{
  "arithmetic": "CPU binary64 exp and subtraction; 100-digit Decimal reference, no CUDA claim",
  "formula": "5.16-5.18 with Phi(z)=exp(-(L+s*z))",
  "parameters": {
    "depth_scale": 0.7,
    "optical_depth": 1.0,
    "steps": [
      1.0,
      0.5623413251903491,
      0.31622776601683794,
      0.1778279410038923,
      0.1,
      0.05623413251903491,
      0.03162277660168379,
      0.01778279410038923,
      0.01,
      0.005623413251903491,
      0.0031622776601683794,
      0.0017782794100389228,
      0.001,
      0.0005623413251903491,
      0.00031622776601683794,
      0.00017782794100389227,
      0.0001,
      5.623413251903491e-05,
      3.1622776601683795e-05,
      1.778279410038923e-05,
      1e-05,
      5.623413251903491e-06,
      3.162277660168379e-06,
      1.778279410038923e-06,
      1e-06,
      5.62341325190349e-07,
      3.162277660168379e-07,
      1.7782794100389227e-07,
      1e-07,
      5.6234132519034905e-08,
      3.162277660168379e-08,
      1.7782794100389228e-08,
      1e-08,
      5.623413251903491e-09,
      3.1622776601683795e-09,
      1.7782794100389228e-09,
      1e-09,
      5.623413251903491e-10,
      3.1622776601683795e-10,
      1.778279410038923e-10,
      1e-10,
      5.6234132519034906e-11,
      3.1622776601683794e-11,
      1.7782794100389227e-11,
      1e-11,
      5.6234132519034904e-12,
      3.1622776601683794e-12,
      1.7782794100389228e-12,
      1e-12,
      5.62341325190349e-13,
      3.162277660168379e-13,
      1.7782794100389227e-13,
      1e-13,
      5.6234132519034906e-14,
      3.1622776601683796e-14,
      1.7782794100389227e-14,
      1e-14,
      5.623413251903491e-15,
      3.1622776601683794e-15,
      1.7782794100389227e-15,
      1e-15,
      5.623413251903491e-16,
      3.1622776601683793e-16,
      1.7782794100389228e-16,
      1e-16
    ]
  },
  "rows": [
    {
      "central_derivative": -0.2790673483144916,
      "derivative_absolute_error": 0.02155173949448197,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 0.18519591711870767,
      "reference_central_derivative": "-0.2790673483144915874156284650655766601955070564497485838219210019782417498369529611671011675344677048",
      "reference_taylor_remainder": "0.0723196917013019455208928566400443355468370195052250533387192078345800101485412574163303044473358216",
      "step": 1.0,
      "taylor_remainder": 0.07231969170130195
    },
    {
      "central_derivative": -0.2642177334001004,
      "derivative_absolute_error": 0.006702124580090785,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 0.1197088564450825,
      "reference_central_derivative": "-0.2642177334001004150740384698387218679037011145513192527389086098567137150563805855565284486293326488",
      "reference_taylor_remainder": "0.0251028122759612622498465386596962165483595721584788996513267651810226614834437537091598643672676209",
      "step": 0.5623413251903491,
      "taylor_remainder": 0.025102812275961256
    },
    {
      "central_derivative": -0.25962381143214014,
      "derivative_absolute_error": 0.0021082026121305164,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 0.07305034814819666,
      "reference_central_derivative": "-0.2596238114321401031451064073291702396352464243737398806319361001575952077385439707133817669823135350",
      "reference_taylor_remainder": "0.00838323754342092928834007071682101276848062340029856514035756063615380089013928793290495334642325859",
      "step": 0.31622776601683794,
      "taylor_remainder": 0.008383237543420907
    },
    {
      "central_derivative": -0.25818116520577,
      "derivative_absolute_error": 0.0006655563857603797,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 0.04305796728664374,
      "reference_central_derivative": "-0.2581811652057702530895295323446184649678359461862221820765445091585401060216341763030932978852408593",
      "reference_taylor_remainder": "0.00273550320618231222720092974303844141002432234800792630987145243644271685472732709139837995273347032",
      "step": 0.1778279410038923,
      "taylor_remainder": 0.0027355032061823353
    },
    {
      "central_derivative": -0.25772596476447224,
      "derivative_absolute_error": 0.00021035594446261463,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 0.024870923752735696,
      "reference_central_derivative": "-0.2577259647644722916374599794518865240143088940068746007854735806159016350789545318267246786296177496",
      "reference_taylor_remainder": "0.00088063712926530903556224705160434641221751174270764864447011545396466200007325886440449490025101268",
      "step": 0.1,
      "taylor_remainder": 0.0008806371292652687
    },
    {
      "central_derivative": -0.25758211806763914,
      "derivative_absolute_error": 6.650924762952037e-05,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 0.014199852606855301,
      "reference_central_derivative": "-0.2575821180676393312272150526228726814389361741720806241206264184236948173455933693170907561183668349",
      "reference_taylor_remainder": "0.00028131426524909888116346733348707692152022831133237884265912297704415762688251094067979288289905923",
      "step": 0.05623413251903491,
      "taylor_remainder": 0.0002813142652490757
    },
    {
      "central_derivative": -0.2575366397766483,
      "derivative_absolute_error": 2.1030956638690146e-05,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 0.008053889482930898,
      "reference_central_derivative": "-0.2575366397766484014485972705773305377446836396461631334326091928693539584867463311392458884223866069",
      "reference_taylor_remainder": "0.000089469086230850363792842108853378107679270890958726895954672039212867516556772121187318118498888436",
      "step": 0.03162277660168379,
      "taylor_remainder": 8.946908623085753e-05
    },
    {
      "central_derivative": -0.25752225928103173,
      "derivative_absolute_error": 6.650461022106313e-06,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 0.004550963190034951,
      "reference_central_derivative": "-0.2575222592810325290370053919063661013467777164593151909258175227005596980726751931034707373188814530",
      "reference_taylor_remainder": "0.000028383859247648081059113833349397461262414819759457607092387461974081105420318438574768423443387262",
      "step": 0.01778279410038923,
      "taylor_remainder": 2.8383859247656414e-05
    },
    {
      "central_derivative": -0.2575177118692984,
      "derivative_absolute_error": 2.1030492887708085e-06,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 0.0025661640355809645,
      "reference_central_derivative": "-0.2575177118693007696757089677828443550699114531981625841423498769425458153488208263105785211522898451",
      "reference_taylor_remainder": "0.000008992052619121266407848412907234148282526620293171015161832051269803545342193393822149378419073179",
      "step": 0.01,
      "taylor_remainder": 8.99205261913191e-06
    },
    {
      "central_derivative": -0.2575162738614741,
      "derivative_absolute_error": 6.650414644537861e-07,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 0.0014452702478339186,
      "reference_central_derivative": "-0.2575162738614746696605476802496848570002528072801208948497636434645726167646432901490604313531145354",
      "reference_taylor_remainder": "0.000002846439376548069733140571576624422029894614567649765452972133655574355195767525601297766355839444",
      "step": 0.005623413251903491,
      "taylor_remainder": 2.846439376519034e-06
    },
    {
      "central_derivative": -0.2575158191244729,
      "derivative_absolute_error": 2.1030446328840213e-07,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 0.0008134352169583692,
      "reference_central_derivative": "-0.2575158191244750030416423309388809661700451487872771405015434650021494687461535817055811732181401771",
      "reference_taylor_remainder": "9.006399577900680646251574540610565739481168245594617940859772840230182831717609731521555104623427E-7",
      "step": 0.0031622776601683794,
      "taylor_remainder": 9.006399578065502e-07
    },
    {
      "central_derivative": -0.257515675324118,
      "derivative_absolute_error": 6.650410838693332e-08,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 0.0004576498056044209,
      "reference_central_derivative": "-0.2575156753241097427257336964397488077460272819270394283101310745754782762150186238753825066520915158",
      "reference_taylor_remainder": "2.848993238519844098017060711604639745144697316650509484556247188364140320918066263131815177972169E-7",
      "step": 0.0017782794100389228,
      "taylor_remainder": 2.8489932383981686e-07
    },
    {
      "central_derivative": -0.2575156298504355,
      "derivative_absolute_error": 2.103042590073656e-08,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 0.00025742549938367887,
      "reference_central_derivative": "-0.2575156298504515109930071868746940985900760944935276135848412324421109043449058265361545573245558457",
      "reference_taylor_remainder": "9.01094363254284506686425430923868217643495657788375098774010414167251877747646683014193692794579E-8",
      "step": 0.001,
      "taylor_remainder": 9.010943633077327e-08
    },
    {
      "central_derivative": -0.2575156154704469,
      "derivative_absolute_error": 6.6504372564502034e-09,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 0.00014478317070554247,
      "reference_central_derivative": "-0.2575156154704191584530865768956996520917676110888376281396610102087892159943446604973646018428050848",
      "reference_taylor_remainder": "2.84980155599796520512493140727070284196062085635484263698473998473498375054534601866193263761544E-8",
      "step": 0.0005623413251903491,
      "taylor_remainder": 2.849801550129519e-08
    },
    {
      "central_derivative": -0.2575156109230254,
      "derivative_absolute_error": 2.103015761534266e-09,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 8.142457331028474e-05,
      "reference_central_derivative": "-0.2575156109230537526289407044903831742727301593558849034140251758044189263641127873455890070931780910",
      "reference_taylor_remainder": "9.01238130455216435153721425510088005834259213891703982965708994903567405655622353601404096881427E-9",
      "step": 0.00031622776601683794,
      "taylor_remainder": 9.012381332822281e-09
    },
    {
      "central_derivative": -0.2575156094852355,
      "derivative_absolute_error": 6.652258743855555e-10,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 4.579062043563731e-05,
      "reference_central_derivative": "-0.2575156094850505591098600396901633368867461355572670935166440147592450050319751300682990109362732560",
      "reference_taylor_remainder": "2.85005724002406103967955938368767431503669266776052177809445982082389450640576336564272090680232E-9",
      "step": 0.00017782794100389227,
      "taylor_remainder": 2.8500571887604426e-09
    },
    {
      "central_derivative": -0.25751560903036763,
      "derivative_absolute_error": 2.103580087897683e-10,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 2.5750659598422487e-05,
      "reference_central_derivative": "-0.2575156090303140227009366928353761411485418196331601215849007619349361585176461808570072783758503359",
      "reference_taylor_remainder": "9.0128360079667426435545846382733713515065929940071461706158259762564805553312758456548227446547E-10",
      "step": 0.0001,
      "taylor_remainder": 9.012835784768733e-10
    },
    {
      "central_derivative": -0.2575156088872371,
      "derivative_absolute_error": 6.72275013435808e-11,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 1.4480881858347505e-05,
      "reference_central_derivative": "-0.2575156088865137037663777296972596418537848986906182599880487437328780625267586222229033700564514315",
      "reference_taylor_remainder": "2.8501381015737418516980196075572094881319384680464885318390501514870458263122016546090816984576E-10",
      "step": 5.623413251903491e-05,
      "taylor_remainder": 2.8501375687007495e-10
    },
    {
      "central_derivative": -0.2575156088419788,
      "derivative_absolute_error": 2.196920423358506e-11,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 8.143268439397833e-06,
      "reference_central_derivative": "-0.2575156088410400501672203012842647703592517190581526222307435952632062267844830339200874191946241945",
      "reference_taylor_remainder": "9.0129798049733864710862650818556348165465765724650065017768535243224419889789870343923484391269E-11",
      "step": 3.1622776601683795e-05,
      "taylor_remainder": 9.012976392407384e-11
    },
    {
      "central_derivative": -0.25751560882782204,
      "derivative_absolute_error": 7.812417379682302e-12,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 4.579318547692779e-06,
      "reference_central_derivative": "-0.2575156088266600182779378964380636073193031339279959757340187816301015307950864696337864441721329544",
      "reference_taylor_remainder": "2.8501636729571392197315092885527815039337117979359889890182178776743199188364710826014055114993E-11",
      "step": 1.778279410038923e-05,
      "taylor_remainder": 2.8501589828795022e-11
    },
    {
      "central_derivative": -0.25751560882580904,
      "derivative_absolute_error": 5.799416502583199e-12,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 2.575147075245532e-06,
      "reference_central_derivative": "-0.2575156088221126529184395017959199508709499558457350415202694664268370488819379203900497162989148472",
      "reference_taylor_remainder": "9.013025278295753463529521575166045787821415274859431462514157295223509691812271505306136304007E-12",
      "step": 1e-05,
      "taylor_remainder": 9.012954564707146e-12
    },
    {
      "central_derivative": -0.25751560882356633,
      "derivative_absolute_error": 3.5567104816891515e-12,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 1.4481138370658897e-06,
      "reference_central_derivative": "-0.2575156088206746497295529961625530325863600387808778349061449233537397040165242479382693451813138550",
      "reference_taylor_remainder": "2.850171759410205091520762119513169202332128086087402687275759910306546875718219904263470915766E-12",
      "step": 5.623413251903491e-06,
      "taylor_remainder": 2.8501445480404766e-12
    },
    {
      "central_derivative": -0.2575156088103814,
      "derivative_absolute_error": 9.628242647607976e-12,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 8.143349555789214e-07,
      "reference_central_derivative": "-0.2575156088202199131936073301151786279412854187191385739573432344571786713069201673582692579904075860",
      "reference_taylor_remainder": "9.013039658294517109334257496440886304799362211323843420031905575414729366706998443418456116669E-13",
      "step": 3.162277660168379e-06,
      "taylor_remainder": 9.013372542008815e-13
    },
    {
      "central_derivative": -0.25751560882313956,
      "derivative_absolute_error": 3.1299407510232413e-12,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 4.579344199395763e-07,
      "reference_central_derivative": "-0.2575156088200761128747190969519841702373070155390913885641625443780491471202038868237369791737319381",
      "reference_taylor_remainder": "2.850174316578355068277883080733422420355179753413462881381163814419019831087266442996372214993E-13",
      "step": 1.778279410038923e-06,
      "taylor_remainder": 2.8498868446190216e-13
    },
    {
      "central_derivative": -0.2575156088091557,
      "derivative_absolute_error": 1.0853928866794149e-11,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 2.5751551868680167e-07,
      "reference_central_derivative": "-0.2575156088200306392211245720842389492943784083555669197333855586915297459791562238197837690807897039",
      "reference_taylor_remainder": "9.01304420565656425570473390771187228031719980462669649181532565989408505763726242944233876032E-14",
      "step": 1e-06,
      "taylor_remainder": 9.013320795707276e-14
    },
    {
      "central_derivative": -0.25751560885318064,
      "derivative_absolute_error": 3.31710214851455e-11,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 1.4481164023472104e-07,
      "reference_central_derivative": "-0.2575156088200162591892357529396478980509826987387931645269523173325773398476402876994834484895257848",
      "reference_taylor_remainder": "2.85017512522664193453993121233865431633856253014569048913819898683568395205188629495151697116E-14",
      "step": 5.62341325190349e-07,
      "taylor_remainder": 2.848632271827712e-14
    },
    {
      "central_derivative": -0.2575156087840501,
      "derivative_absolute_error": 3.5959513144945277e-11,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 8.143357665968409e-08,
      "reference_central_derivative": "-0.2575156088200117118238763008720178073988082401433059901654577400094464490604047044341881888743142960",
      "reference_taylor_remainder": "9.01304564365942192088117614756888834307798181544142613469428445473341807198540449124303116669E-15",
      "step": 3.162277660168379e-07,
      "taylor_remainder": 9.031933479161396e-15
    },
    {
      "central_derivative": -0.25751560863584233,
      "derivative_absolute_error": 1.8416729252734854e-10,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 4.579346762900727e-08,
      "reference_central_derivative": "-0.2575156088200102738206874189993114963840032119971172233697849777688590912237776929759044353244304053",
      "reference_taylor_remainder": "2.85017538094375513684391052318343200997976186613091405374672820589285398680502374907709668367E-15",
      "step": 1.7782794100389227e-07,
      "taylor_remainder": 2.8638188049483733e-15
    },
    {
      "central_derivative": -0.25751560883691127,
      "derivative_absolute_error": 1.6901646748834764e-11,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 2.5751559995512707e-08,
      "reference_central_derivative": "-0.2575156088200098190841514737967008328948855757938270038280394237738971047772069930876716599803740294",
      "reference_taylor_remainder": "9.0130460983959247304293051726934824906457056777411643028481908389740795462282900858949876032E-16",
      "step": 1e-07,
      "taylor_remainder": 8.864882547893854e-16
    },
    {
      "central_derivative": -0.25751560890253783,
      "derivative_absolute_error": 8.252820649090609e-11,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 1.4481166599189521e-08,
      "reference_central_derivative": "-0.2575156088200096752838325856098488929769328214177244466591910487573919241865456798665641665233685102",
      "reference_taylor_remainder": "2.8501754618086137557342748459404913296226472700936124237962892987435940538803253455007981280E-16",
      "step": 5.6234132519034905e-08,
      "taylor_remainder": 2.729148543664767e-16
    },
    {
      "central_derivative": -0.25751560799411255,
      "derivative_absolute_error": 8.25897072953552e-10,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 8.143358432022296e-09,
      "reference_central_derivative": "-0.2575156088200096298101789910896285456987547977416653075912772642702791588260197945939498008614184032",
      "reference_taylor_remainder": "9.0130462421962403190320499858972021924527730803526740007220009655308036267477060219443116669E-17",
      "step": 3.162277660168379e-08,
      "taylor_remainder": 1.3713945993216486e-16
    },
    {
      "central_derivative": -0.25751560832368015,
      "derivative_absolute_error": 4.96329477517321e-10,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 4.579347012700907e-09,
      "reference_central_derivative": "-0.2575156088200096154301471022709483809074738606613608622974206823217129823497331423309336756556035447",
      "reference_taylor_remainder": "2.8501754873803284275372260788200458697523086426471641894988240480889756438487516772032510008E-17",
      "step": 1.7782794100389228e-08,
      "taylor_remainder": 3.658170028504935e-17
    },
    {
      "central_derivative": -0.2575156060613537,
      "derivative_absolute_error": 2.7586559148140566e-09,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 2.5751560328579615e-09,
      "reference_central_derivative": "-0.2575156088200096108827817428189261535315180395106668290853559932658016961109981293996705634485462267",
      "reference_taylor_remainder": "9.013046287669894762479141577047816294627346780871429885472267016785268237888046907501296852E-18",
      "step": 1e-08,
      "taylor_remainder": 5.5342134657465786e-17
    },
    {
      "central_derivative": -0.25751560791539446,
      "derivative_absolute_error": 9.046151605573982e-10,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 1.4481166821234126e-09,
      "reference_central_derivative": "-0.2575156088200096094447785539370579322704812898053704613425182257119372461282843871427399656182350686",
      "reference_taylor_remainder": "2.850175495466814706707732538513875871393457151667748675190071000033625096807747819714046895E-18",
      "step": 5.623413251903491e-09,
      "taylor_remainder": 5.0870251095806615e-18
    },
    {
      "central_derivative": -0.2575156062386958,
      "derivative_absolute_error": 2.5813138293528937e-09,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 8.143358765089204e-10,
      "reference_central_derivative": "-0.2575156088200096089900420179918557013251232137574631588625100631477614293630824372495106856361553840",
      "reference_taylor_remainder": "9.013046302049927324106479654628331090690321385779608500146692127845422369232233619350220768E-19",
      "step": 3.1622776601683795e-09,
      "taylor_remainder": 1.9592744642140634e-17
    },
    {
      "central_derivative": -0.25751561612773377,
      "derivative_absolute_error": 7.307724148031269e-09,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 4.579347456790117e-10,
      "reference_central_derivative": "-0.2575156088200096088462416991036688602593321876973539368812632147079504526823801154436523989776694357",
      "reference_taylor_remainder": "2.850175498023986042098701049415549121699878833083616815426894702971989491761849994332510008E-19",
      "step": 1.7782794100389228e-09,
      "taylor_remainder": 4.0750750956501327e-17
    },
    {
      "central_derivative": -0.2575155921835659,
      "derivative_absolute_error": 1.6636443722628513e-08,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 2.575156199391415e-10,
      "reference_central_derivative": "-0.2575156088200096088007680455091486401842539886158808686875485644529997528400280313219557722902815373",
      "reference_taylor_remainder": "9.01304630659729271985632335639667245816131438308495253263632892204116796603775614264684865E-20",
      "step": 1e-09,
      "taylor_remainder": 1.1119131882951254e-17
    },
    {
      "central_derivative": -0.25751559804396074,
      "derivative_absolute_error": 1.0776048886551592e-08,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 1.4481166266122614e-10,
      "reference_central_derivative": "-0.2575156088200096087863880136203299562779546842712805071406106164208912859339455307340421277368933266",
      "reference_taylor_remainder": "2.85017549883263478428692471228702474580770231027252216440952695405187492338340365714046895E-20",
      "step": 5.623413251903491e-10,
      "taylor_remainder": 6.059817634083849e-18
    },
    {
      "central_derivative": -0.2575155974616121,
      "derivative_absolute_error": 1.13583975003273e-08,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 8.143358209977691e-11,
      "reference_central_derivative": "-0.2575156088200096087818406482608779339730919437133694933046359193576151786366527758870769147411567415",
      "reference_taylor_remainder": "9.01304630803529586879684705511414487426569100047562521775577719812738688138635880350220768E-21",
      "step": 3.1622776601683795e-10,
      "taylor_remainder": 3.5918406666665376e-18
    },
    {
      "central_derivative": -0.2575155068709835,
      "derivative_absolute_error": 1.0194902611004864e-07,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 4.5793480119016294e-11,
      "reference_central_derivative": "-0.2575156088200096087804026450719960656015617440914847556164162077112523814480600579865473424371565879",
      "reference_taylor_remainder": "2.85017549908835197255670560804543123906500795421783084783421389287025625304390697786745024E-21",
      "step": 1.778279410038923e-10,
      "taylor_remainder": 9.626190217483446e-18
    },
    {
      "central_derivative": -0.25751567545029275,
      "derivative_absolute_error": 6.663028312425823e-08,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 2.5751567545029275e-11,
      "reference_central_derivative": "-0.2575156088200096087799479085360508633513157605162784819661242820158933995958971463323707407311265652",
      "reference_taylor_remainder": "9.0130463084900319783554688012796452414418641419478723555008381413349120146916175037567357E-22",
      "step": 1e-10,
      "taylor_remainder": 6.6630283101284384e-18
    },
    {
      "central_derivative": -0.25751510447227444,
      "derivative_absolute_error": 5.043477351862613e-07,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 1.4481138510546998e-11,
      "reference_central_derivative": "-0.2575156088200096087798041082171626765139587716231216988061005258738836769770190799981398050171293071",
      "reference_taylor_remainder": "2.8501754991692163993269014713961262279538474619160162997781634827284131907676782873370633E-22",
      "step": 5.6234132519034906e-11,
      "taylor_remainder": 2.836155737742171e-17
    },
    {
      "central_derivative": -0.2575152463782653,
      "derivative_absolute_error": 3.6244174433930354e-07,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 8.14331935217183e-12,
      "reference_central_derivative": "-0.2575156088200096087797586345635681562983625827961816272532203179147442090993229781064461315981132682",
      "reference_taylor_remainder": "9.0130463086338319868407024238075450324303924660573182174699351643231132762174694214633230E-23",
      "step": 3.1622776601683794e-11,
      "taylor_remainder": 3.92169899279009e-17
    },
    {
      "central_derivative": -0.2575165994384857,
      "derivative_absolute_error": 9.906184760821724e-07,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 4.5793924208226144e-12,
      "reference_central_derivative": "-0.2575156088200096087797442545316793376149163437734248133771679905171780966528123129079644012798177882",
      "reference_taylor_remainder": "2.8501754991947879276029585892319171042788817290647224317486199712899309635004073583363715E-23",
      "step": 1.7782794100389227e-11,
      "taylor_remainder": 4.537154000723928e-17
    },
    {
      "central_derivative": -0.2575134550042435,
      "derivative_absolute_error": 2.153815766126055e-06,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 2.5751623056180506e-12,
      "reference_central_derivative": "-0.2575156088200096087797397071663198855934562439004067734335300043059662355141204168091440498877613301",
      "reference_taylor_remainder": "9.013046308679304203471133920780502802691123384512393016063334006139070976834437935876702E-24",
      "step": 1e-11,
      "taylor_remainder": 6.217417954623303e-18
    },
    {
      "central_derivative": -0.25751609161564704,
      "derivative_absolute_error": 4.827956374131581e-07,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 1.448119402169823e-12,
      "reference_central_derivative": "-0.2575156088200096087797382691631310037254521798049498427208185882523008048402903741357926144865348665",
      "reference_taylor_remainder": "2.850175499202874436369656097502556453880916701525475943145564102636473732646363356422191E-24",
      "step": 5.6234132519034904e-12,
      "taylor_remainder": 2.7149593854240013e-18
    },
    {
      "central_derivative": -0.2575108578364296,
      "derivative_absolute_error": 4.750983580048551e-06,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 8.143485885625523e-13,
      "reference_central_derivative": "-0.2575156088200096087797378144265950585233344307544966399566555577567569348349799848949109912260704362",
      "reference_taylor_remainder": "9.013046308693685672323676977763093215145086104893921669996148418712374359069594214633230E-25",
      "step": 3.1622776601683794e-12,
      "taylor_remainder": 1.2731646376607453e-17
    },
    {
      "central_derivative": -0.257518160249203,
      "derivative_absolute_error": 2.551429193364818e-06,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 4.579669976578771e-13,
      "reference_central_derivative": "-0.2575156088200096087797376706262761703365120523146781806287914229088382008877229956942693685518152479",
      "reference_taylor_remainder": "2.850175499205432103137311077210836793288827635637329816308693666572505159472868752848139E-25",
      "step": 1.7782794100389228e-12,
      "taylor_remainder": 3.2292729616332647e-17
    },
    {
      "central_derivative": -0.2575439861374207,
      "derivative_absolute_error": 2.837731741106575e-05,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 2.575717417130363e-13,
      "reference_central_derivative": "-0.2575156088200096087797376251526225758162870661961150590278511892923014462676160851045874534866779481",
      "reference_taylor_remainder": "9.01304630869823232878745086143138077801617735070480426523461409002639948006786728247808E-26",
      "step": 1e-12,
      "taylor_remainder": 5.613289302671006e-17
    },
    {
      "central_derivative": -0.2575457059168257,
      "derivative_absolute_error": 3.0097096816061875e-05,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 1.4482859356235167e-13,
      "reference_central_derivative": "-0.2575156088200096087797376107725906869976053267296801547361820859380951788434479939154420685655179437",
      "reference_taylor_remainder": "2.85017549920624025645087516913342867091904990638140573678044569802527139165863356422191E-26",
      "step": 5.62341325190349e-13,
      "taylor_remainder": 1.6924841307919748e-17
    },
    {
      "central_derivative": -0.25751963492010105,
      "derivative_absolute_error": 4.026100091425455e-06,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 8.143485885625523e-14,
      "reference_central_derivative": "-0.2575156088200096087797376062252253275455838806312797053861269638907111950649073481541050348633270286",
      "reference_taylor_remainder": "9.01304630869966988969529076144765055585676543823124067822799675966860779011350252777700E-27",
      "step": 3.162277660168379e-13,
      "taylor_remainder": 1.2731646376607453e-18
    },
    {
      "central_derivative": -0.25768984942810724,
      "derivative_absolute_error": 0.00017424060809762,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 4.5852210917018965e-14,
      "reference_central_derivative": "-0.2575156088200096087797376047872221386637158499301211238606813005584160289151850011453376052234786216",
      "reference_taylor_remainder": "2.85017549920649614522529025217670326807131789205015082141212631361224531256246771920372E-27",
      "step": 1.7782794100389227e-13,
      "taylor_remainder": 5.874042419289488e-17
    },
    {
      "central_derivative": -0.2575717417130363,
      "derivative_absolute_error": 5.6132893026694664e-05,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 2.5757174171303632e-14,
      "reference_central_derivative": "-0.2575156088200096087797376043324856027185136968289159807742103232630438680525529219652233333331469503",
      "reference_taylor_remainder": "9.0130463087001259785973809119887726488935820354034141902191021413485213528597718711691E-28",
      "step": 1e-13,
      "taylor_remainder": 5.613289302669744e-18
    },
    {
      "central_derivative": -0.2576444202540878,
      "derivative_absolute_error": 0.00012881143407816875,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 1.4488410471358293e-14,
      "reference_central_derivative": "-0.2575156088200096087797376041886852838303268611843069260763574588015134519119434291551515157055214691",
      "reference_taylor_remainder": "2.8501754992065769664036131669207353411651467817433123553144615325323719383816104038161E-28",
      "step": 5.6234132519034906e-14,
      "taylor_remainder": 7.243599253916495e-18
    },
    {
      "central_derivative": -0.2571685515732433,
      "derivative_absolute_error": 0.00034705724676631355,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 8.1601392309949e-15,
      "reference_central_derivative": "-0.2575156088200096087797376041432116302358066487743466887734334348987440614441165068850059437258868642",
      "reference_taylor_remainder": "9.0130463087002705850064674831014524470526575469516120800239712051399377189932681256819E-29",
      "step": 3.1622776601683796e-14,
      "taylor_remainder": 1.6780661833142476e-17
    },
    {
      "central_derivative": -0.2575337683563761,
      "derivative_absolute_error": 1.815953636646883e-05,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 4.6074255521944e-15,
      "reference_central_derivative": "-0.2575156088200096087797376041288315983469879629589078349499206893665108359437370513298813072488816936",
      "reference_taylor_remainder": "2.8501754992066023795036001330438101958223468071443665719322878695906086101483033840520E-29",
      "step": 1.7782794100389227e-14,
      "taylor_remainder": 2.807850291179262e-17
    },
    {
      "central_derivative": -0.2581268532253489,
      "derivative_absolute_error": 0.0006112444053392729,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 2.609024107869118e-15,
      "reference_central_derivative": "-0.2575156088200096087797376041242842329875359417672041728119997359988862424302793265156168473396879332",
      "reference_taylor_remainder": "9.013046308700314683766674024983246869206437911379837861905586329844921056215849671765E-30",
      "step": 1e-14,
      "taylor_remainder": 3.386801966902183e-17
    },
    {
      "central_derivative": -0.26159299374457184,
      "derivative_absolute_error": 0.004077384924562222,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 1.4988010832439613e-15,
      "reference_central_derivative": "-0.2575156088200096087797376041228462297986540736927475448930727185504881871713715430013443342011342868",
      "reference_taylor_remainder": "2.850175499206611264327504207256883332690224208813055748948394501801430388579842118015E-30",
      "step": 5.623413251903491e-15,
      "taylor_remainder": 5.0684396033523615e-17
    },
    {
      "central_derivative": -0.2545354264718108,
      "derivative_absolute_error": 0.002980182348198801,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 8.326672684688674e-16,
      "reference_central_derivative": "-0.2575156088200096087797376041223914932627088713983942319030613367248523420174965454695047179350487806",
      "reference_taylor_remainder": "9.013046308700329539335141084502751854574092167528021634202286575899017628023336057186E-31",
      "step": 3.1622776601683794e-15,
      "taylor_remainder": 1.8331411552691734e-17
    },
    {
      "central_derivative": -0.265337821942933,
      "derivative_absolute_error": 0.00782221312292336,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 4.996003610813204e-16,
      "reference_central_derivative": "-0.2575156088200096087797376041222476929438206845612248355920310058086018308977523082913245534027966305",
      "reference_taylor_remainder": "2.850175499206613023161251129719358762180364681168841689436784994358320901483033840520E-31",
      "step": 1.7782794100389227e-15,
      "taylor_remainder": 4.166565615305978e-17
    },
    {
      "central_derivative": -0.2498001805406602,
      "derivative_absolute_error": 0.007715428279349429,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 2.7755575615628914e-16,
      "reference_central_derivative": "-0.2575156088200096087797376041222022192902261643526258175765963700096243932045290979017502832421826995",
      "reference_taylor_remainder": "9.01304630870033503317189627169931685640603132481468971958867009810075237170522271581E-32",
      "step": 1e-15,
      "taylor_remainder": 2.004014733627951e-17
    },
    {
      "central_derivative": -0.29614301178630775,
      "derivative_absolute_error": 0.03862740296629813,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 1.6653345369377348e-16,
      "reference_central_derivative": "-0.2575156088200096087797376041221878392583373456685632326914630310928638868963342463307219321152438078",
      "reference_taylor_remainder": "2.85017549920661463014758542996975447872250758134763020135848223056743388579842118015E-32",
      "step": 5.623413251903491e-16,
      "taylor_remainder": 2.1721784972729705e-17
    },
    {
      "central_derivative": -0.2633125101432526,
      "derivative_absolute_error": 0.005796901323242953,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 1.1102230246251565e-16,
      "reference_central_derivative": "-0.2575156088200096087797376041221832918929778936454885433601429205851465039769696428877073982304507690",
      "reference_taylor_remainder": "9.01304630870033496260568333267010492505060493392131237171900532884695401829995307416E-33",
      "step": 3.1622776601683793e-16,
      "taylor_remainder": 2.958871677089808e-17
    },
    {
      "central_derivative": -0.46824321519341106,
      "derivative_absolute_error": 0.21072760637340143,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 1.1102230246251565e-16,
      "reference_central_derivative": "-0.2575156088200096087797376041221818538897890117773586374266228028068561244694434024755296185933575177",
      "reference_taylor_remainder": "2.85017549920661456166342267303501401813145672733468400124242993904955240773044965178E-33",
      "step": 1.7782794100389228e-16,
      "taylor_remainder": 6.522883196968958e-17
    },
    {
      "central_derivative": -0.27755575615628914,
      "derivative_absolute_error": 0.020040147336279512,
      "exact_derivative": -0.2575156088200096,
      "forward_difference": 0.0,
      "reference_central_derivative": "-0.2575156088200096087797376041221813991532530665751205401857239712705633692831701485817247217301164585",
      "reference_taylor_remainder": "9.0130463087003351484016536287083250740876703074954627827864403102836010977181521810E-34",
      "step": 1e-16,
      "taylor_remainder": 2.5751560882000962e-17
    }
  ]
}
