.02193602641069006,
-        0.02980001095383432, 0.02364036352805737,
-        0.03566742298660092, 0.0901769635289683,
-        0.04023410528284037, 0.1575736612169138,
-        0.0442110049482293, 0.221743062150858,
-        0.04869809870617736, 0.2940499060453847,
-        0.01726461340854506, 0.02350655101084081,
-        0.0239919520224083, 0.02817607209777294,
-        0.09173675182820953, 0.03176838133583184,
-        0.1600219376374877, 0.03469194451695863,
-        0.2221486436776174, 0.0373876350116119,
-        0.2814712676591709, 0.04053195010515956,
-        0.349859771934868, 0.01394572558988917,
-        0.01901965402711647, 0.02425291169233543,
-        0.02282720812165174, 0.09294575674653435,
-        0.02575013323611407, 0.1622227426315588,
-        0.0280770541578923, 0.2243919049772138,
-        0.03005377306193452, 0.2802435651401261,
-        0.03196472247412495, 0.3348331353768858,
-        0.03423680369928859, 0.398901664156519,
-        0.01150212461258425, 0.01570710434739234,
-        0.02445103607680476, 0.01887147450684578,
-        0.093887110326411, 0.02130209293934879,
-        0.1640457400037581, 0.02322314183593871,
-        0.2267657098371261, 0.02480419563989607,
-        0.2818605427391582, 0.02620108024481186,
-        0.3319747646481704, 0.02760343567567814,
-        0.3822711818317003, 0.02928725018247521,
-        0.4419889482818066, 0.009650189035331108,
-        0.01319127118048348, 0.02460463437251803,
-        0.01586242507387037, 0.0946291469184127,
-        0.01791697874611395, 0.1655306545097223,
-        0.01953741662819831, 0.2288845437800309,
-        0.0208544873661066, 0.2840687821706643,
-        0.02197276738303543, 0.332762163420867,
-        0.02299581340430604, 0.3779528907207973,
-        0.02405334751606276, 0.4244163000944219,
-        0.02532773055505536, 0.4799238174596328,
-        0.008212831461177801, 0.01123533801931148,
-        0.0247259253919068, 0.01351988263110243,
-        0.09522208667469109, 0.01527968649293853,
-        0.1667413647253854, 0.01666740304836073,
-        0.2306916351605186, 0.01778972104750926,
-        0.2862271893660237, 0.01872598244401872,
-        0.3345934460509904, 0.01954407472805166,
-        0.3778520013827246, 0.02031544030249,
-        0.4188775043096391, 0.02113066217102199,
-        0.4619185110779211, 0.02211266742157054,
-        0.5134449754977242, 0.007074719613815112,
-        0.009684509591053977, 0.02482326781574381,
-        0.01166040318768419, 0.09570219065303219,
-        0.0131845989014643, 0.1677351729038757,
-        0.01438717215812115, 0.2322139970245483,
-        0.01535795943897448, 0.2881631572191675,
-        0.01616136143489047, 0.3366119552764601,
-        0.01684787625840699, 0.3791920530521655,
-        0.01746359793359561, 0.4179163657739238,
-        0.01805925334195525, 0.4554086296687285,
-        0.01869919690078058, 0.495380320313383,
-        0.01946782991114719, 0.5431953913817005,
-        0.006158116280205625, 0.008434133870779752,
-        0.02490250308471492, 0.01015973796908432,
-        0.09609568511780181, 0.01149255448537381,
-        0.1685578212579456, 0.01254496388900155,
-        0.2334953976202505, 0.0133941202672405,
-        0.2898496927042313, 0.01409430683259744,
-        0.3385311597112782, 0.01468607650095395,
-        0.380955385363272, 0.01520306181269769,
-        0.4187183922578105, 0.01567773486210682,
-        0.4536627812581018, 0.01614693417033556,
-        0.4881324072137513, 0.01665708022899876,
-        0.5253402953586265, 0.0172671276878042,
-        0.569731047549543, 0.005408899288459016,
-        0.007411165652735432, 0.02496784203339785,
-        0.008931010375660927, 0.09642194989632852,
-        0.01010622203571924, 0.1692450860120974,
-        0.01103497280658699, 0.2345784420179126,
-        0.01178444954979593, 0.2913056300783272,
-        0.01240145878830343, 0.3402656182942943,
-        0.01292005530031986, 0.382756777938251,
-        0.0133668781100104, 0.4201602339064523,
-        0.01376523513966666, 0.4539235794662016,
-        0.01413868046925951, 0.4856954694207845,
-        0.01451444200099929, 0.5175484724211766,
-        0.01492644572980292, 0.5522503690808819,
-        0.01541651122328756, 0.5934874290489524,
-        0.004788707289765767, 0.006563722805402352,
-        0.0250223058569931, 0.00791241650301333,
-        0.09669512238638367, 0.008956313102014822,
-        0.1698239427218661, 0.009781969024648538,
-        0.2354985079518828, 0.01044851744036037,
-        0.2925601105800896, 0.01099693219507985,
-        0.3418012690877302, 0.0114565920869984,
-        0.3844521174650939, 0.01184970544276362,
-        0.4217763245489749, 0.01219446847463953,
-        0.4550117593290032, 0.01250758855429112,
-        0.4854408050495134, 0.01280655793511545,
-        0.514526804170333, 0.01311180392585363,
-        0.54409412649029, 0.01344843304771755,
-        0.5765229845165943, 0.01384655622092475,
-        0.6148795064211108, 0.004269409473142479,
-        0.005853691221954542, 0.02506818803768801,
-        0.007058488452666192, 0.09692609816181726,
-        0.007991811416685026, 0.170315738084356,
-        0.008730579305889177, 0.2362853743226745,
-        0.009327287399213484, 0.2936438651173445,
-        0.009818197983040462, 0.3431514772416978,
-        0.01022909697576184, 0.3859958359229893,
-        0.01057909230023007, 0.4233725763238417,
-        0.01088320687501712, 0.4564025740290915,
-        0.0111543058671517, 0.4861671131891395,
-        0.01140470198717317, 0.5137949407970326,
-        0.01164762828827466, 0.5405812657784165,
-        0.01189859698528282, 0.568127910648508,
-        0.0121763907812416, 0.5984802463148428,
-        0.0125029779529791, 0.6341959825388761,
-        0.003830262680422776, 0.00525292423946998,
-        0.02510718258012232, 0.006335607341496969,
-        0.0971230041110362, 0.007174964200736387,
-        0.1707366515477548, 0.007839821469171155,
-        0.2369623770049865, 0.008377122084280812,
-        0.2945833847967025, 0.00881923346650051,
-        0.3443363340392364, 0.009189060633588098,
-        0.3873807210303031, 0.00950337880056659,
-        0.4248706039873364, 0.00977504705184527,
-        0.4578585641947919, 0.01001457306569686,
-        0.4873111192988822, 0.01023132837651919,
-        0.5141675256404127, 0.01043459649534057,
-        0.5394214279393358, 0.01063454146082206,
-        0.5642188354052674, 0.01084307018096031,
-        0.5899649430016252, 0.01107438039614643,
-        0.6184184090843611, 0.01134470195438803,
-        0.6517206797990772, 0.003454097785831183,
-        0.004738087690909603, 0.02514098616718916,
-        0.005715864568881495, 0.09729414530950285,
-        0.006474399737140852, 0.1711037123670141,
-        0.007075625560198937, 0.2375553213635903,
-        0.007561765789488958, 0.2954111541648083,
-        0.007961900378019847, 0.3453896252983967,
-        0.008296546652001753, 0.388630302094808,
-        0.008580623356383654, 0.4262600339398994,
-        0.008825386359541219, 0.459288916256125,
-        0.009039751450513937, 0.4886139630455138,
-        0.009231266796183848, 0.5150610315193943,
-        0.009406897826583457, 0.5394434170928742,
-        0.00957372005944463, 0.5626311157802961,
-        0.009739556257960885, 0.5856281920506604,
-        0.009913518363761172, 0.6096518917386764,
-        0.01010629643624125, 0.6361953557375821,
-        0.01032986385558493, 0.6670333276830246,
-        0.003131660281084644, 0.004296601495430642,
-        0.02516987418923732, 0.005184210888756367,
-        0.09744072529384443, 0.005873198129887241,
-        0.1714189769006723, 0.006419613566950146,
-        0.2380664100570842, 0.006861660893085171,
-        0.2961280333876439, 0.007225632384805198,
-        0.346308042021841, 0.007530044942257158,
-        0.3897316580976775, 0.007788304877568383,
-        0.4275077537500284, 0.00801043093415683,
-        0.4606200718057599, 0.008204207591967733,
-        0.4899241115804965, 0.008376002129523446,
-        0.5161793704075401, 0.008531389917004646,
-        0.5400945718660145, 0.008675676859844068,
-        0.5623795630774431, 0.008814368379677447,
-        0.5838024839647016, 0.0089535958165003,
-        0.6052506199023558, 0.009100459154569437,
-        0.6277890216584121, 0.00926316620573667,
-        0.6527013571399886, 0.00945074055537075,
-        0.6814810379908328, 0.002843902743022214,
-        0.003902467368190393, 0.02519598783827689,
-        0.004709429895823432, 0.09757348323445655,
-        0.005336152661315786, 0.1717052034351406,
-        0.005833455676281756, 0.2385318286257855,
-        0.006235971415149352, 0.2967834040784211,
-        0.006567522559559145, 0.3471521575495951,
-        0.006844866528765064, 0.3907519751170857,
-        0.007080101687099548, 0.4286785748173565,
-        0.007282213357366904, 0.461897608939992,
-        0.007458094741776693, 0.4912372216070018,
-        0.007613251892383208, 0.5174141871126332,
-        0.007752321382046524, 0.5410706897885087,
-        0.007879480568321315, 0.5628149979263304,
-        0.007998799282231232, 0.5832647350414633,
-        0.008114557939046675, 0.6030926481771959,
-        0.008231531848213921, 0.623073488760433,
-        0.008355206753895566, 0.6441267697250795,
-        0.008491839744291131, 0.6673428282976036,
-        0.008648214015485161, 0.6939680907913989,
-        0.002388386682754135, 0.003278278227000989,
-        0.02523707236937346, 0.003957198838737114,
-        0.09778285117940604, 0.004484932501394734,
-        0.1721579526332683, 0.004904057483051761,
-        0.2392707453970052, 0.005243583901636578,
-        0.2978287368553751, 0.00552345600742706,
-        0.348506768678122, 0.005757685183723855,
-        0.3924033610212076, 0.005956358204781419,
-        0.4305980352749587, 0.006126919713095007,
-        0.4640361265644109, 0.006275007901630985,
-        0.4935170207127558, 0.006405016526854853,
-        0.519714357285112, 0.00652048877918682,
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-        0.5840623664365776, 0.006808059512718916,
-        0.6023621974962409, 0.006892851836922015,
-        0.6198777517486085, 0.006976537015760206,
-        0.6371392310474401, 0.007062164945929763,
-        0.6547536993606798, 0.007153184521396811,
-        0.6734273362784953, 0.007253430606435754,
-        0.6939734212185117, 0.007366943161281851,
-        0.7172914790760468, 0.002034217998243191,
-        0.002792734020582961, 0.02526908982706098,
-        0.003371787305020115, 0.097946430626842,
-        0.00382220106251195, 0.1725128108619325,
-        0.004180174912236582, 0.2398521447789659,
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-        0.00470973753959748, 0.3495841277608567,
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-        0.005080243210917943, 0.4321540636611387,
-        0.005226234784652425, 0.4657990145921906,
-        0.005352893648837146, 0.4954473934553277,
-        0.005463875356202293, 0.521753178861748,
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-        0.005995679940966749, 0.650916092177813,
-        0.006057989063542723, 0.6661462081376089,
-        0.006122321685397079, 0.681832779782845,
-        0.00619091247673213, 0.6985240974244095,
-        0.006266191569573649, 0.7168360261395987,
-        0.006350658968555684, 0.7374314365934664,
-        0.001753390300533029, 0.002407592405123618,
-        0.025294539852267, 0.002907262330175829,
-        0.09807671703676038, 0.00329614305335325,
-        0.172796146245125, 0.003605393786629613,
-        0.240317752902561, 0.003856241133152162,
-        0.2993193629853389, 0.004063271707574896,
-        0.3504538499243808, 0.004236723270781009,
-        0.3948018542411614, 0.004383951358482999,
-        0.433426391661283, 0.004510362519918408,
-        0.4672550951343391, 0.00462001758635921,
-        0.4970655128750277, 0.004716030788908096,
-        0.5235015776135139, 0.004800840911719355,
-        0.5470972903869747, 0.004876401000932111,
-        0.5682998788764699, 0.004944315587632199,
-        0.5874903820382004, 0.005005943872710219,
-        0.6050015924522462, 0.005062480886612362,
-        0.6211339094140743, 0.005115024538196171,
-        0.6361697673414449, 0.005164633649628788,
-        0.6503872077614197, 0.005212379842880342,
-        0.664072947534986, 0.005259393975018879,
-        0.6775349550821846, 0.005306905271212799,
-        0.6911140242391297, 0.005356268008877997,
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-        0.8993107995269396, 0.0001415962989297887,
-        0.9004479180657531, 0.0001416806853595467,
-        0.9015575237779277, 0.0001417630361221969,
-        0.9026406099291728, 0.0001418434247280258,
-        0.9036981246901897, 0.0001419219213591954,
-        0.9047309737757363, 0.0001419985930647974,
-        0.9057400229075616, 0.0001420735039429043,
-        0.9067261001151347, 0.0001421467153106468,
-        0.9076899978868622, 0.0001422182858632548,
-        0.908632475183385, 0.0001422882718229183,
-        0.9095542593235423, 0.0001423567270782516,
-        0.9104560477526908, 0.0001424237033150753,
-        0.911338509702248, 0.0001424892501391719,
-        0.9122022877485889, 0.0001425534151916154,
-        0.9130479992787559, 0.0001426162442572255,
-        0.9138762378698273, 0.0001426777813666525,
-        0.9146875745882436, 0.0001427380688925579,
-        0.9154825592148789, 0.0001427971476403172,
-        0.916261721401193, 0.0001428550569336404,
-        0.917025571761375, 0.0001429118346954711,
-        0.9177746029050118, 0.0001429675175245004,
-        0.9185092904144644, 0.0001430221407676021,
-        0.9192300937708135, 0.0001430757385884771,
-        0.9199374572319491, 0.000143128344032768,
-        0.9206318106661012, 0.000143179989089888,
-        0.9213135703438758, 0.0001432307047517914,
-        0.9219831396916189, 0.0001432805210688911,
-        0.9226409100087367, 0.0001433294672033191,
-        0.923287261151399, 0.0001433775714797077,
-        0.9239225621848796, 0.000143424861433657,
-        0.9245471720066236, 0.0001434713638580431,
-        0.9251614399419787, 0.000143517104847309,
-        0.9257657063143877, 0.0001435621098398706,
-        0.9263603029917071, 0.000143606403658759,
-        0.9269455539101992, 0.0001436500105506133,
-        0.9275217755776247, 0.000143692954223128,
-        0.9280892775567625, 0.0001437352578810521,
-        0.9286483629305795, 0.0001437769442608283,
-        0.9291993287501823, 0.0001438180356639552,
-        0.9297424664665896, 0.0001438585539891476,
-        0.9302780623472868, 0.0001438985207633644,
-        0.9308063978784351, 0.0001439379571717663,
-        0.9313277501535416, 0.0001439768840866617,
-        0.9318423922493136, 0.0001440153220954916,
-        0.9323505935893585, 0.0001440532915279006,
-        0.932852620296316, 0.0001440908124819338,
-        0.9333487355329478, 0.0001441279048493981,
-        0.933839199832643, 0.0001441645883404158,
-        0.934324271419735, 0.0001442008825071996,
-        0.9348042065199632, 0.0001442368067670687,
-        0.9352792596613518, 0.000144272380424723,
-        0.935749683965716, 0.0001443076226937871,
-        0.936215731430945, 0.0001443425527176319,
-        0.936677653204151, 0.0001443771895894746,
-        0.9371356998457099, 0.0001444115523717566,
-        0.9375901215841609, 0.0001444456601147895,
-        0.9380411685618638, 0.0001444795318746588,
-        0.9384890910712563, 0.0001445131867303672,
-        0.9389341397814829, 0.0001445466438001951,
-        0.9393765659551052, 0.0001445799222572509,
-        0.9398166216545342, 0.000144613041344178,
-        0.9402545599377586, 0.0001446460203869812,
-        0.9406906350428731, 0.000144678878807928,
-        0.9411251025608388, 0.0001447116361374763,
-        0.9415582195958393, 0.0001447443120251743,
-        0.9419902449125173, 0.0001447769262494714,
-        0.9424214390693088, 0.000144809498726375,
-        0.942852064537012, 0.0001448420495168817,
-        0.943282385801656, 0.0001448745988331048,
-        0.9437126694506554, 0.0001449071670430162,
-        0.9441431842411634, 0.0001449397746737126,
-        0.9445742011494633, 0.0001449724424131142,
-        0.9450059934001559, 0.0001450051911099938,
-        0.9454388364738392, 0.0001450380417722341,
-        0.9458730080918976, 0.0001450710155632024,
-        0.946308788176958, 0.0001451041337961289,
-        0.9467464587875015, 0.0001451374179263711,
-        0.9471863040250684, 0.000145170889541443,
-        0.9476286099124387, 0.0001452045703486834,
-        0.9480736642411287, 0.0001452384821604381,
-        0.9485217563865096, 0.0001452726468766264,
-        0.94897317708883, 0.0001453070864645653,
-        0.9494282181984106, 0.0001453418229359214,
-        0.9498871723832844, 0.0001453768783206665,
-        0.9503503327975676, 0.0001454122746379124,
-        0.9508179927088858, 0.0001454480338635091,
-        0.9512904450832298, 0.0001454841778942922,
-        0.9517679821256925, 0.0001455207285088794,
-        0.9522508947756375, 0.00014555770732492,
-        0.9527394721549711, 0.0001455951357527194,
-        0.9532340009683443, 0.0001456330349451717,
-        0.9537347648542913, 0.0001456714257439507,
-        0.9542420436865237, 0.0001457103286219321,
-        0.9547561128248467, 0.0001457497636218381,
-        0.9552772423154445, 0.0001457897502911246,
-        0.955805696040601, 0.0001458303076131549,
-        0.9563417308182725, 0.0001458714539347385,
-        0.9568855954523308, 0.0001459132068901443,
-        0.957437529734715, 0.000145955583321735,
-        0.9579977634012095, 0.0001459985991974088,
-        0.9585665150430652, 0.0001460422695250747,
-        0.9591439909772242, 0.0001460866082644329,
-        0.9597303840784822, 0.0001461316282363772,
-        0.9603258725775256, 3.429496445563442e-5,
-        4.71390180589219e-5, 0.02545140450924156,
-        5.698005902228804e-5, 0.09888482887297308,
-        6.46665154872123e-5, 0.1745672748051217,
-        7.080319239456012e-5, 0.2432554843126429,
-        7.580213079430914e-5, 0.3035563500747286,
-        7.994640198168628e-5, 0.3560733630370389,
-        8.343456150015368e-5, 0.4018508725952348,
-        8.640911033247278e-5, 0.4419236498367694,
-        8.897459090834537e-5, 0.477195809384324,
-        9.120925845958284e-5, 0.5084236299136395,
-        9.317276496329196e-5, 0.5362298756774806,
-        9.491132926180562e-5, 0.5611253276477577,
-        9.646129005158931e-5, 0.5835295355152852,
-        9.785159643187924e-5, 0.6037885335602649,
-        9.910558598615793e-5, 0.6221892621956204,
-        0.000100242275747997, 0.6389710741614671,
-        0.0001012773140638229, 0.6543348452257979,
-        0.0001022236924158808, 0.668450178968302,
-        0.0001030922846881736, 0.6814611164733789,
-        0.000103892260607767, 0.6934906792512014,
-        0.0001046314062227422, 0.7046445019124451,
-        0.0001053163748547551, 0.7150137530267155,
-        0.0001059528854651743, 0.7246774971389701,
-        0.0001065458808280527, 0.7337046159216464,
-        0.0001070996546816144, 0.7421553796866258,
-        0.0001076179547185671, 0.7500827400704289,
-        0.000108104066598062, 0.7575333991194183,
-        0.0001085608829314993, 0.7645486980661065,
-        0.0001089909602824242, 0.7711653599123298,
-        0.0001093965665385209, 0.7774161128496166,
-        0.0001097797204987463, 0.7833302160485504,
-        0.0001101422251266719, 0.7889339050599856,
-        0.0001104856956203599, 0.7942507707081078,
-        0.0001108115832166325, 0.7993020827048136,
-        0.0001111211954666116, 0.8041070671151008,
-        0.0001114157135775683, 0.8086831451312193,
-        0.0001116962073042465, 0.8130461392755103,
-        0.0001119636477840458, 0.8172104520762232,
-        0.0001122189186395992, 0.8211892213917328,
-        0.0001124628256154204, 0.8249944558535597,
-        0.0001126961049694284, 0.8286371533240166,
-        0.0001129194308029721, 0.8321274047940588,
-        0.0001131334214826889, 0.8354744857604804,
-        0.0001133386452827434, 0.8386869368027751,
-        0.0001135356253556231, 0.8417726348159535,
-        0.0001137248441228562, 0.8447388561361401,
-        0.0001139067471630854, 0.847592332612694,
-        0.0001140817466633488, 0.8503393015273689,
-        0.0001142502244897405, 0.8529855501323292,
-        0.0001144125349255261, 0.8555364554704203,
-        0.000114569007117969, 0.8579970200494635,
-        0.0001147199472693837, 0.8603719038646763,
-        0.000114865640603067, 0.8626654531972963,
-        0.0001150063531306337, 0.8648817265611982,
-        0.0001151423332437714, 0.8670245181211877,
-        0.0001152738131504335, 0.8690973788654197,
-        0.0001154010101729216, 0.8711036357789597,
-        0.0001155241279231094, 0.8730464092349987,
-        0.0001156433573681646, 0.8749286287938791,
-        0.000115758877798493, 0.8767530475772949,
-        0.0001158708577082165, 0.8785222553652559,
-        0.0001159794555972724, 0.8802386905462134,
-        0.0001160848207031594, 0.8819046510357806,
-        0.0001161870936694311, 0.8835223042664072,
-        0.0001162864071572288, 0.8850936963389427,
-        0.0001163828864054445, 0.8866207604170093,
-        0.0001164766497444822, 0.8881053244363083,
-        0.0001165678090680486, 0.8895491181932601,
-        0.0001166564702669258, 0.8909537798705544,
-        0.0001167427336282587, 0.892320862051182,
-        0.0001168266942035215, 0.893651837267199,
-        0.0001169084421479998, 0.8949481031247646,
-        0.0001169880630343355, 0.896210987042823,
-        0.0001170656381424237, 0.8974417506390828,
-        0.0001171412447277278, 0.8986415937936533,
-        0.0001172149562698677, 0.8998116584177496,
-        0.0001172868427031662, 0.9009530319522595,
-        0.0001173569706306669, 0.9020667506186153,
-        0.0001174254035230018, 0.9031538024423191,
-        0.0001174922019033529, 0.9042151300675857,
-        0.0001175574235196376, 0.9052516333798847,
-        0.0001176211235049476, 0.9062641719516429,
-        0.0001176833545271722, 0.9072535673250101,
-        0.0001177441669286597, 0.9082206051443592,
-        0.0001178036088566899, 0.9091660371500875,
-        0.0001178617263854677, 0.9100905830442862,
-        0.0001179185636302828, 0.910994932237941,
-        0.0001179741628544263, 0.9118797454885111,
-        0.0001180285645694077, 0.9127456564359945,
-        0.0001180818076289649, 0.9135932730449129,
-        0.0001181339293173255, 0.9144231789590457,
-        0.0001181849654321338, 0.9152359347751857,
-        0.0001182349503624295, 0.9160320792416857,
-        0.0001182839171620296, 0.9168121303871106,
-        0.0001183318976186388, 0.9175765865838867,
-        0.0001183789223189884, 0.9183259275514641,
-        0.000118425020710278, 0.9190606153031572,
-        0.0001184702211581763, 0.9197810950405108,
-        0.000118514551001616, 0.9204877959987503,
-        0.0001185580366045994, 0.9211811322466059,
-        0.0001186007034052168, 0.9218615034435585,
-        0.0001186425759620638, 0.9225292955573307,
-        0.0001186836779982295, 0.9231848815442406,
-        0.0001187240324430169, 0.9238286219948466,
-        0.0001187636614715423, 0.9244608657471405,
-        0.0001188025865423529, 0.9250819504693824,
-        0.0001188408284331903, 0.9256922032145273,
-        0.0001188784072750181, 0.9262919409480546,
-        0.0001189153425844261, 0.9268814710508878,
-        0.000118951653294512, 0.9274610917989764,
-        0.0001189873577843384, 0.928031092821002,
-        0.0001190224739070536, 0.9285917555355758,
-        0.0001190570190167592, 0.9291433535691963,
-        0.0001190910099942032, 0.9296861531561591,
-        0.0001191244632713702, 0.9302204135215227,
-        0.0001191573948550362, 0.9307463872481658,
-        0.0001191898203493515, 0.9312643206289019,
-        0.0001192217549775109, 0.931774454004551,
-        0.000119253213602564, 0.9322770220888102,
-        0.0001192842107474197, 0.9327722542807086,
-        0.0001193147606140906, 0.933260374965378,
-        0.0001193448771022213, 0.9337416038038212,
-        0.0001193745738269449, 0.9342161560123183,
-        0.0001194038641361023, 0.9346842426320593,
-        0.0001194327611268635, 0.9351460707895553,
-        0.0001194612776617823, 0.9356018439483411,
-        0.0001194894263843151, 0.936051762152442,
-        0.0001195172197338335, 0.9364960222620436,
-        0.0001195446699601559, 0.9369348181817692,
-        0.0001195717891376224, 0.9373683410819361,
-        0.0001195985891787351, 0.9377967796131313,
-        0.0001196250818473841, 0.9382203201144163,
-        0.0001196512787716769, 0.9386391468154388,
-        0.0001196771914563876, 0.9390534420327067,
-        0.0001197028312950406, 0.9394633863602434,
-        0.0001197282095816411, 0.9398691588548227,
-        0.0001197533375220634, 0.9402709372159495,
-        0.0001197782262451063, 0.94066889796073,
-        0.0001198028868132232, 0.941063216593744,
-        0.0001198273302329317, 0.9414540677720091,
-        0.0001198515674649078, 0.9418416254650982,
-        0.000119875609433767, 0.942226063110445,
-        0.0001198994670375319, 0.9426075537638465,
-        0.0001199231511567857, 0.9429862702451438,
-        0.0001199466726635097, 0.943362385279036,
-        0.0001199700424295984, 0.9437360716309537,
-        0.0001199932713350474, 0.9441075022378914,
-        0.0001200163702758047, 0.9444768503340695,
-        0.0001200393501712764, 0.944844289571268,
-        0.0001200622219714742, 0.9452099941336445,
-        0.0001200849966637913, 0.9455741388468206,
-        0.0001201076852793909, 0.9459368992809881,
-        0.0001201302988991895, 0.9462984518477588,
-        0.0001201528486594163, 0.9466589738904483,
-        0.000120175345756726, 0.9470186437674541,
-        0.0001201978014528419, 0.9473776409283557,
-        0.0001202202270787045, 0.9477361459823309,
-        0.0001202426340380965, 0.9480943407584549,
-        0.0001202650338107162, 0.9484524083574091,
-        0.0001202874379546662, 0.9488105331941014,
-        0.0001203098581083251, 0.9491689010306606,
-        0.0001203323059915656, 0.9495276989992437,
-        0.0001203547934062821, 0.9498871156140531,
-        0.000120377332236188, 0.9502473407719423,
-        0.0001203999344458418, 0.950608565740949,
-        0.0001204226120788594, 0.9509709831360716,
-        0.0001204453772552672, 0.9513347868815795,
-        0.0001204682421679518, 0.951700172159119,
-        0.0001204912190781571, 0.9520673353408602,
-        0.0001205143203099825, 0.9524364739069084,
-        0.0001205375582438321, 0.9528077863461863,
-        0.000120560945308766, 0.9531814720399889,
-        0.0001205844939737027, 0.9535577311273962,
-        0.000120608216737424, 0.9539367643517374,
-        0.0001206321261173331, 0.9543187728872938,
-        0.0001206562346369151, 0.9547039581454467,
-        0.0001206805548118562, 0.9550925215594878,
-        0.0001207050991347726, 0.9554846643473366,
-        0.0001207298800585086, 0.9558805872514442,
-        0.0001207549099779616, 0.9562804902552012,
-        0.0001207802012103997, 0.9566845722752253,
-        0.0001208057659742362, 0.9570930308289628,
-        0.0001208316163662374, 0.9575060616771147,
-        0.0001208577643371385, 0.9579238584404856,
-        0.0001208842216656548, 0.9583466121909501,
-        0.0001209109999308791, 0.958774511016349,
-        0.0001209381104830662, 0.9592077395592462,
-        0.0001209655644128141, 0.9596464785296278,
-        0.0001209933725186615, 0.9600909041917725,
-        0.000121021545273132, 0.9605411878256951,
-        0.0001210500927872672, 0.9609974951637525,
-        0.0001210790247737047, 0.9614599858031972,
-        0.0001211083505083695, 0.9619288125956789,
-        0.0001211380787908609, 0.9624041210149245,
-        0.0001211682179036361, 0.9628860485040655,
-        0.0001211987755701019, 0.9633747238043349,
-        0.0001212297589117476, 0.9638702662671197
-    ]
-
-    ROCK2ConstantCache{T, T2, typeof(zprev)}(ms, fp1, fp2, recf, zprev, 1, 1, 1, 0, 200)
-end
-
-function ROCK4ConstantCache(T, T2, zprev)
-    ms = SVector{50, Int}(
-        1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19,
-        20,
-        22, 24, 26, 28, 30, 32, 34, 36, 38, 41, 44, 47, 50, 53, 56, 59,
-        63, 67, 71, 76, 81, 86,
-        92, 98, 105, 112, 120, 129, 138, 148)
-    fpa = [(-0.149352078672699, 0.629768962985252,
-               -0.355201061573650, 0.0146745996307541,
-               -0.0558517281602565, 0.590312931352706)
-           (-0.179313593132677, 0.522354978881996,
-               -0.268020263243268, 0.0410644459848542,
-               -0.0673692676033641, 0.534974252895965)
-           (-0.182428104178289, 0.488581974232839,
-               -0.243999027372673, 0.0403844469216897,
-               -0.0621100542563179, 0.510891501054959)
-           (-0.177747282156689, 0.475598890858970,
-               -0.236544145857569, 0.0357873367680739,
-               -0.0561802405454197, 0.498502393780149)
-           (-0.171097214294784, 0.471021380996139,
-               -0.235432301175529, 0.0305165148305403,
-               -0.0508758913107147, 0.491537536121394)
-           (-0.164446145110292, 0.470315341552133,
-               -0.237054736024656, 0.0253636332272387,
-               -0.0462365759807733, 0.487394153808489)
-           (-0.158427655171257, 0.471468878620055,
-               -0.239853802450812, 0.0205746749952032,
-               -0.0421744356707249, 0.484829913014008)
-           (-0.153293058075572, 0.473282079177035,
-               -0.242910850765406, 0.0163722321103915,
-               -0.0387108095861697, 0.483081034299037)
-           (-0.148972804305139, 0.475296959544537,
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-        0.8343474538279233, 0.0005127590534347159,
-        0.8358812817402723, 0.0005131973502504269,
-        0.8373858295066677, 0.0005136272493279681,
-        0.8388621052231878, 0.0005140490517517615,
-        0.8403111020816669, 0.0005144630551056335,
-        0.8417338027616508, 0.0005148695548966082,
-        0.8431311841041218, 0.0005152688460744951,
-        0.8445042221173288, 0.0005156612246635426,
-        0.8458538973693004, 0.0005160469895237514,
-        0.8471812008262565, 0.0005164264442608728,
-        0.8484871402011642, 0.0005167998993056541,
-        0.8497727468820885, 0.0005171676741845232,
-        0.8510390835157447, 0.0005175301000056107,
-        0.8522872523277160, 0.0005178875221857676,
-        0.8535184042670900, 0.0005182403034460151,
-        0.8547337490696901, 0.0005185888271046153,
-        0.8559345663404898, 0.0005189335006986103,
-        0.8571222177620127, 0.0005192747599661662,
-        0.8582981605412726, 0.0005196130732232652,
-        0.8594639622127785, 0.0005199489461690734,
-        0.8606213169188581, 0.0005202829271545004,
-        0.8617720632905069, 0.0005206156129478311,
-        0.8629182040514101, 0.0005209476550295670,
-        0.8640619274638366, 0.0005212797664454193,
-        0.8652056307266341, 0.0005216127292413131,
-        0.8663519454211874, 0.0005219474024967696,
-        0.8675037650792340, 0.0005222847309624981,
-        0.8686642749148173, 0.0005226257542936992,
-        0.8698369837189167, 0.0005229716168515654,
-        0.8710257578565097, 0.0005233235780207398,
-        0.8722348572285707, 0.0005236830229588920,
-        0.8734689729618574, 0.0005240514736547882,
-        0.8747332664628638, 0.0005244306001218837,
-        0.8760334093141518, 0.0005248222314940908,
-        0.8773756232962860, 0.0005252283667175941,
-        0.8787667195815746, 0.0005256511844461572,
-        0.8802141358619505, 0.0005260930516464654,
-        0.8817259698386895, 0.0005265565303044835,
-        0.8833110071141399, 0.0005270443814944088,
-        0.8849787410860012, 0.0005275595659308863,
-        0.8867393819581020, 0.0005281052399771031,
-        0.8886038514594998, 0.0005286847459332971,
-        0.8905837593259870, 0.0005293015952926587,
-        0.8926913570756628, 0.0005299594435392922,
-        0.8949394641477838, 0.0005306620549953031,
-        0.8973413611324083, 0.0005314132562256762,
-        0.8999106446760794, 0.0005322168766096216,
-        0.9026610388027025, 0.0005330766749183085,
-        0.9056061579514983, 0.0005339962511354281,
-        0.9087592181279729, 0.0001291672658807919,
-        0.0001569411415132314, 0.007144429374444041,
-        0.0001812286696375032, 0.03374884163870904,
-        0.0002024891487895646, 0.06836875906346668,
-        0.0002211729609091939, 0.1057051970576302,
-        0.0002376757078934563, 0.1431775337300160,
-        0.0002523309440420044, 0.1795193851821314,
-        0.0002654155096114621, 0.2141350485529856,
-        0.0002771580968905830, 0.2467819320733997,
-        0.0002877477478365611, 0.2774056154477370,
-        0.0002973412539386665, 0.3060510531385813,
-        0.0003060692727883761, 0.3328136064982617,
-        0.0003140412687616450, 0.3578116754563008,
-        0.0003213494654089220, 0.3811713698313008,
-        0.0003280719982928522, 0.4030180284424702,
-        0.0003342754323013638, 0.4234716859228214,
-        0.0003400167776073826, 0.4426448303068433,
-        0.0003453451109288780, 0.4606414878637722,
-        0.0003503028857160415, 0.4775570675004032,
-        0.0003549269964559184, 0.4934786274558236,
-        0.0003592496478431822, 0.5084853632454121,
-        0.0003632990683734921, 0.5226491973781846,
-        0.0003671000992804959, 0.5360354006553708,
-        0.0003706746830802694, 0.5487032048025572,
-        0.0003740422708473267, 0.5607063844089743,
-        0.0003772201633670793, 0.5720937971957492,
-        0.0003802237982173855, 0.5829098782647340,
-        0.0003830669924186714, 0.5931950878770883,
-        0.0003857621484003172, 0.6029863145180096,
-        0.0003883204295409269, 0.6123172361692740,
-        0.0003907519103608007, 0.6212186432401899,
-        0.0003930657055071256, 0.6297187267546153,
-        0.0003952700809230814, 0.6378433353164356,
-        0.0003973725499905643, 0.6456162041780895,
-        0.0003993799569511753, 0.6530591594781886,
-        0.0004012985495172340, 0.6601923004327613,
-        0.0004031340422649590, 0.6670341619826434,
-        0.0004048916721408514, 0.6736018601298540,
-        0.0004065762471981460, 0.6799112219451941,
-        0.0004081921895038212, 0.6859769020007800,
-        0.0004097435730108617, 0.6918124867754874,
-        0.0004112341570695012, 0.6974305883977158,
-        0.0004126674161504436, 0.7028429289271262,
-        0.0004140465662688992, 0.7080604162333366,
-        0.0004153745885277149, 0.7130932124031323,
-        0.0004166542501385347, 0.7179507954967295,
-        0.0004178881232298605, 0.7226420153762622,
-        0.0004190786017085115, 0.7271751442443414,
-        0.0004202279164050269, 0.7315579224557873,
-        0.0004213381487029441, 0.7357976001001488,
-        0.0004224112428257702, 0.7399009747952365,
-        0.0004234490169331078, 0.7438744260815747,
-        0.0004244531731582231, 0.7477239467635279,
-        0.0004254253067028491, 0.7514551715040853,
-        0.0004263669140908001, 0.7550734029462083,
-        0.0004272794006696848, 0.7585836356036648,
-        0.0004281640874393643, 0.7619905777378661,
-        0.0004290222172765655, 0.7652986714139369,
-        0.0004298549606170237, 0.7685121109086968,
-        0.0004306634206495281, 0.7716348596250679,
-        0.0004314486380701255, 0.7746706656513523,
-        0.0004322115954393903, 0.7776230760895890,
-        0.0004329532211809737, 0.7804954502645794,
-        0.0004336743932555310, 0.7832909719139642,
-        0.0004343759425404994, 0.7860126604497781,
-        0.0004350586559430094, 0.7886633813730524,
-        0.0004357232792703970, 0.7912458559151491,
-        0.0004363705198802944, 0.7937626699724827,
-        0.0004370010491300795, 0.7962162823950203,
-        0.0004376155046435118, 0.7986090326833559,
-        0.0004382144924106579, 0.8009431481441662,
-        0.0004387985887356742, 0.8032207505493939,
-        0.0004393683420456565, 0.8054438623405243,
-        0.0004399242745725549, 0.8076144124157677,
-        0.0004404668839190812, 0.8097342415347859,
-        0.0004409966445185832, 0.8118051073727768,
-        0.0004415140089980146, 0.8138286892532131,
-        0.0004420194094523807, 0.8158065925862987,
-        0.0004425132586383796, 0.8177403530382282,
-        0.0004429959510943727, 0.8196314404545940,
-        0.0004434678641933102, 0.8214812625597571,
-        0.0004439293591347870, 0.8232911684526717,
-        0.0004443807818820194, 0.8250624519185151,
-        0.0004448224640492010, 0.8267963545745015,
-        0.0004452547237444166, 0.8284940688674631,
-        0.0004456778663730607, 0.8301567409401316,
-        0.0004460921854065215, 0.8317854733825585,
-        0.0004464979631207512, 0.8333813278847675,
-        0.0004468954713092401, 0.8349453278065194,
-        0.0004472849719748584, 0.8364784606800110,
-        0.0004476667180050050, 0.8379816806613994,
-        0.0004480409538345297, 0.8394559109472592,
-        0.0004484079161009533, 0.8409020461724398,
-        0.0004487678342966111, 0.8423209548062871,
-        0.0004491209314224874, 0.8437134815648469,
-        0.0004494674246486925, 0.8450804498574688,
-        0.0004498075259867541, 0.8464226642871850,
-        0.0004501414429791688, 0.8477409132253626,
-        0.0004504693794119635, 0.8490359714824147,
-        0.0004507915360563808, 0.8503086030978187,
-        0.0004511081114462013, 0.8515595642743328,
-        0.0004514193026976681, 0.8527896064831288,
-        0.0004517253063794774, 0.8539994797685749,
-        0.0004520263194408489, 0.8551899362836138,
-        0.0004523225402062811, 0.8563617340890786,
-        0.0004526141694462433, 0.8575156412528867,
-        0.0004529014115337412, 0.8586524402878235,
-        0.0004531844756974208, 0.8597729329695807,
-        0.0004534635773826384, 0.8608779455798124,
-        0.0004537389397327130, 0.8619683346221994,
-        0.0004540107952033793, 0.8630449930628203,
-        0.0004542793873242631, 0.8641088571494663,
-        0.0004545449726219747, 0.8651609138678200,
-        0.0004548078227201481, 0.8662022090955665,
-        0.0004550682266323894, 0.8672338565183648,
-        0.0004553264932646083, 0.8682570473740338,
-        0.0004555829541435220, 0.8692730610930815,
-        0.0004558379663881761, 0.8702832769045586,
-        0.0004560919159410250, 0.8712891864758329,
-        0.0004563452210743556, 0.8722924076528336,
-        0.0004565983361864682, 0.8732946993631147,
-        0.0004568517558999058, 0.8742979777371169,
-        0.0004571060194709263, 0.8753043334925269,
-        0.0004573617155151244, 0.8763160506117581,
-        0.0004576194870483323, 0.8773356263222484,
-        0.0004578800368343567, 0.8783657923622515,
-        0.0004581441330213403, 0.8794095374796469,
-        0.0004584126150361641, 0.8804701310663527,
-        0.0004586863996908342, 0.8815511477743261,
-        0.0004589664874357118, 0.8826564928888149,
-        0.0004592539686711794, 0.8837904281482389,
-        0.0004595500300013319, 0.8849575975954920,
-        0.0004598559602799827, 0.8861630529202465,
-        0.0004601731562602071, 0.8874122776038270,
-        0.0004605031276134677, 0.8887112090056589,
-        0.0004608475010329713, 0.8900662573321374,
-        0.0004612080230785231, 0.8914843202051330,
-        0.0004615865613575363, 0.8929727913000981,
-        0.0004619851035704269, 0.8945395612571059,
-        0.0004624057538807515, 0.8961930087896581,
-        0.0004628507260045860, 0.8979419796374420,
-        0.0004633223323547168, 0.8997957507473553,
-        0.0004638229685297288, 0.9017639768452591,
-        0.0004643550924143431, 0.9038566164094044,
-        0.0004649211971655587, 0.9060838340132801,
-        0.0004655237774111018, 0.9084558761162183,
-        0.0004661652880954744, 0.9109829176962647,
-        0.0004668480955879464, 0.9136748776971255
-    ]
-
-    _fpa = map(x -> SVector{6, T}(x), fpa)
-    _fpb = map(x -> SVector{4, T}(x), fpb)
-    _fpbe = map(x -> SVector{5, T}(x), fpbe)
-    ROCK4ConstantCache{eltype(_fpa), eltype(_fpb), eltype(_fpbe), T2, typeof(zprev)}(ms,
-        _fpa,
-        _fpb,
-        _fpbe,
-        recf,
-        zprev,
-        1, 1,
-        1, 0,
-        152)
-end
-
-function ESERK5ConstantCache(zprev)
-    ms = [
-        1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 25, 30, 35,
-        40, 45, 50, 60, 70, 80, 90,
-        100, 150, 200, 250, 300, 350, 400, 450, 500, 600, 700, 800, 900, 1000, 1200, 1400,
-        1600, 1800, 2000]
-    Cᵤ = [1, -64, 486, -1024, 625]
-    Cₑ = [1, -32, 162, -256, 125]
-    Bᵢ = [0.51000000000000000000, 0.49000000000000000000,
-        0.15175595325054784514243973703433162892622352081811541271,
-        0.4776587289992695398100803506208911614317019722425127830533,
-        0.3705853177501826150474799123447772096420745069393718042367,
-        0.171292271855634748274302568345977333137780187276509375111,
-        -0.142394363264918735501782787535994907865493057653096376214,
-        0.3031160937815012006356183084140929657730712942298386293,
-        0.667985997627782786591861910775924608954641576146748371803,
-        -0.2395607163123067106628641054321945729049318796662228882758,
-        0.0322753316670842254789679591276287281776581352286896612159,
-        0.1311198549137829290449396289890724944618997972541672447189,
-        0.4420263297245774635901262045359551693827496339040954996064,
-        0.6341392000068620925488303127795381808826243132792704827345,
-        -0.0705527233174208787197482567012020748, -0.28314320544924802791643836910100325622,
-        0.19785090029766025895627566014160733854, -0.42177903459881749394659312103987771203,
-        0.34798179035774081281423544657031887843, 1.22964227271008532881226864013015682608,
-        -0.023312108626697192778954029514024155590455567466604125321,
-        -0.133587241606424763164999610937242437020685580372892917197,
-        -0.807816187727509870414818584094023142999629225128357391874,
-        0.035476895783242056771711790729782516422751007751815116498,
-        0.149607787788030927665027003231661098177436901731326766172,
-        0.57498834712543318780630073306500660354701244451330594928,
-        1.204642507263925654115732697518839517463570018971406602442,
-        -0.06183255936954052372346637670968840324,
-        0.24585010938894813663007172333107991903, -0.22278728293517506331040227550535600357,
-        -1.15228036070198057531767004885883669258, 0.27248345332452279643055687285311892589,
-        -0.94663509712136048123663124969573327248, 0.49107351303189728397292372218922624695,
-        2.37412822438268842655461763239618928,
-        0.267629933137095245141975809560761081772265274435597289728,
-        -0.006141586913407430655973481502643365713649790710295868616,
-        -0.075413760530132378580716897804667838399145117853966422589,
-        -0.413732608581709348691129801944743112619079061906883568263,
-        -2.219755953356489632106290970858486877686158726479341880497,
-        0.041831600717443209915013866154013953177078863044028484934,
-        0.198251969249198553353762337987712861100318955878803016743,
-        0.859429079700333096723067072151535793932185170639840432677,
-        2.347901326577668684900292066256517504436184432952218515884,
-        0.04334233496728318173316556549400405312, 0.28314718674373824327128333993303395952,
-        -0.19691175059131013000473375960242211319, 1.0143522195178293575154435082688758514,
-        -0.54456448978467780165114785396914473844,
-        -3.44227306031624992637612263891716183315,
-        0.41616051745839018146471699669491474031, -1.99431152490366256986310650480329437152,
-        0.76615984404425241607002155607656609488, 4.65489872286440704784047979083,
-        0.01185981511609708439591263798032260188, 0.08313810798594927518141308800422658388,
-        1.36524308048041620952880042718654864619, -0.01827474030589477217044171499310793939,
-        -0.17628501318837535533115360122055965499,
-        -1.01698852621620427516096462226557091393,
-        -5.59376138718872207707282115748, 0.05312126866410229999185962171436582123,
-        0.28375149392681463287142512194791155436, 1.3863138835464458632096743126042793536,
-        4.62188201717937111455629588652, 0.03969981439217597320648548760187749161,
-        -0.26123314150702799097976575231108173978, 0.22377746288085075525371428197050370229,
-        1.69666756226863378995937682521810719807, -0.49131949600957692517825210290306837642,
-        3.1080707614085650333516840811827436161, -1.22864881730603059070878872425149963605,
-        -9.11689366539937630043735086892, 0.67785105301773902362095145917851111,
-        -4.10631720372905360414597657171939847232, 1.26937540263078554905007063379542835836,
-        9.18897026735231528700785125117, -0.27217328167460956131476047439990910903,
-        0.00232423179456403254837083539454086331, 0.05835150404451187539144020461201262805,
-        0.42883425599848069725879046327775141413, 4.95905709165333544549841757169,
-        -0.03977266751636963109146218894149857435,
-        -0.36571787671245400376083804163342213853,
-        -2.31568252687422134776066391768411540054, -13.43925313136367349501729212019,
-        0.07077616236834410843502486226791398161, 0.42282994010986272157251902585583891218,
-        2.34796383346795816363119912676449258734, 9.14246246470427099460925465297,
-        -0.03232911686897840419632830592607494535,
-        -0.28041462996958647581873583696711945616,
-        0.20724033413910790425827799265356162173, -1.58579023135541602567366698739041278356,
-        0.78922415382841551949951795717071921361, 6.76103173539977893909117415311,
-        -1.12806447574673841730721198743265087628, 8.4128930401780590648783621418,
-        -2.68103276352794485617211013468853083618, -22.64411393742258884318225036397,
-        1.15338533203053367320846851344449345606, -8.36649294273889607381551803959,
-        2.18999145420808421833691176599430999249, 18.2044720478461697768931091318,
-        -0.00667461933209428360036059839767196909,
-        -0.06273416882765801260467188444545123031,
-        -1.91860065644695596557081912874590006998, 0.01081950272692567798463347457716599767,
-        0.18620287400700286111119582520568003694, 1.51685497093458109071452221097531826534,
-        15.48467225224063382408542314168, -0.07629435549619645150060099149748659182,
-        -0.70994280729761713821480657439726187699,
-        -5.09786121288496023233135783192012886576,
-        -31.31366293050426656280475363934, 0.09668925281447020816755087806058848403,
-        0.64160729399321059791833884085849337916, 4.11515766267157779011538851714,
-        18.13376694140134659653031776024, -0.03037494879224957381,
-        0.26769482655261944704, -0.23423482472351800365,
-        -2.23691169833583813897, 0.73825815998211408164,
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-        -4.77952069574062132773, -13.83712910260980066823,
-        30.22884728823828481836, -40.22732139168714127209,
-        35.42041732704110756913, -14.72954694341913217670,
-        -20.52079756438108759653, 54.30165974703549380820,
-        -64.09572187213066740696, 20.63081185725096133865,
-        75.12719825943990770156, -133.60939683556816248711,
-        -169.50737144934362277127, -59.48433955333090494833,
-        -41.63904512849007488740, -33.99231401054399270834,
-        19.54080797462349394777, 4.55502829849072021773,
-        -15.26117612129312206548, 12.97777918779591033172,
-        -4.38161720143158106566, -4.25701440147834819783,
-        9.57161442668551210033, -10.59074149413601162451,
-        8.22425561888591261095, -3.93551997564432465282,
-        -0.59370052425162889165, 4.25231302764825969120,
-        -6.28295485383557483772, 6.63113776496695006557,
-        -5.45322092404674041433, 3.32464860860422728450,
-        -0.72174179537998761624, -1.73600276622615212752,
-        3.72743418815548643863, -4.90913278589302759514,
-        5.27762917881411297572, -4.79342985877045535403,
-        3.69931246402335478507, -2.12717898344685396594,
-        0.40716115481260672926, 1.31486650739087851392,
-        -2.75775841592583503825, 3.86536728993510170227,
-        -4.47202198976235720806, 4.64146528060607099775,
-        -4.32202935651763553437, 3.67117967066754946615,
-        -2.70824590474662896256, 1.63231086955569804076,
-        -0.47938686375067485201, -0.56076131477905943878,
-        1.47891213073261185151, -2.12807286467000489338,
-        2.54809034284746172005, -2.64587684032847691995,
-        2.51129265429602321902, -2.09752062090623825341,
-        1.53021396994055591811, -0.79016565313862696662,
-        0.01782425772482717011, 0.79982916520908431401,
-        -1.52777964579206115836, 2.19063008943328085820,
-        -2.67322919924064095198, 3.02233610023077803319,
-        -3.14920215486500643109, 3.12536382300724291383,
-        -2.88752930281527486756, 2.52802255896745631247,
-        -2.00261060574737204121, 1.41628854711359730700,
-        -0.73474316150517171575, 0.06613683269867334791,
-        0.62320295862315566726, -1.23050434390276075547,
-        1.79624444392047655228, -2.22909643671861124048,
-        2.58083743625210493278, -2.77445838998999194658,
-        2.87431465786761730641, -2.81750613892182055764,
-        2.67943921313475463819, -2.40869196929474282953,
-        2.08823023903227200648, -1.67401470819087916375,
-        1.25212618399791075774, -0.78135788804567496424,
-        0.34647002877269694743, 0.09504147401617690782,
-        -0.46340533305202302738, 0.80551049590822643154,
-        -1.04900109572744959507, 1.24687233037410738490,
-        -1.33519138989903529691, 1.37337515387613695594,
-        -1.30558596407717164567, 1.19676074700220591573,
-        -0.99776831700801149605, 0.77728685867111679819,
-        -0.49082644856614821016, 0.20855911059356316284,
-        0.11169134801791683054, -0.40057182512454353462,
-        0.70015651007021295626, -0.94394799546326590978,
-        1.17571877487340503698, -1.33334423676399360659,
-        1.46349593470744543389, -1.50928811310242139143,
-        1.52081703631328757353, -1.44662827430008245067,
-        1.34011944582467523723, -1.15485550349734777953,
-        0.94686886965187611054, -0.67386296859152894356,
-        0.39345309523237803617, -0.06630420019528697473,
-        -0.24964180933781424110, 0.59204882237304268244,
-        -0.90393067744921606899, 1.22251525424021401101,
-        -1.49292595163198793529, 1.75299746308000492512,
-        -1.95087108654695273735, 2.12574385640498420003,
-        -2.22936578206585656048, 2.30271551767697424395,
-        -2.30139869882997150086, 2.26825371194373959227,
-        -2.16265972775240644665, 2.02908445392619007919,
-        -1.83031751931261355004, 1.61197782461515704000,
-        -1.33969227404366431067, 1.05958332281437939137,
-        -0.73941469259667325087, 0.42508010949271729517,
-        -0.08573686336920882667, -0.23368506985916576157,
-        0.56334347730314737746, -0.85993865931544666292,
-        1.15355380075085678371, -1.40306234169566979020,
-        1.63893898008094884844, -1.82261333889625243287,
-        1.98524726049448907439, -2.09103327073781963819,
-        2.17193843983594758740, -2.19495042784403082692,
-        2.19279208859516039354, -2.13512131262470017390,
-        2.05522349364857603859, -1.92517378376399994622,
-        1.77851640906494634642, -1.58939926139562182072,
-        1.39124984075851809706, -1.15989237858786520263,
-        0.92822999525679505961, -0.67335391614435835539,
-        0.42724042918907328970, -0.16786040866833609742,
-        -0.07410194924083186863, 0.32013291647182384736,
-        -0.54114372345734851333, 0.75834338179222204879,
-        -0.94446353697409390904, 1.12061818577059857382,
-        -1.26149810880578239214, 1.38821734834325427599,
-        -1.47747830175773553485, 1.55040654453367743315,
-        -1.58568918912120992992, 1.60440097318669594451,
-        -1.58711959590678031162, 1.55474689021980583270,
-        -1.48960550996303919824, 1.41225945797069551979,
-        -1.30659672321418773855, 1.19265347258985410228,
-        -1.05568707180035192827, 0.91500792573222911042,
-        -0.75704682984927684775, 0.60019784096280848207,
-        -0.43188318301938188881, 0.26940973700598153107,
-        -0.10103385877493661904, -0.05716681331738498323,
-        0.21622718922519248985, -0.36140680255428325740,
-        0.50312173808986693224, -0.62804062257029935612,
-        0.74601488413363170604, -0.84515939411641261003,
-        0.93478192847318342107, -1.00444972820381295264,
-        1.06291948259806057209, -1.10119141383965923886,
-        1.12744135344740170623, -1.13406409667194973956,
-        1.12860920190047031575, -1.10481531618038042453,
-        1.06955121381055628937, -1.01784259371584329124,
-        0.95581962191674607610, -0.87973738345246554893,
-        0.79493084675791947369, -0.69882976314208455904,
-        0.59592157689506852769, -0.48476115234862016123,
-        0.36894175992122868468, -0.24809962142074662439,
-        0.12489275394198096070, -0.85780827449441809929,
-        1.87311135815871554477, -1.40838964617257844658,
-        1.51177330515780683484, -0.99819347485982323764,
-        1.05784841870849533052, -0.50747983332533763701,
-        0.53701836782916634316, 0.03515625425156850004,
-        -0.01958264392830722650, 0.59646954782771133274,
-        -0.57707569418250370674, 1.14046822460767693919,
-        -1.09891348545263389802, 1.63063587025018597032,
-        -1.54921720273101470866, 2.03234901936288192559,
-        -1.89523754379765452249, 2.31534194103619794802,
-        -2.10978152453728418081, 2.45605233636000264141,
-        -2.17343321962911106837, 2.43967327697667801800,
-        -2.07639382788092863308, 2.26173990559339310735,
-        -1.81977592374179253376, 1.92909539899777526806,
-        -1.41620936898234117685, 1.46010995330698256645,
-        -0.88965215790011287211, 0.88406865636163978195,
-        -0.27434751260641593307, 0.23969758860449907889,
-        0.38707318844511401368, -0.42714022949747076918,
-        1.04627669175666393464, -1.06647999374421464935,
-        1.65257006860975330653, -1.62785434758215363793,
-        2.15669926350085283673, -2.06422649348368292266,
-        2.51484582334094231015, -2.33597443519399039502,
-        2.69251859555245420808, -2.41460749404885000047,
-        2.66801136586207343626, -2.28588196314601921344,
-        2.43509577132545906863, -1.95199470173242173310,
-        2.00464505489753097578, -1.43257446865560900129,
-        1.40494018730467207234, -0.76426160869441739365,
-        0.68049511586879374292, 0.00123442695606782024,
-        -0.11065074693540660755, 0.80058792341807583082,
-        -0.90109327923956672457, 1.56367006680671272179,
-        -1.61945564791642437896, 2.21942855837988206602,
-        -2.19664754902769399081, 2.70240304689617705236,
-        -2.57249974687655136307, 2.95933029642088785138,
-        -2.70218270891704470671, 2.95521357734111900228,
-        -2.56176201377990286900, 2.67820118059230916074,
-        -2.15224301550462726595, 2.14265054817842415247,
-        -1.50152244741964424612, 1.38985446423221148393,
-        -0.66379972140869081265, 0.48607545398525398017,
-        0.28379641335707150862, -0.48223176779533366565,
-        1.24734915997572115565, -1.41584609513250203605,
-        2.12474506029864507184, -2.21237845027716373281,
-        2.81608240133038556507, -2.77725694698999969745,
-        3.23496724231648480341, -3.03503998360083082630,
-        3.31952785645927539449, -2.93980156225781152912,
-        3.04183396255613835990, -2.48325019944946179251,
-        2.41439383249833383616, -1.69930609927331621734,
-        1.49254767036226332344, -0.66409209398160262694,
-        0.37189332009631109743, 0.50930286450736328430,
-        -0.81963473024248156840, 1.68136930431824160870,
-        -1.93478793241133373293, 2.70143811420589274874,
-        -2.82417238408201676236, 3.42633704446697207047,
-        -3.35588896499030386877, 3.74043501951139623074,
-        -3.43533939724581305342, 3.57452036928739946831,
-        -3.02245910744027179717, 2.92066509752646119580,
-        -2.14350895444062006234, 1.84028647864847472171,
-        -0.89482393420570593978, 0.46310393387632242668,
-        0.56336838130760025223, -1.02436837438441696868,
-        2.02378529626559799937, -2.40079020822687994041,
-        3.25877267922739788375, -3.44075290845240600035,
-        4.05427119825817428023, -3.95087416588613837831,
-        4.24676459902850300665, -3.80616006419662511462,
-        3.75749216065801716624, -2.98043272692543714797,
-        2.61744612953490563001, -1.56431234847746858385,
-        0.97689064952889437254, 0.23495547119555709736,
-        -0.90542870272534381471, 2.11545108151931193774,
-        -2.69548274454682879053, 3.72458975879092957229,
-        -4.03777504989926061540, 4.72114648584837492962,
-        -4.62337978488568079882, 4.84654382750967194227,
-        -4.26121124425948316627, 3.99242777829729877936,
-        -2.93795928890069291128, 2.24891680607976507389,
-        -0.85071251929934832425, -0.08199969576345185474,
-        1.60187176569509603929, -2.51966469929374348169,
-        3.87817012841315111871, -4.48842352034151659268,
-        5.40044080607088172741, -5.44406191014984397469,
-        5.69550708319509180200, -5.02167434231604570272,
-        4.54119726028438996934, -3.17080776703337274824,
-        2.07951317135702717920, -0.23575542432270046866,
-        -1.14634107652135908140, 3.05971292687276674727,
-        -4.26627257252743330440, 5.74920081827091955518,
-        -6.28199543916729918891, 6.87853996202356565703,
-        -6.36676099678099127743, 5.83323571970965737421,
-        -4.19763530741292623105, 2.64766298494007656927,
-        -0.20999396108836054786, -1.82844539669973205065,
-        4.35625482986863321599, -6.03185618623979191710,
-        7.72604861288495836646, -8.12956796039805240639,
-        8.19730238541001199337, -6.76095271771287187335,
-        4.96372751166680181711, -1.86432702668585648098,
-        -1.15336316764613067143, 4.80067756449165372601,
-        -7.51335681582440262360, 9.90572301763357287996,
-        -10.44052035142463452644, 9.90771576476919335619,
-        -7.11188150283440201349, 3.33639304322946816939,
-        2.00730798404884636099, -6.99958912648036690740,
-        11.67785575660025187972, -13.81125972418755942783,
-        13.52632834426499641722, -9.23127753746672041757,
-        2.31352987610601390500, 6.99210139750832038175,
-        -15.18394391708127422191, 20.17921613415559889404,
-        -17.77065719241926089467, 7.42012437818138437251,
-        10.21108605923605416876, -27.10756935805689593622,
-        32.01137420331927074812, -10.28571466942930534572,
-        -37.58600600492959387111, 66.81980314062600712077,
-        84.74613000143813223985, 23.68169873246636214503
-    ]
-
-    ESERK5ConstantCache{eltype(Bᵢ), typeof(zprev)}(ms, Cᵤ, Cₑ, zprev, Bᵢ, 1, 0, 0)
-end
-
-function ESERK4ConstantCache(zprev)
-    ms = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 30, 40, 50, 60, 70, 80, 90, 100, 150, 200,
-        250, 300, 350, 400, 450, 500, 600,
-        700, 800, 900, 1000, 1200, 1400, 1600, 1800, 2000, 2200, 2400, 2600, 2800, 3000,
-        3200, 3400, 3600, 3800, 4000]
-    Cᵤ = [-1, 24, -81, 64]
-    Cₑ = [-1, 12, -27, 16]
-    Bᵢ = [0.12903031034899166767, 0.49462625286801110977,
-        0.37634343678299722256, -0.25248538379384922845,
-        0.0065129464125214976767, 0.077186857588232424888,
-        0.55518167170340454810, 0.61360390808969075779,
-        0.026821833388298651543, -0.23844614933200639399,
-        -0.76943611658030427733, -0.052379853152861735529,
-        0.014179167753833524172, 0.92215895856320626202,
-        1.0971021593598339691, 0.25456740224713096152,
-        0.046650908225896002831, 0.14338240606715926211,
-        -0.92613081680893540712, -1.9465727592802500489,
-        -0.22144586882206719459, -0.11306492247477732176,
-        1.7563236328818076488, 2.0062900179640360971,
-        -0.066728473228038671792, 0.25232940302011953164,
-        1.1618884569876829303, 0.30350571523961683903,
-        0.50164054491810920617, -2.7931536927570665119,
-        -4.5295780253657152091, -0.67188363351729623860,
-        -0.38028484476745363464, 3.5211542882361179678,
-        3.7011102612339237911, -0.22431641894434376622,
-        -0.095212294131596456968, -0.39596847648837331130,
-        1.5284841107814154297, 3.8039868210217295398,
-        1.2748002881339524556, 1.4157736944833311983,
-        -7.5764772925210534979, -10.058311860474665258,
-        -1.8033764221743628045, -0.91352231639864554315,
-        7.1873465915995468184, 6.8567935751130651961,
-        0.089633515403911625246, -0.28058971818545412769,
-        -1.3824512672524968206, -0.77303175201857023245,
-        -1.5054660351670404849, 6.1730354661466545938,
-        10.754498058418705882, 4.3754431703836324144,
-        3.4971707874515048441, -19.298377373880449908,
-        -21.679197201200411906, -4.5191317892538197684,
-        -1.9184207257501124480, 14.733353242310913785,
-        12.733531622593032552, 0.18247485290633446391,
-        0.15274956187126426045, 0.64305376735887396864,
-        -2.2301480378809042523, -5.5912992223215940830,
-        -3.8785240908687354398, -4.5794572425185702147,
-        20.708131963663656349, 27.955189820169577510,
-        13.320032683463520330, 7.8389594854218088941,
-        -47.067374517798599568, -45.775942402086720154,
-        -10.813302946259980633, -3.7039215919752813971,
-        30.157452498885583404, 23.681925417969766563,
-        -0.097496630081181789625, 0.29986310469645080236,
-        1.4037890194877929136, 1.5019213232893944033,
-        2.7814662532429699717, -11.031104364448240771,
-        -18.653182893706351952, -15.410792988965120823,
-        -12.002012749248651095, 62.249447374437296304,
-        68.829893077389427609, 37.401422569058439149,
-        16.180781599286180762, -111.13869336487127875,
-        -95.226922191927817420, -25.004904139630761658,
-        -6.6651890801149859487, 61.495029689806802999,
-        44.086684392299635293, -0.13498139344748607042,
-        -0.21525311823596157527, -0.80567432398268767083,
-        2.9079063658764704467, 6.7344997071883137943,
-        8.7901999385692458306, 9.2101568948499024988,
-        -43.467787907851503104, -55.663043205814981634,
-        -53.099690977542503108, -27.875819065008162801,
-        173.86926246376423709, 163.22159290197214870,
-        99.026615560070335116, 30.755338538621012402,
-        -255.88882993067805104, -195.89303206890559761,
-        -56.298488281187615457, -11.121564850970185422,
-        124.82065890461286859, 82.127933848100201016,
-        0.043661038580818492087, -0.11786144997441083010,
-        0.066386010208599287316, -0.076031148164367425586,
-        0.0052073294838449464829, -0.00090264731399954452596,
-        -0.068664542746013045468, 0.038528424050786266651,
-        -0.0059497960280323823689, -0.25252424104948956848,
-        -0.30428563069431871063, -0.45243252339670828448,
-        0.0082359241356843848668, 0.17761473004016235521,
-        -0.17473299903356992805, 0.15389866793915295439,
-        -0.089825185246879795782, 0.059183329009329878301,
-        -0.022928853429258550581, 0.011338764099281519687,
-        -0.038106847893825768972, 0.23171435974630057980,
-        -0.012156947119830843975, 0.10138743758292338331,
-        0.17465860724959391537, -0.14081481729919138403,
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-        0.10173714826821183124e+04, 0.91747019366100539628e+04,
-        0.46340291299984746729e+04, -0.87329649608139861812e+04,
-        -0.55433052687182125737e+04, 0.16029120724397130289e+04,
-        0.48680865479898811827e+04, 0.64751478493581244038e+04,
-        -0.48313945268456091071e+04, -0.92955821146728612803e+04,
-        0.35281661904997631609e+04, 0.64605558055334267920e+04,
-        0.11608077620936271614e+04, -0.27735793522652406864e+04,
-        -0.70908744431112390885e+04, 0.19287728777168758825e+04,
-        0.96383337691693905072e+04, -0.24335493589356724442e+04,
-        -0.72491541030107073311e+04, 0.57662869671116129666e+03,
-        0.34084555433698383240e+04, 0.41172111939473097664e+04,
-        -0.23487732924977813127e+04, -0.79731092864742504389e+04,
-        0.41273766690001784809e+04, 0.77864192378159259533e+04,
-        -0.50036833010470427325e+04, -0.47842457022250109731e+04,
-        0.24287714909488558988e+04, 0.31448004040389537295e+04,
-        0.17680405482055916764e+04, -0.49935276804549648659e+04,
-        -0.35975521092947674333e+04, 0.80954596838453971941e+04,
-        0.16841537855774295167e+04, -0.86887734414030328480e+04,
-        0.12397240739429601035e+04, 0.59728774205046402130e+04,
-        -0.15663435179491611962e+04, -0.29344029299790431651e+04,
-        -0.10729191707340373796e+04, 0.28989973199427486179e+04,
-        0.35499586651882186743e+04, -0.58123312056355825916e+04,
-        -0.27909604982371329243e+04, 0.84216562524209839466e+04,
-        -0.86954899944978205895e+03, -0.78256015718077442216e+04,
-        0.41785640428678889293e+04, 0.44955941480278825111e+04,
-        -0.44361254587504108713e+04, -0.15809387861524990058e+04,
-        0.22297439835174304790e+04, 0.15562524447756900372e+04,
-        -0.62434146271168992826e+03, -0.37120425036472161082e+04,
-        0.19498717241166420990e+04, 0.49949047588885005098e+04,
-        -0.54486184566506244664e+04, -0.30647381650787465333e+04,
-        0.80622564736170406832e+04, -0.14443338661404723098e+04,
-        -0.73116593719241282088e+04, 0.55766367267822124631e+04,
-        0.35114366064077562442e+04, -0.67196356246951527282e+04,
-        0.68306116276408249632e+03, 0.47844430374816802214e+04,
-        -0.26828373207446925335e+04, -0.19841396830600369867e+04,
-        0.20976917033900476781e+04, 0.70929541270542154052e+03,
-        -0.74337667565967433347e+03, -0.14589252941614317933e+04,
-        0.79622014543800298725e+03, 0.26180614002148154214e+04,
-        -0.27816916453992239440e+04, -0.20411299589341176670e+04,
-        0.51304713081131676518e+04, -0.96962000017965999632e+03,
-        -0.54962388625997218696e+04, 0.49599178775674590725e+04,
-        0.27128712352985849066e+04, -0.73229951026628423278e+04,
-        0.21915500020996305466e+04, 0.61925142240155510081e+04,
-        -0.65777290502678079065e+04, -0.17781813454617592924e+04,
-        0.79044451061247500547e+04, -0.36988864379850415389e+04,
-        -0.53131107868412273092e+04, 0.73557046404508546402e+04,
-        0.12526548734101274363e+03, -0.73091567300231808986e+04,
-        0.49711949543704004100e+04, 0.36722156771955815202e+04,
-        -0.74199383633172237751e+04, 0.16170718321645119886e+04,
-        0.61091920617995483553e+04, -0.58829266769935093180e+04,
-        -0.18303824980870599575e+04, 0.70731607763612219060e+04,
-        -0.32176788913918280741e+04, -0.47006588196878819872e+04,
-        0.65460839574757474111e+04, -0.18206344217074124572e+04,
-        -0.51854952927731701493e+04, 0.75465792449255395695e+04,
-        0.14070794477255964239e+03, -0.75270693942358711865e+04,
-        0.52219156928188795064e+04, 0.42489818504477761962e+04,
-        -0.79398220013686659513e+04, 0.11769901128346532460e+04,
-        0.74408376809737610529e+04, -0.58324958384604533421e+04,
-        -0.35851443469375994937e+04, 0.83578996778169293975e+04,
-        -0.14223162695466201058e+04, -0.73798123288824272095e+04,
-        0.61300169308071845080e+04, 0.39553839206937032031e+04,
-        -0.83602188384370510903e+04, 0.10843412023292914910e+04,
-        0.80118898233242607603e+04, -0.54698554490549568072e+04,
-        -0.48523442377406991000e+04, 0.83917340079642817727e+04,
-        0.53384203297947146893e+03, -0.85901808462261324166e+04,
-        0.41521506418771887184e+04, 0.67270389146228790196e+04,
-        -0.74298196818057667770e+04, -0.29290287922558109130e+04,
-        0.91253225113483131281e+04, -0.12268348491408717109e+04,
-        -0.84806777039003991376e+04, 0.53136102602313358148e+04,
-        0.63694568892915540346e+04, -0.80024191207681878950e+04,
-        -0.28355841532263802947e+04, 0.94624291637728856585e+04,
-        -0.82651133844049218169e+03, -0.90780027231560798100e+04,
-        0.45293225553600314015e+04, 0.76535019640731443360e+04,
-        -0.72204676517604675610e+04, -0.50159639629514558692e+04,
-        0.92069420096276480763e+04, 0.21820915648714285453e+04,
-        -0.98611118194872251479e+04, 0.10113640410689308737e+04,
-        0.98529847161467259866e+04, -0.36824452916154796185e+04,
-        -0.88105849299555993639e+04, 0.62029689190119397608e+04,
-        0.75405175448427498850e+04, -0.79157792409397707161e+04,
-        -0.57064425378763025947e+04, 0.93904635126541252248e+04,
-        0.40769927820681036792e+04, -0.10120641097328700198e+05,
-        -0.22378389795005696215e+04, 0.10772041328828780024e+05,
-        0.86499122566505457144e+03, -0.10886699391899544935e+05,
-        0.54149550161213221600e+03, 0.11139467214708329266e+05,
-        -0.13743149497552317371e+04, -0.11055467182951240829e+05,
-        0.21782163624211029855e+04, 0.11274222891714340221e+05,
-        -0.23685883450878818621e+04, -0.11275220894652618881e+05,
-        0.24921683029036598782e+04, 0.11642599377110374917e+05,
-        -0.19533568359960729595e+04, -0.11791720255835569333e+05,
-        0.12812940320112279551e+04, 0.12228808067296828085e+05,
-        0.13049220347760814320e+03, -0.12276042891140197753e+05,
-        -0.17431688915583179096e+04, 0.12329001702121158814e+05,
-        0.41101285089335287921e+04, -0.11591640456331238966e+05,
-        -0.65728418503610591870e+04, 0.10355277330614546372e+05,
-        0.94723054710995129426e+04, -0.77825208187399548478e+04,
-        -0.11836333156901733673e+05, 0.42601730613677955262e+04,
-        0.13615670166302339567e+05, 0.71647767408526533472e+03,
-        -0.13470144813662906017e+05, -0.61029488432773960085e+04,
-        0.11202729553819483044e+05, 0.11410641572315646044e+05,
-        -0.58521348898103851752e+04, -0.14457396025418684076e+05,
-        -0.15489820731811139467e+04, 0.13983478056957756053e+05,
-        0.97628475114968296111e+04, -0.82585930340686027193e+04,
-        -0.15070272789552347604e+05, -0.14030548528919839555e+04,
-        0.14505691601466058273e+05, 0.11892138515485894459e+05,
-        -0.58690494650585042109e+04, -0.16591938853345487587e+05,
-        -0.72582373463576113863e+04, 0.10969822128611267544e+05,
-        0.16998853969978445093e+05, 0.41456920067252594890e+04,
-        -0.13433806454642601238e+05, -0.17131338256935676327e+05,
-        -0.33201919992458151683e+04, 0.14153479004903647365e+05,
-        0.18623552949754670408e+05, 0.62173186565348323711e+04,
-        -0.11876189692225992985e+05, -0.20373924770429599448e+05,
-        -0.12721756385222292010e+05, 0.48348152481630559123e+04,
-        0.19401866992965591635e+05, 0.21263092308084495016e+05,
-        0.97625969465391426638e+04, -0.77338662148548528421e+04,
-        -0.21450598726820167940e+05, -0.24860469027090668533e+05,
-        -0.17202592514410633157e+05, -0.24602626967227870409e+04,
-        0.13564524633590572193e+05, 0.26049289150730266556e+05,
-        0.32607776131937429454e+05, 0.33286476750654575881e+05,
-        0.29677673617310894770e+05, 0.23855266755063235905e+05,
-        0.17600000629922538792e+05, 0.12055043514257156858e+05,
-        0.77261851943537112675e+04, 0.46600030005294438524e+04,
-        0.26565335388615176271e+04, 0.14362290604894146782e+04,
-        0.73839297968214145840e+03, 0.36179603617373243196e+03,
-        0.16925505549075319323e+03, 0.75714419197234306580e+02,
-        0.32428468207838903936e+02, 0.13312218976079659427e+02,
-        0.52425658721108199245e+01, 0.19821616473717063034e+01,
-        0.71997259217186937441, 0.25136746085818584273,
-        0.84394221493349880214e-01, 0.27257466787145225029e-01,
-        0.84713700759025487713e-02, 0.25340428177399788347e-02,
-        0.72968577040068377613e-03, 0.20228491989842200638e-03,
-        0.53990445757808367246e-04, 0.13873731599654503841e-04,
-        0.34321621417141247236e-05, 0.81732384504757285166e-06,
-        0.18732903311821788379e-06, 0.41315440025942135325e-07,
-        0.87661115201652485437e-08, 0.17887877364455834488e-08,
-        0.35092661013625587041e-09, 0.66161594643733598419e-10,
-        0.11982062763938392685e-10, 0.20834032743503809564e-11,
-        0.34760548372179332104e-12, 0.55616120578893337081e-13,
-        0.85274089970997959124e-14, 0.12520097870955820205e-14,
-        0.17587845500270760964e-15, 0.23617693993931203833e-16,
-        0.30286598999218694148e-17, 0.37049217075049367313e-18,
-        0.43182269949978378907e-19, 0.47891948589016694136e-20,
-        0.50469336847711077898e-21, 0.50456413463071236884e-22,
-        0.47772164145834966821e-23, 0.42753383048522807842e-24,
-        0.36089467763568325814e-25, 0.28666786647597024377e-26,
-        0.21370793013259747423e-27, 0.14908028854322500963e-28,
-        0.96990231752949149297e-30, 0.58627050845859327484e-31,
-        0.32782957945702488152e-32, 0.16873590958364086158e-33,
-        0.79478197221766885549e-35, 0.34024440183946799566e-36,
-        0.13130426251485154863e-37, 0.45226389160035131993e-39,
-        0.13733435793187908330e-40, 0.36194622600098632253e-42,
-        0.81109792573263635093e-44, 0.15027026086025338929e-45,
-        0.22098056283279005105e-47, 0.24183893120880619259e-49,
-        0.17509531235990047362e-51, 0.62906701403698332886e-54
-    ]
-
-    ESERK4ConstantCache{eltype(Bᵢ), typeof(zprev)}(ms, Cᵤ, Cₑ, zprev, Bᵢ, 1, 0, 0)
-end
-
-function SERK2ConstantCache(zprev)
-    ms = [10, 20, 30, 40, 50, 60, 80, 100, 150, 200, 250]
-    Bᵢ = [-0.96362760400868230359,
-        -1.44600406818307636314,
-        45.70873580547182513101,
-        21.77666554440200741283,
-        -347.48805911864252493615,
-        -85.13943254169653584995,
-        927.12331469668538375117,
-        119.26005393567274381894,
-        -1013.54002814119894537725,
-        -54.02407949187814040215,
-        389.73246098337597231875,
-        -0.86721690285776698026,
-        -0.14247964606254165387,
-        -3.42874922514483193581,
-        3.31129999294675858579,
-        40.26458190656864388757,
-        6.21625585676302527816,
-        49.91496636080542259606,
-        -49.60291259660618834459,
-        -301.85262401649691810235,
-        -39.59682671920758423312,
-        -191.08213803615251435986,
-        196.90114563541760617227,
-        799.11070006504678531201,
-        76.95241936604297450231,
-        265.69350414417590400262,
-        -286.18278976196086205164,
-        -871.05995882277682085260,
-        -45.11225312859123448561,
-        -121.28287419671590896542,
-        137.67098469196315591034,
-        335.17496503284280606749,
-        -0.55552086456412841375,
-        -0.66637137556846204323,
-        0.32841341615080460459,
-        1.13286106389630703006,
-        -5.78406832376563251330,
-        5.39220351112540630112,
-        27.19910702656031276092,
-        26.81822323262986529357,
-        -13.36297457317238013275,
-        -10.98063978011500907428,
-        83.11884806933920799565,
-        -82.60257882008195906565,
-        -216.70911268002635097218,
-        -159.84229677365436828040,
-        80.68055068116780148557,
-        26.82613763535254847170,
-        -321.91265424845295228806,
-        337.59508526194247224339,
-        608.80276919553148218256,
-        294.37312132011533094555,
-        -150.78252961473515370017,
-        -22.12614711973167658243,
-        461.09353713065712554453,
-        -506.15490935635142477622,
-        -700.09775705192021177936,
-        -165.37179901028432027488,
-        86.09410471137518072737,
-        5.20218086081884489857,
-        -219.65432596547356070005,
-        250.86521029018081208051,
-        282.08133215105397084699,
-        -0.35562638797822015979,
-        -0.96920761460842985713,
-        0.50712704647579098793,
-        -0.19881356188030135934,
-        0.87060525762980689457,
-        -2.70169713195842708942,
-        -2.06966650654738471005,
-        5.35675430280412978590,
-        20.33247106765178457977,
-        36.13250646805210664070,
-        -18.72136240923262917590,
-        7.05834552818738369950,
-        -11.41711283297713031004,
-        35.21949128031247511217,
-        39.07800060513270778983,
-        -89.42490151485905869322,
-        -174.07691846417199599273,
-        -205.64366790028512355093,
-        106.27283716515583478213,
-        -38.62940246231941898714,
-        37.46381704091592013128,
-        -118.12109169672949349206,
-        -184.49202529961010554871,
-        388.49875886421608583987,
-        504.16143673655602697181,
-        369.15654437403549081864,
-        -191.38221982229620721228,
-        67.25392406888734342374,
-        -44.18384742198838210925,
-        142.40993474499103399467,
-        304.86693716918244945191,
-        -607.78033491695282464207,
-        -585.69396476150939179206,
-        -204.84058258834846810714,
-        106.99004289659143296376,
-        -36.43217257257210661692,
-        17.30702637562075452138,
-        -55.86298231535410963033,
-        -161.29195264411046650821,
-        310.22372123782685093829,
-        236.12926859606432117289,
-        -0.50756220355217507301,
-        -0.56050268297758665259,
-        0.00291753781535847171,
-        0.19139373844506024636,
-        -0.13861814582400311391,
-        -2.81456462077018754186,
-        3.84654994607172628918,
-        -4.11653976287417489033,
-        -0.72612663327699966676,
-        6.06736711554703500582,
-        23.77854592119173560150,
-        23.19875248127983979884,
-        -1.17247608520798385356,
-        -6.96343073995197947568,
-        5.09143221050110650339,
-        34.02475921928724744703,
-        -44.64064080736773121316,
-        52.83203805767665528492,
-        19.53569468626604432870,
-        -101.14886356390445598663,
-        -177.52579447039758520077,
-        -145.01001529188047811658,
-        13.73897451355871268674,
-        37.72595714751182072177,
-        -27.93148131718527338307,
-        -115.94473470939605874719,
-        148.44543421552094741855,
-        -190.65966851094114531406,
-        -99.70559724393923772823,
-        434.33859621501676429034,
-        468.74354519033653332372,
-        279.66762682937394401961,
-        -36.29554341729693334173,
-        -64.49478440803135015358,
-        48.11012873286868796185,
-        150.25827273347411505711,
-        -190.98609860753094835673,
-        260.36071707464839164459,
-        167.29766039095417795579,
-        -670.85011085660073604231,
-        -511.29698877250666555483,
-        -163.55372232431253110008,
-        25.65278607533514687589,
-        34.39828263844597699972,
-        -25.65925004310830459531,
-        -65.76727185536445574598,
-        84.31194862881892504447,
-        -119.58186159906821899312,
-        -88.35293627529978266466,
-        338.54504377337661935599,
-        197.24075987524443576149,
-        -0.47915337514860878443,
-        -0.46942193202031889943,
-        -0.27641291121172062439,
-        0.49679229986838996380,
-        -0.41740583828251531795,
-        0.23467075562112899023,
-        -0.74942506179570167468,
-        -0.33407066855369210723,
-        -0.11131355930744686600,
-        -1.53073730812523667311,
-        -1.65151679038455911908,
-        7.48452803719470427524,
-        20.11376150647138061345,
-        22.26924496382475737732,
-        8.14589560726002659408,
-        -17.89564518402425008503,
-        15.32006286484124402136,
-        -8.75939608117697154910,
-        7.44986626032478138626,
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