$SPAD/src/input e1.input

Timothy Daly December 3, 2016

Abstract

This is a regression test for E1(x)

Contents

2

— * —

)set break resume
)spool e1.output
)set message test on
)set message auto off
)clear all

———-

Here we enter the value of Gamma — * —

--S 1 of 7
machineFraction (G:DFLOAT:=0.577215664901532860606512)
--R
--R
--R         649887063340739
--R   (1)  ----------------
--R        1125899906842624
--R                                                      Type: Fraction(Integer)
--E 1

———-

Since the E1 function varies over a couple hundred orders of magnitude it is necessary to scale the computations to put the results into a reasonable range. We use the function listed in Abramowitz and Stegun, “Handbook of Mathematical Functions”, Dover Publications, Inc. New York 1965. pp238

— * —

--S 2 of 7
f(x)==x^-1 * (E1(x)::DFLOAT + log(x) + G)
--R
--R                                                                   Type: Void
--E 2

———-

This table computes the Exponential Integral E1(x) for x in 0.01 to 0.50. Column 1 is the point of evaluation, column 2 is the reference value of E1(x) from the book Abramowitz and Stegun, “Handbook of Mathematical Functions”, Dover Publications, Inc. New York 1965. pp238

— * —

--S 3 of 7
t3:List List Fraction Integer:=[[machineFraction (x::DFLOAT) for x in line]_
 for line in _
[[0.01,0.9975055452, f(0.01), f(0.01)-0.9975055452],_
[0.02,0.9950221392, f(0.02), f(0.02)-0.9950221392],_
[0.03,0.9925497201, f(0.03), f(0.03)-0.9925497201],_
[0.04,0.9900882265, f(0.04), f(0.04)-0.9900882265],_
[0.05,0.9876375971, f(0.05), f(0.05)-0.9876375971],_
[0.06,0.9851977714, f(0.06), f(0.06)-0.9851977714],_
[0.07,0.9827686889, f(0.07), f(0.07)-0.9827686889],_
[0.08,0.9803502898, f(0.08), f(0.08)-0.9803502898],_
[0.09,0.9779425142, f(0.09), f(0.09)-0.9779425142],_
[0.10,0.9755453033, f(0.10), f(0.10)-0.9755453033],_
[0.11,0.9731585980, f(0.11), f(0.11)-0.9731585980],_
[0.12,0.9707823399, f(0.12), f(0.12)-0.9707823399],_
[0.13,0.9684164710, f(0.13), f(0.13)-0.9684164710],_
[0.14,0.9660609336, f(0.14), f(0.14)-0.9660609336],_
[0.15,0.9637156702, f(0.15), f(0.15)-0.9637156702],_
[0.16,0.9613806240, f(0.16), f(0.16)-0.9613806240],_
[0.17,0.9590557383, f(0.17), f(0.17)-0.9590557383],_
[0.18,0.9567409569, f(0.18), f(0.18)-0.9567409569],_
[0.19,0.9544362237, f(0.19), f(0.19)-0.9544362237],_
[0.20,0.9521414833, f(0.20), f(0.20)-0.9521414833],_
[0.21,0.9498566804, f(0.21), f(0.21)-0.9498566804],_
[0.22,0.9475817603, f(0.22), f(0.22)-0.9475817603],_
[0.23,0.9453166684, f(0.23), f(0.23)-0.9453166684],_
[0.24,0.9430613506, f(0.24), f(0.24)-0.9430613506],_
[0.25,0.9408157528, f(0.25), f(0.25)-0.9408157528],_
[0.26,0.9385798221, f(0.26), f(0.26)-0.9385798221],_
[0.27,0.9363535046, f(0.27), f(0.27)-0.9363535046],_
[0.28,0.9341367481, f(0.28), f(0.28)-0.9341367481],_
[0.29,0.9319294997, f(0.29), f(0.29)-0.9319294997],_
[0.30,0.9297317075, f(0.30), f(0.30)-0.9297317075],_
[0.31,0.9275433196, f(0.31), f(0.31)-0.9275433196],_
[0.32,0.9253642845, f(0.32), f(0.32)-0.9253642845],_
[0.33,0.9231945510, f(0.33), f(0.33)-0.9231945510],_
[0.34,0.9210340684, f(0.34), f(0.34)-0.9210340684],_
[0.35,0.9188827858, f(0.35), f(0.35)-0.9188827858],_
[0.36,0.9167406533, f(0.36), f(0.36)-0.9167406533],_
[0.37,0.9146076209, f(0.37), f(0.37)-0.9146076209],_
[0.38,0.9124836388, f(0.38), f(0.38)-0.9124836388],_
[0.39,0.9103686582, f(0.39), f(0.39)-0.9103686582],_
[0.40,0.9082626297, f(0.40), f(0.40)-0.9082626297],_
[0.41,0.9061655048, f(0.41), f(0.41)-0.9061655048],_
[0.42,0.9040772350, f(0.42), f(0.42)-0.9040772350],_
[0.43,0.9019977725, f(0.43), f(0.43)-0.9019977725],_
[0.44,0.8999270693, f(0.44), f(0.44)-0.8999270693],_
[0.45,0.8978650778, f(0.45), f(0.45)-0.8978650778],_
[0.46,0.8958117511, f(0.46), f(0.46)-0.8958117511],_
[0.47,0.8937670423, f(0.47), f(0.47)-0.8937670423],_

[0.48,0.8917309048, f(0.48), f(0.48)-0.8917309048],_
[0.49,0.8897032920, f(0.49), f(0.49)-0.8897032920],_
[0.50,0.8876841584, f(0.50), f(0.50)-0.8876841584]]]
--R
--R   Compiling function f with type Float -> DoubleFloat
--R
--R   (3)
--R      2882303761517117  4492365601662723 280772850091425        199923
--R   [[------------------,----------------,---------------,- ----------------],
--R     288230376151711744 4503599627370496 281474976710656   4503599627370496
--R      2882303761517117  2240590667663257 560147666890375        101757
--R    [------------------,----------------,---------------,- ----------------],
--R     144115188075855872 2251799813685248 562949953421312   2251799813685248
--R      1080863910568919 2235023274794525 2235023274781933         787
--R    [-----------------,----------------,----------------,- ---------------],
--R     36028797018963968 2251799813685248 2251799813685248   140737488355328
--R      2882303761517117 4458960967929315 2229480483886525        156265
--R    [-----------------,----------------,----------------,- ----------------],
--R     72057594037927936 4503599627370496 2251799813685248   4503599627370496
--R      3602879701896397 1111981078569163 277995269656455       56657
--R    [-----------------,----------------,---------------,----------------],
--R     72057594037927936 1125899906842624 281474976710656 1125899906842624
--R      1080863910568919 4436936316163283 8873872632518599      192033
--R    [-----------------,----------------,----------------,----------------],
--R     18014398509481984 4503599627370496 9007199254740992 9007199254740992
--R      1261007895663739 4425996701121431 2212998350642857      164283
--R    [-----------------,----------------,----------------,----------------],
--R     18014398509481984 4503599627370496 2251799813685248 4503599627370496
--R      2882303761517117 2207552599917919 2207552599777725         70097
--R    [-----------------,----------------,----------------,- ----------------],
--R     36028797018963968 2251799813685248 2251799813685248   1125899906842624
--R      3242591731706757 2202130771270443 8808523085514533      432761
--R    [-----------------,----------------,----------------,----------------],
--R     36028797018963968 2251799813685248 9007199254740992 9007199254740992
--R      3602879701896397 8786930928849835 2196732732142155        281215
--R    [-----------------,----------------,----------------,- ----------------],
--R     36028797018963968 9007199254740992 2251799813685248   9007199254740992
--R      990791918021509 2191358349662597 1095679174805559         51479
--R    [----------------,----------------,----------------,- ----------------],
--R     9007199254740992 2251799813685248 1125899906842624   2251799813685248
--R     1080863910568919 2186007492115749 8744029968675015      212019
--R    [----------------,----------------,----------------,----------------],
--R     9007199254740992 2251799813685248 9007199254740992 9007199254740992
--R     1170935903116329 8722720115870101 8722720116131645       32693
--R    [----------------,----------------,----------------,----------------],
--R     9007199254740992 9007199254740992 9007199254740992 1125899906842624
--R     1261007895663739 4350751660578153 8701503321001285        155021
--R    [----------------,----------------,----------------,- ----------------],
--R     9007199254740992 4503599627370496 9007199254740992   9007199254740992
--R      5404319552844595 1085047383300957 8680379066763613      355957

--R    [-----------------,----------------,----------------,----------------],
--R     36028797018963968 1125899906842624 9007199254740992 9007199254740992
--R      2882303761517117 4329673420007615 1082418355021025       76485
--R    [-----------------,----------------,----------------,----------------],
--R     18014398509481984 4503599627370496 1125899906842624 4503599627370496
--R      3062447746611937 539900383204427 8638406131212201         58631
--R    [-----------------,---------------,----------------,- ----------------],
--R     18014398509481984 562949953421312 9007199254740992   9007199254740992
--R      3242591731706757 1077194554246233 8617556433117933        851931
--R    [-----------------,----------------,----------------,- ----------------],
--R     18014398509481984 1125899906842624 9007199254740992   9007199254740992
--R      3422735716801577 4298398621404223 2149199310577695        248833
--R    [-----------------,----------------,----------------,- ----------------],
--R     18014398509481984 4503599627370496 2251799813685248   4503599627370496
--R      3602879701896397 4288064029393871 1072016007299635        195331
--R    [-----------------,----------------,----------------,- ----------------],
--R     18014398509481984 4503599627370496 1125899906842624   4503599627370496
--R      7566047373982433 267360886994051 8555548384142333      332701
--R    [-----------------,---------------,----------------,----------------],
--R     36028797018963968 281474976710656 9007199254740992 9007199254740992
--R      990791918021509 8535057725180317 8535057725449499      134591
--R    [----------------,----------------,----------------,----------------],
--R     4503599627370496 9007199254740992 9007199254740992 4503599627370496
--R      517913957147607 8514655591106717 8514655591337513       57699
--R    [----------------,----------------,----------------,----------------],
--R     2251799813685248 9007199254740992 9007199254740992 2251799813685248
--R     1080863910568919 8494341494299353 8494341493919799        189777
--R    [----------------,----------------,----------------,- ----------------],
--R     4503599627370496 9007199254740992 9007199254740992   4503599627370496
--R     1 8474114947468745 132408046068487      914423
--R    [-,----------------,---------------,----------------],
--R     4 9007199254740992 140737488355328 9007199254740992
--R     1170935903116329 2113493868533513 8453975472966707        1167345
--R    [----------------,----------------,----------------,- ----------------],
--R     4503599627370496 2251799813685248 9007199254740992   9007199254740992
--R      607985949695017 2108480647201809 8433922588940829      133593
--R    [----------------,----------------,----------------,----------------],
--R     2251799813685248 2251799813685248 9007199254740992 9007199254740992
--R     1261007895663739 4206977910656247 2103488955146641        362965
--R    [----------------,----------------,----------------,- ----------------],
--R     4503599627370496 4503599627370496 2251799813685248   4503599627370496
--R      5224175567749775 4197037347584493 8394074695174917       5931
--R    [-----------------,----------------,----------------,----------------],
--R     18014398509481984 4503599627370496 9007199254740992 9007199254740992
--R      5404319552844595 4187139371451535 8374278742946419       43349
--R    [-----------------,----------------,----------------,----------------],
--R     18014398509481984 4503599627370496 9007199254740992 9007199254740992
--R      5584463537939415 4177283748520553 8354567497090819       49713
--R    [-----------------,----------------,----------------,----------------],
--R     18014398509481984 4503599627370496 9007199254740992 9007199254740992

--R     2882303761517117 8334940493712331 8334940493726925       7297
--R    [----------------,----------------,----------------,----------------],
--R     9007199254740992 9007199254740992 9007199254740992 4503599627370496
--R     2972375754064527 519712329484259 4157698635941277       67205
--R    [----------------,---------------,----------------,----------------],
--R     9007199254740992 562949953421312 4503599627370496 4503599627370496
--R     3062447746611937 1036992171810443 8295937373474689        1008855
--R    [----------------,----------------,----------------,- ----------------],
--R     9007199254740992 1125899906842624 9007199254740992   9007199254740992
--R     3152519739159347 4138280171726043 8276560343289725        162361
--R    [----------------,----------------,----------------,- ----------------],
--R     9007199254740992 4503599627370496 9007199254740992   9007199254740992
--R     3242591731706757 4128632864597265 4128632864481965         28825
--R    [----------------,----------------,----------------,- ----------------],
--R     9007199254740992 4503599627370496 4503599627370496   1125899906842624
--R     3332663724254167 32179894849027 8238053080963919        386993
--R    [----------------,--------------,----------------,- ----------------],
--R     9007199254740992 35184372088832 9007199254740992   9007199254740992
--R     3422735716801577 2054730487840677 8218921952567437      1204729
--R    [----------------,----------------,----------------,----------------],
--R     9007199254740992 2251799813685248 9007199254740992 9007199254740992
--R     3512807709348987 2049967974919649 8199871899844143      165547
--R    [----------------,----------------,----------------,----------------],
--R     9007199254740992 2251799813685248 9007199254740992 9007199254740992
--R     3602879701896397 4090451240671467 8180902481636575      293641
--R    [----------------,----------------,----------------,----------------],
--R     9007199254740992 4503599627370496 9007199254740992 9007199254740992
--R      7385903388887613 4081006629753277 4081006629770655       8689
--R    [-----------------,----------------,----------------,----------------],
--R     18014398509481984 4503599627370496 4503599627370496 2251799813685248
--R      7566047373982433 1017900474665037 8143203797890169      569873
--R    [-----------------,----------------,----------------,----------------],
--R     18014398509481984 1125899906842624 9007199254740992 9007199254740992
--R      7746191359077253 4062236832120017 4062236831865817        31775
--R    [-----------------,----------------,----------------,- ---------------],
--R     18014398509481984 4503599627370496 4503599627370496   562949953421312
--R      990791918021509 8105822427920205 4052911213406161        1107883
--R    [----------------,----------------,----------------,- ----------------],
--R     2251799813685248 9007199254740992 4503599627370496   9007199254740992
--R     2026619832316723 4043624829809061 8087249659558689         59433
--R    [----------------,----------------,----------------,- ----------------],
--R     4503599627370496 4503599627370496 9007199254740992   9007199254740992
--R      517913957147607 8068754936896143 8068754937058771       40657
--R    [----------------,----------------,----------------,----------------],
--R     1125899906842624 9007199254740992 9007199254740992 2251799813685248
--R     2116691824864133 2012584459329155 2012584459261035         8515
--R    [----------------,----------------,----------------,- ---------------],
--R     4503599627370496 2251799813685248 2251799813685248   281474976710656
--R     1080863910568919 4015998970572035 8031997939871911        1272159
--R    [----------------,----------------,----------------,- ----------------],

--R     2251799813685248 4503599627370496 9007199254740992   9007199254740992
--R     2206763817411543 8013734828643007 8013734828506949         68029
--R    [----------------,----------------,----------------,- ----------------],
--R     4503599627370496 9007199254740992 9007199254740992   4503599627370496
--R     1  999443511248233 1998887022126037        370429
--R    [-,----------------,----------------,- ----------------]]
--R     2 1125899906842624 2251799813685248   2251799813685248
--R                                          Type: List(List(Fraction(Integer)))
--E 3

———-

The actual table values from above are:

[1.0E-2,                 0.99750554520000001,
0.99750554515544154,
-4.455846802642327E-11]
[2.0E-2,                 0.99502213920000004,
0.99502213915481641,
-4.5183634611589696E-11]
[2.9999999999999999E-2,  0.99254972009999998,
0.99254972009439713,
-5.602851516073315E-12]
[4.0000000000000001E-2,  0.99008822649999995,
0.99008822646530492,
-3.4695024631048454E-11]
[5.0000000000000003E-2,  0.98763759709999999,
0.98763759715033261,
5.0332626955196247E-11]
[5.9999999999999998E-2,  0.98519777139999998,
0.98519777142131459,
2.1314616738266068E-11]
[7.0000000000000007E-2,  0.98276868890000002,
0.98276868893648617,
3.648614743667622E-11]
[8.0000000000000002E-2,  0.98035028980000005,
0.98035028973773719,
-6.2262861533213254E-11]
[8.9999999999999997E-2,  0.9779425142,
0.97794251424804735,
4.8047343881307825E-11]
[0.10000000000000001,    0.9755453033,
0.97554530326877553,
-3.1224467456070215E-11]
[0.11,                   0.97315859800000004,
0.97315859797713988,
-2.2860158210846748E-11]
[0.12,                   0.97078233989999996,
0.97078233992354002,
2.3540058791127194E-11]
[0.13,                   0.96841647099999995,

0.96841647102903816,
2.9038216275978357E-11]
[0.14000000000000001,    0.9660609336,
0.96606093358279166,
-1.7208345859387464E-11]
[0.14999999999999999,    0.96371567020000004,
0.96371567023951998,
3.9519942873766922E-11]
[0.16,                   0.96138062400000002,
0.96138062401698243,
1.6982415473876245E-11]
[0.17000000000000001,    0.95905573830000002,
0.95905573829349,
-6.5100147494945304E-12]
[0.17999999999999999,    0.95674095690000005,
0.9567409568054186,
-9.4581453780051561E-11]
[0.19,                   0.95443622370000003,
0.95443622364474956,
-5.525047086507584E-11]
[0.20000000000000001,    0.95214148330000004,
0.9521414832566294,
-4.3370640412376815E-11]
[0.20999999999999999,    0.94985668040000004,
0.94985668043693772,
3.6937675140791271E-11]
[0.22,                   0.94758176029999996,
0.94758176032988584,
2.9885871555279664E-11]
[0.23000000000000001,    0.94531666839999995,
0.9453166684256229,
2.562294820762645E-11]
[0.23999999999999999,    0.94306135059999996,
0.94306135055786067,
-4.2139292055765054E-11]
[0.25,                   0.94081575279999996,
0.94081575290152264,
1.015226791523105E-10]
[0.26000000000000001,    0.93857982210000002,
0.93857982197039913,
-1.2960088557889549E-10]
[0.27000000000000002,    0.9363535046,
0.93635350461483224,
1.4832246542084704E-11]
[0.28000000000000003,    0.93413674810000003,
0.93413674801940527,
-8.0594753093521376E-11]
[0.28999999999999998,    0.93192949970000005,
0.93192949970065808,
6.5802918669533028E-13]

[0.29999999999999999,    0.9297317075,
0.92973170750481327,
4.8132609009599037E-12]
[0.31,                   0.92754331960000003,
0.92754331960551961,
5.5195847892264283E-12]
[0.32000000000000001,    0.92536428449999997,
0.92536428450162023,
1.6202594821379535E-12]
[0.33000000000000002,    0.92319455100000003,
0.92319455101492243,
1.4922396651684267E-11]
[0.34000000000000002,    0.92103406840000002,
0.92103406828799361,
-1.1200640415154339E-10]
[0.34999999999999998,    0.91888278580000005,
0.91888278578197524,
-1.8024803871696804E-11]
[0.35999999999999999,    0.91674065329999999,
0.91674065327439791,
-2.5602076014763497E-11]
[0.37,                   0.91460762090000003,
0.91460762085703573,
-4.2964298785364008E-11]
[0.38,                   0.91248363880000005,
0.91248363893375239,
1.3375234253487633E-10]
[0.39000000000000001,    0.91036865820000001,
0.91036865821837942,
1.8379409105762079E-11]
[0.40000000000000002,    0.90826262970000005,
0.90826262973260075,
3.2600699917395559E-11]
[0.40999999999999998,    0.90616550480000002,
0.90616550480385905,
3.8590242112945816E-12]
[0.41999999999999998,    0.90407723500000003,
0.90407723506326909,
6.3269056660431033E-11]
[0.42999999999999999,    0.90199777250000002,
0.90199777244355628,
-5.6443738571942959E-11]
[0.44,                   0.89992706929999999,
0.89992706917700038,
-1.2299961049677677E-10]
[0.45000000000000001,    0.89786507780000002,
0.8978650777934013,
-6.5987215691620804E-12]
[0.46000000000000002,    0.8958117511,
0.89581175111805511,

                          1.8055112960269071E-11]
 [0.46999999999999997,    0.89376704230000004,
                          0.89376704226974857,
                         -3.0251467997288728E-11]
 [0.47999999999999998,    0.89173090479999995,
                          0.89173090465876237,
                         -1.412375771892016E-10]
 [0.48999999999999999,    0.88970329199999998,
                          0.88970329198489473,
                         -1.510525038384003E-11]
 [0.5,                    0.88768415840000003,
                          0.88768415823549685,
                         -1.6450318884864146E-10]

This table computes the Exponential Integral E1(x) for x in 0.50 to 2.00. Column 1 is the point of evaluation, column 2 is the reference value of E1(x) from the book Abramowitz and Stegun, “Handbook of Mathematical Functions”, Dover Publications, Inc. New York 1965. pp239-241

— * —

--S 4 of 7
t4:List List Fraction Integer:=[[machineFraction (x::DFLOAT) for x in line]_
 for line in _
[[0.50, 0.559773595, E1(0.50), E1(0.50)-0.559773595],_
[0.51, 0.547822352, E1(0.51), E1(0.51)-0.547822352],_
[0.52, 0.536219798, E1(0.52), E1(0.52)-0.536219798],_
[0.53, 0.524951510, E1(0.53), E1(0.53)-0.524951510],_
[0.54, 0.514003886, E1(0.54), E1(0.54)-0.514003886],_
[0.55, 0.503364081, E1(0.55), E1(0.55)-0.503364081],_
[0.56, 0.493019959, E1(0.56), E1(0.56)-0.493019959],_
[0.57, 0.482960034, E1(0.57), E1(0.57)-0.482960034],_
[0.58, 0.473173433, E1(0.58), E1(0.58)-0.473173433],_
[0.59, 0.463649849, E1(0.59), E1(0.59)-0.463649849],_
[0.60, 0.454379503, E1(0.60), E1(0.60)-0.454379503],_
[0.61, 0.445353112, E1(0.61), E1(0.61)-0.445353112],_
[0.62, 0.436561854, E1(0.62), E1(0.62)-0.436561854],_
[0.63, 0.427997338, E1(0.63), E1(0.63)-0.427997338],_
[0.64, 0.419651581, E1(0.64), E1(0.64)-0.419651581],_
[0.65, 0.411516976, E1(0.65), E1(0.65)-0.411516976],_
[0.66, 0.403586275, E1(0.66), E1(0.66)-0.403586275],_
[0.67, 0.395852563, E1(0.67), E1(0.67)-0.395852563],_
[0.68, 0.388309243, E1(0.68), E1(0.68)-0.388309243],_
[0.69, 0.380950010, E1(0.69), E1(0.69)-0.380950010],_
[0.70, 0.373768843, E1(0.70), E1(0.70)-0.373768843],_
[0.71, 0.366759981, E1(0.71), E1(0.71)-0.366759981],_
[0.72, 0.359917914, E1(0.72), E1(0.72)-0.359917914],_
[0.73, 0.353237364, E1(0.73), E1(0.73)-0.353237364],_
[0.74, 0.346713279, E1(0.74), E1(0.74)-0.346713279],_
[0.75, 0.340340813, E1(0.75), E1(0.75)-0.340340813],_

[0.76, 0.334115321, E1(0.76), E1(0.76)-0.334115321],_
[0.77, 0.328032346, E1(0.77), E1(0.77)-0.328032346],_
[0.78, 0.322087610, E1(0.78), E1(0.78)-0.322087610],_
[0.79, 0.316277004, E1(0.79), E1(0.79)-0.316277004],_
[0.80, 0.310596579, E1(0.80), E1(0.80)-0.310596579],_
[0.81, 0.305042539, E1(0.81), E1(0.81)-0.305042539],_
[0.82, 0.299611236, E1(0.82), E1(0.82)-0.299611236],_
[0.83, 0.294299155, E1(0.83), E1(0.83)-0.294299155],_
[0.84, 0.289102918, E1(0.84), E1(0.84)-0.289102918],_
[0.85, 0.284019269, E1(0.85), E1(0.85)-0.284019269],_
[0.86, 0.279045070, E1(0.86), E1(0.86)-0.279045070],_
[0.87, 0.274177301, E1(0.87), E1(0.87)-0.274177301],_
[0.88, 0.269413046, E1(0.88), E1(0.88)-0.269413046],_
[0.89, 0.264749496, E1(0.89), E1(0.89)-0.264749496],_
[0.90, 0.260183939, E1(0.90), E1(0.90)-0.260183939],_
[0.91, 0.255713758, E1(0.91), E1(0.91)-0.255713758],_
[0.92, 0.251336425, E1(0.92), E1(0.92)-0.251336425],_
[0.93, 0.247049501, E1(0.93), E1(0.93)-0.247049501],_
[0.94, 0.242850627, E1(0.94), E1(0.94)-0.242850627],_
[0.95, 0.238737524, E1(0.95), E1(0.95)-0.238737524],_
[0.96, 0.234707988, E1(0.96), E1(0.96)-0.234707988],_
[0.97, 0.230759890, E1(0.97), E1(0.97)-0.230759890],_
[0.98, 0.226891167, E1(0.98), E1(0.98)-0.226891167],_
[0.99, 0.223099826, E1(0.99), E1(0.99)-0.223099826],_
[1.00, 0.219383934, E1(1.00), E1(1.00)-0.219383934],_
[1.01, 0.215741624, E1(1.01), E1(1.01)-0.215741624],_
[1.02, 0.212171083, E1(1.02), E1(1.02)-0.212171083],_
[1.03, 0.208670559, E1(1.03), E1(1.03)-0.208670559],_
[1.04, 0.205238352, E1(1.04), E1(1.04)-0.205238352],_
[1.05, 0.201872813, E1(1.05), E1(1.05)-0.201872813],_
[1.06, 0.198572347, E1(1.06), E1(1.06)-0.198572347],_
[1.07, 0.195335403, E1(1.07), E1(1.07)-0.195335403],_
[1.08, 0.192160479, E1(1.08), E1(1.08)-0.192160479],_
[1.09, 0.189046118, E1(1.09), E1(1.09)-0.189046118],_
[1.10, 0.185990905, E1(1.10), E1(1.10)-0.185990905],_
[1.11, 0.182993465, E1(1.11), E1(1.11)-0.182993465],_
[1.12, 0.180052467, E1(1.12), E1(1.12)-0.180052467],_
[1.13, 0.177166615, E1(1.13), E1(1.13)-0.177166615],_
[1.14, 0.174334651, E1(1.14), E1(1.14)-0.174334651],_
[1.15, 0.171555354, E1(1.15), E1(1.15)-0.171555354],_
[1.16, 0.168827535, E1(1.16), E1(1.16)-0.168827535],_
[1.17, 0.166150040, E1(1.17), E1(1.17)-0.166150040],_
[1.18, 0.163521748, E1(1.18), E1(1.18)-0.163521748],_
[1.19, 0.160941567, E1(1.19), E1(1.19)-0.160941567],_
[1.20, 0.158408437, E1(1.20), E1(1.20)-0.158408437],_
[1.21, 0.155921324, E1(1.21), E1(1.21)-0.155921324],_
[1.22, 0.153479226, E1(1.22), E1(1.22)-0.153479226],_
[1.23, 0.151081164, E1(1.23), E1(1.23)-0.151081164],_
[1.24, 0.148726188, E1(1.24), E1(1.24)-0.148726188],_
[1.25, 0.146413373, E1(1.25), E1(1.25)-0.146413373],_

[1.26, 0.144141815, E1(1.26), E1(1.26)-0.144141815],_
[1.27, 0.141910639, E1(1.27), E1(1.27)-0.141910639],_
[1.28, 0.139718989, E1(1.28), E1(1.28)-0.139718989],_
[1.29, 0.137566032, E1(1.29), E1(1.29)-0.137566032],_
[1.30, 0.135450958, E1(1.30), E1(1.30)-0.135450958],_
[1.31, 0.133372975, E1(1.31), E1(1.31)-0.133372975],_
[1.32, 0.131331314, E1(1.32), E1(1.32)-0.131331314],_
[1.33, 0.129325224, E1(1.33), E1(1.33)-0.129325224],_
[1.34, 0.127353972, E1(1.34), E1(1.34)-0.127353972],_
[1.35, 0.125416844, E1(1.35), E1(1.35)-0.125416844],_
[1.36, 0.123513146, E1(1.36), E1(1.36)-0.123513146],_
[1.37, 0.121642198, E1(1.37), E1(1.37)-0.121642198],_
[1.38, 0.119803337, E1(1.38), E1(1.38)-0.119803337],_
[1.39, 0.117995919, E1(1.39), E1(1.39)-0.117995919],_
[1.40, 0.116219313, E1(1.40), E1(1.40)-0.116219313],_
[1.41, 0.114472903, E1(1.41), E1(1.41)-0.114472903],_
[1.42, 0.112756090, E1(1.42), E1(1.42)-0.112756090],_
[1.43, 0.111068287, E1(1.43), E1(1.43)-0.111068287],_
[1.44, 0.109408923, E1(1.44), E1(1.44)-0.109408923],_
[1.45, 0.107777440, E1(1.45), E1(1.45)-0.107777440],_
[1.46, 0.106173291, E1(1.46), E1(1.46)-0.106173291],_
[1.47, 0.104595946, E1(1.47), E1(1.47)-0.104595946],_
[1.48, 0.103044882, E1(1.48), E1(1.48)-0.103044882],_
[1.49, 0.101519593, E1(1.49), E1(1.49)-0.101519593],_
[1.50, 0.100019582, E1(1.50), E1(1.50)-0.100019582],_
[1.51, 0.098544365, E1(1.51), E1(1.51)-0.098544365],_
[1.52, 0.097093466, E1(1.52), E1(1.52)-0.097093466],_
[1.53, 0.095666424, E1(1.53), E1(1.53)-0.095666424],_
[1.54, 0.094262786, E1(1.54), E1(1.54)-0.094262786],_
[1.55, 0.092882108, E1(1.55), E1(1.55)-0.092882108],_
[1.56, 0.091523960, E1(1.56), E1(1.56)-0.091523960],_
[1.57, 0.090187917, E1(1.57), E1(1.57)-0.090187917],_
[1.58, 0.088873566, E1(1.58), E1(1.58)-0.088873566],_
[1.59, 0.087580504, E1(1.59), E1(1.59)-0.087580504],_
[1.60, 0.086308334, E1(1.60), E1(1.60)-0.086308334],_
[1.61, 0.085056670, E1(1.61), E1(1.61)-0.085056670],_
[1.62, 0.083825133, E1(1.62), E1(1.62)-0.083825133],_
[1.63, 0.082613354, E1(1.63), E1(1.63)-0.082613354],_
[1.64, 0.081420970, E1(1.64), E1(1.64)-0.081420970],_
[1.65, 0.080247627, E1(1.65), E1(1.65)-0.080247627],_
[1.66, 0.079092978, E1(1.66), E1(1.66)-0.079092978],_
[1.67, 0.077956684, E1(1.67), E1(1.67)-0.077956684],_
[1.68, 0.076838412, E1(1.68), E1(1.68)-0.076838412],_
[1.69, 0.075737839, E1(1.69), E1(1.69)-0.075737839],_
[1.70, 0.074654644, E1(1.70), E1(1.70)-0.074654644],_
[1.71, 0.073588518, E1(1.71), E1(1.71)-0.073588518],_
[1.72, 0.072539154, E1(1.72), E1(1.72)-0.072539154],_
[1.73, 0.071506255, E1(1.73), E1(1.73)-0.071506255],_
[1.74, 0.070489527, E1(1.74), E1(1.74)-0.070489527],_
[1.75, 0.069488685, E1(1.75), E1(1.75)-0.069488685],_

[1.76, 0.068503447, E1(1.76), E1(1.76)-0.068503447],_
[1.77, 0.067533539, E1(1.77), E1(1.77)-0.067533539],_
[1.78, 0.066578691, E1(1.78), E1(1.78)-0.066578691],_
[1.79, 0.065638641, E1(1.79), E1(1.79)-0.065638641],_
[1.80, 0.064713129, E1(1.80), E1(1.80)-0.064713129],_
[1.81, 0.063801903, E1(1.81), E1(1.81)-0.063801903],_
[1.82, 0.062904715, E1(1.82), E1(1.82)-0.062904715],_
[1.83, 0.062021320, E1(1.83), E1(1.83)-0.062021320],_
[1.84, 0.061151482, E1(1.84), E1(1.84)-0.061151482],_
[1.85, 0.060294967, E1(1.85), E1(1.85)-0.060294967],_
[1.86, 0.059451545, E1(1.86), E1(1.86)-0.059451545],_
[1.87, 0.058620994, E1(1.87), E1(1.87)-0.058620994],_
[1.88, 0.057803091, E1(1.88), E1(1.88)-0.057803091],_
[1.89, 0.056997623, E1(1.89), E1(1.89)-0.056997623],_
[1.90, 0.056204378, E1(1.90), E1(1.90)-0.056204378],_
[1.91, 0.055423149, E1(1.91), E1(1.91)-0.055423149],_
[1.92, 0.054653731, E1(1.92), E1(1.92)-0.054653731],_
[1.93, 0.053895927, E1(1.93), E1(1.93)-0.053895927],_
[1.94, 0.053149540, E1(1.94), E1(1.94)-0.053149540],_
[1.95, 0.052414380, E1(1.95), E1(1.95)-0.052414380],_
[1.96, 0.051690257, E1(1.96), E1(1.96)-0.051690257],_
[1.97, 0.050976988, E1(1.97), E1(1.97)-0.050976988],_
[1.98, 0.050274392, E1(1.98), E1(1.98)-0.050274392],_
[1.99, 0.049582291, E1(1.99), E1(1.99)-0.049582291],_
[2.00, 0.048900511, E1(2.00), E1(2.00)-0.048900511]]]
--R
--R
--R   (4)
--R     1 2520996153853843 2520996152845761        504041
--R   [[-,----------------,----------------,- ----------------],
--R     2 4503599627370496 4503599627370496   2251799813685248
--R     2296835809958953 4934345080664857 2467172539345369        1974119
--R    [----------------,----------------,----------------,- ----------------],
--R     4503599627370496 9007199254740992 4503599627370496   9007199254740992
--R     1170935903116329 4829838564922965 1207459640883145        1390385
--R    [----------------,----------------,----------------,- ----------------],
--R     2251799813685248 9007199254740992 2251799813685248   9007199254740992
--R     2386907802506363 2364171424823579 2364171425340887      129327
--R    [----------------,----------------,----------------,----------------],
--R     4503599627370496 4503599627370496 4503599627370496 1125899906842624
--R      607985949695017 2314867709456587  578716927028909        1340951
--R    [----------------,----------------,----------------,- ----------------],
--R     1125899906842624 4503599627370496 1125899906842624   4503599627370496
--R     2476979795053773  566737571905823 2266950289390477      1767185
--R    [----------------,----------------,----------------,----------------],
--R     4503599627370496 1125899906842624 4503599627370496 4503599627370496
--R     1261007895663739 2220364503638617  8881458010528123        4026345
--R    [----------------,----------------,-----------------,- -----------------],
--R     2251799813685248 4503599627370496 18014398509481984   18014398509481984
--R     5134103575202365 1087529314578621  8700234521044531      4415563

--R    [----------------,----------------,-----------------,-----------------],
--R     9007199254740992 2251799813685248 18014398509481984 18014398509481984
--R     5224175567749775  8523934786161673 4261967396063357      5965041
--R    [----------------,-----------------,----------------,-----------------],
--R     9007199254740992 18014398509481984 9007199254740992 18014398509481984
--R     5314247560297185 4176186574373573 1044046643495507        391545
--R    [----------------,----------------,----------------,- ----------------],
--R     9007199254740992 9007199254740992 2251799813685248   9007199254740992
--R     5404319552844595 2046343360395591 2046343361248583      833
--R    [----------------,----------------,----------------,-------------],
--R     9007199254740992 4503599627370496 4503599627370496 4398046511104
--R     5494391545392005  8022768437005963 4011384219969539      2933115
--R    [----------------,-----------------,----------------,-----------------],
--R     9007199254740992 18014398509481984 9007199254740992 18014398509481984
--R     5584463537939415 1966099802998573 1966099802310385        172047
--R    [----------------,----------------,----------------,- ----------------],
--R     9007199254740992 4503599627370496 4503599627370496   1125899906842624
--R      709316941310853  481882162983091  7710114614971581      7242125
--R    [----------------,----------------,-----------------,-----------------],
--R     1125899906842624 1125899906842624 18014398509481984 18014398509481984
--R     2882303761517117 3779885407634079  472485675800387        1230983
--R    [----------------,----------------,----------------,- ----------------],
--R     4503599627370496 9007199254740992 1125899906842624   9007199254740992
--R     1463669878895411  7413230799080933  7413230798170841        227523
--R    [----------------,-----------------,-----------------,- ----------------],
--R     2251799813685248 18014398509481984 18014398509481984   4503599627370496
--R     2972375754064527 3635181995403693 3635181993522683        940505
--R    [----------------,----------------,----------------,- ----------------],
--R     4503599627370496 9007199254740992 9007199254740992   4503599627370496
--R     377176468792279  7131045820881823  445690364269139      7424401
--R    [---------------,-----------------,----------------,-----------------],
--R     562949953421312 18014398509481984 1125899906842624 18014398509481984
--R     3062447746611937 3497578724158639  6995157444801331        3515947
--R    [----------------,----------------,-----------------,- -----------------],
--R     4503599627370496 9007199254740992 18014398509481984   18014398509481984
--R     1553741871442821 3431292646165573  6862585300640307      8309161
--R    [----------------,----------------,-----------------,-----------------],
--R     2251799813685248 9007199254740992 18014398509481984 18014398509481984
--R     3152519739159347 3366610444115003 3366610446218267      65727
--R    [----------------,----------------,----------------,---------------],
--R     4503599627370496 9007199254740992 9007199254740992 281474976710656
--R      799388933858263  825870056883005 103233757225971      924763
--R    [----------------,----------------,---------------,----------------],
--R     1125899906842624 2251799813685248 281474976710656 2251799813685248
--R     3242591731706757  810463091687183  6483704731876793        1620671
--R    [----------------,----------------,-----------------,- -----------------],
--R     4503599627370496 2251799813685248 18014398509481984   18014398509481984
--R     1643813863990231  6363358643534945  6363358652368601      1104207
--R    [----------------,-----------------,-----------------,----------------],
--R     2251799813685248 18014398509481984 18014398509481984 2251799813685248

--R     3332663724254167  6245831176435211  780728896837991        1731283
--R    [----------------,-----------------,----------------,- -----------------],
--R     4503599627370496 18014398509481984 2251799813685248   18014398509481984
--R     3 3065517517211543 3065517516411975        49973
--R    [-,----------------,----------------,- ---------------],
--R     4 9007199254740992 9007199254740992   562949953421312
--R     3422735716801577 3009443270308747  376180408890767      817389
--R    [----------------,----------------,----------------,----------------],
--R     4503599627370496 9007199254740992 1125899906842624 9007199254740992
--R     1733885856537641 2954652702422139  5909305411690919      6846641
--R    [----------------,----------------,-----------------,-----------------],
--R     2251799813685248 9007199254740992 18014398509481984 18014398509481984
--R     3512807709348987 2901107280753307  5802214566783441      5276827
--R    [----------------,----------------,-----------------,-----------------],
--R     4503599627370496 9007199254740992 18014398509481984 18014398509481984
--R      889460926405673  5697539989441027 1424384996278745        4326047
--R    [----------------,-----------------,----------------,- -----------------],
--R     1125899906842624 18014398509481984 4503599627370496   18014398509481984
--R     3602879701896397  5595210549787803 2797605270800517        8186769
--R    [----------------,-----------------,----------------,- -----------------],
--R     4503599627370496 18014398509481984 9007199254740992   18014398509481984
--R     1823957849085051  686894732486275  686894732936303      112507
--R    [----------------,----------------,----------------,---------------],
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--R    [----------------,-----------------,----------------,-----------------],
--R     1125899906842624 36028797018963968 9007199254740992 36028797018963968
--R     8511803295730237  64173618425951   128347237764691      912789
--R    [----------------,----------------,----------------,----------------],
--R     4503599627370496 1125899906842624 2251799813685248 2251799813685248
--R     4278419646001971  506244031634781  506244033206851      786035
--R    [----------------,----------------,----------------,----------------],

--R     2251799813685248 9007199254740992 9007199254740992 4503599627370496
--R     8601875288277647  7987317541891183   499207341747061        73938207
--R    [----------------,------------------,----------------,- ------------------],
--R     4503599627370496 144115188075855872 9007199254740992   144115188075855872
--R     1080863910568919  3938216361056117  123069261591561      9873835
--R    [----------------,-----------------,----------------,-----------------],
--R      562949953421312 72057594037927936 2251799813685248 72057594037927936
--R     8691947280825057  3883610828063799  485451352204859        10424927
--R    [----------------,-----------------,----------------,- -----------------],
--R     4503599627370496 72057594037927936 9007199254740992   72057594037927936
--R     4368491638549381  957456994155653   478728499055479      3955305
--R    [----------------,-----------------,----------------,-----------------],
--R     2251799813685248 18014398509481984 9007199254740992 18014398509481984
--R     8782019273372467  3776854115789689  236053380291295        31128969
--R    [----------------,-----------------,----------------,- -----------------],
--R     4503599627370496 72057594037927936 4503599627370496   72057594037927936
--R     2206763817411543  3724675554622163  465584443563007        6118107
--R    [----------------,-----------------,----------------,- -----------------],
--R     1125899906842624 72057594037927936 9007199254740992   72057594037927936
--R     8872091265919877  918319776645081   229579943573143        2352509
--R    [----------------,-----------------,----------------,- -----------------],
--R     4503599627370496 18014398509481984 4503599627370496   18014398509481984
--R     4458563631096791  905662932309913   14150983191703        8040921
--R    [----------------,-----------------,---------------,- -----------------],
--R     2251799813685248 18014398509481984 281474976710656   18014398509481984
--R     8962163258467287  446597574543551  446597570280771        1065695
--R    [----------------,----------------,----------------,- ----------------],
--R     4503599627370496 9007199254740992 9007199254740992   2251799813685248
--R        3523653169885229  440456643606101        21036421
--R    [2,-----------------,----------------,- -----------------]]
--R       72057594037927936 9007199254740992   72057594037927936
--R                                          Type: List(List(Fraction(Integer)))
--E 4

———-

The actual table values from above are:

 [0.5,                  0.55977359500000001,
                        0.55977359477616084,
                       -2.2383916942203541E-10]
 [0.51000000000000001,  0.54782235199999996,
                        0.54782235178082872,
                       -2.1917123671499894E-10]
 [0.52000000000000002,  0.53621979799999997,
                        0.53621979784563623,
                       -1.5436374400934483E-10]
 [0.53000000000000003,  0.52495150999999995,
                        0.52495151011486541,
                        1.148654504845581E-10]

[0.54000000000000004,  0.51400388600000002,
0.51400388570224909,
-2.9775093501882566E-10]
[0.55000000000000004,  0.50336408099999996,
0.50336408139239386,
3.9239389515444145E-10]
[0.56000000000000005,  0.49301995900000001,
0.49301995877649291,
-2.2350710171537003E-10]
[0.56999999999999995,  0.48296003399999998,
0.48296003424511297,
2.451129854641465E-10]
[0.57999999999999996,  0.47317343299999998,
0.47317343333112627,
3.3112629305165342E-10]
[0.58999999999999997,  0.463649849,
0.46364984895652972,
-4.3470282928836923E-11]
[0.59999999999999998,  0.45437950300000002,
0.45437950318940223,
1.8940221613306107E-10]
[0.60999999999999999,  0.445353112,
0.44535311216282059,
1.628205903436708E-10]
[0.62,                 0.43656185400000003,
0.43656185384719148,
-1.5280854359644991E-10]
[0.63,                 0.427997338,
0.42799733840201848,
4.0201847406606817E-10]
[0.64000000000000001,  0.419651581,
0.41965158086333326,
-1.366667334856686E-10]
[0.65000000000000002,  0.41151697599999998,
0.41151697594947956,
-5.0520421179811592E-11]
[0.66000000000000003,  0.40358627499999999,
0.40358627479116588,
-2.088341166661678E-10]
[0.67000000000000004,  0.39585256299999999,
0.39585256341213687,
4.1213688017904815E-10]
[0.68000000000000005,  0.38830924300000003,
0.38830924280482559,
-1.9517443217154096E-10]
[0.68999999999999995,  0.38095001000000001,
0.38095001046125104,
4.6125103736471829E-10]
[0.69999999999999996,  0.37376884300000002,
0.37376884323350923,

2.3350921196652052E-10]
[0.70999999999999996,  0.36675998100000001,
0.36675998141067723,
4.1067721445742222E-10]
[0.71999999999999997,  0.35991791400000001,
0.35991791391003464,
-8.9965368488265085E-11]
[0.72999999999999998,  0.353237364,
0.35323736449036641,
4.9036641414090809E-10]
[0.73999999999999999,  0.34671327899999999,
0.34671327890389447,
-9.6105512437105745E-11]
[0.75, 0.34034081300000002,
0.34034081291123008,
-8.8769935846499948E-11]
[0.76000000000000001,  0.33411532100000002,
0.33411532109074837,
9.0748353276381977E-11]
[0.77000000000000002,  0.32803234599999997,
0.3280323463800649,
3.8006492397713032E-10]
[0.78000000000000003,  0.32208761000000002,
0.32208761029292271,
2.9292268610703331E-10]
[0.79000000000000004,  0.31627700399999997,
0.31627700375985612,
-2.4014384925052923E-10]
[0.80000000000000004,  0.31059657899999998,
0.31059657854554301,
-4.5445697205437341E-10]
[0.81000000000000005, 0.305042539,
0.30504253919985258,
1.9985257893040398E-10]
[0.81999999999999995,  0.299611236,
0.29961123550328894,
-4.967110611708847E-10]
[0.82999999999999996,  0.29429915499999998,
0.29429915537086676,
3.7086678172926213E-10]
[0.83999999999999997,  0.28910291799999999,
0.28910291818146794,
1.8146795177642616E-10]
[0.84999999999999998,  0.28401926900000002,
0.2840192685024614,
-4.975386214134403E-10]
[0.85999999999999999,  0.27904507000000001,
0.27904507018183955,
1.818395434227682E-10]
[0.87,                 0.27417730099999998,

0.27417730078237224,
-2.1762774915501382E-10]
[0.88,                 0.26941304599999999,
0.26941304633432023,
3.343202381600463E-10]
[0.89000000000000001,  0.26474949599999997,
0.26474949638510148,
3.8510150623949357E-10]
[0.90000000000000002,  0.26018393899999998,
0.26018393932599954,
3.259995606796906E-10]
[0.91000000000000003,  0.25571375800000001,
0.25571375797753926,
-2.2460755477737848E-11]
[0.92000000000000004,  0.25133642499999997,
0.25133642541656154,
4.1656156302138925E-10]
[0.93000000000000005,  0.247049501,
0.24704950102931605,
2.9316049587890802E-11]
[0.93999999999999995,  0.24285062700000001,
0.24285062677606084,
-2.2393917276097852E-10]
[0.94999999999999996,  0.23873752400000001,
0.23873752365373468,
-3.4626532197101767E-10]
[0.95999999999999996,  0.23470798800000001,
0.23470798834425491,
3.4425490236245082E-10]
[0.96999999999999997,  0.23075989,
0.23075989003689171,
3.6891711907571789E-11]
[0.97999999999999998,  0.226891167,
0.22689116741400336,
4.1400335937247235E-10]
[0.98999999999999999,  0.223099826,
0.22309982579017718,
-2.0982282578074773E-10]
[1.,                   0.219383934,
0.21938393439552029,
3.9552028319178589E-10]
[1.01,                 0.21574162399999999,
0.21574162379448991,
-2.0551008117486447E-10]
[1.02,                 0.21217108300000001,
0.2121710834322488,
4.3224879231473778E-10]
[1.03,                 0.20867055900000001,
0.20867055930107367,
3.0107366599807506E-10]

[1.04,                 0.20523835200000001,
0.20523835171985597,
-2.8014404684917338E-10]
[1.05,                 0.20187281300000001,
0.20187281322019657,
2.2019655543381589E-10]
[1.0600000000000001,   0.19857234700000001,
0.19857234653302808,
-4.6697193334388487E-10]
[1.0700000000000001,   0.19533540299999999,
0.19533540267009863,
-3.2990135623300887E-10]
[1.0800000000000001,   0.192160479,
0.19216047909501838,
9.5018382051392791E-11]
[1.0900000000000001,   0.18904611800000001,
0.18904611797891213,
-2.1087881441061995E-11]
[1.1000000000000001,   0.18599090500000001,
0.18599090453604011,
-4.6395989827807682E-10]
[1.1100000000000001,   0.18299346499999999,
0.1829934654350395,
4.3503950442058681E-10]
[1.1200000000000001,   0.18005246699999999,
0.18005246728171573,
2.8171573407398398E-10]
[1.1299999999999999,   0.177166615,
0.17716661516956422,
1.6956422377312208E-10]
[1.1399999999999999,   0.17433465100000001,
0.17433465129443812,
2.9443811278007104E-10]
[1.1499999999999999,   0.17155535399999999,
0.1715553536299986,
-3.7000139063714244E-10]
[1.1599999999999999,   0.168827535,
0.16882753466078662,
-3.3921337960762799E-10]
[1.1699999999999999,   0.16615004,
0.16615004016994619,
1.6994619600474437E-10]
[1.1799999999999999,   0.16352174799999999,
0.16352174807880468,
7.8804684999767005E-11]
[1.1899999999999999,   0.16094156700000001,
0.1609415673356836,
3.3568359203428599E-10]
[1.2,                  0.15840843700000001,
0.15840843685146253,

-1.4853748786514132E-10]
[1.21,                 0.155921324,
0.15592132447956802,
4.7956802418092082E-10]
[1.22,                 0.153479226,
0.15347922603818942,
3.8189423845480519E-11]
[1.23,                 0.15108116399999999,
0.15108116437265298,
3.7265299179800593E-10]
[1.24,                 0.14872618800000001,
0.14872618845599739,
4.559973787454652E-10]
[1.25,                 0.14641337300000001,
0.14641337252591019,
-4.7408982295493729E-10]
[1.26,                 0.14414181500000001,
0.14414181525628297,
2.5628296707047582E-10]
[1.27,                 0.14191063900000001,
0.14191063896174164,
-3.8258368695309741E-11]
[1.28,                 0.13971898899999999,
0.1397189888335964,
-1.6640358535546795E-10]
[1.29,                 0.137566032,
0.13756603220574354,
2.0574353332136752E-10]
[1.3,                  0.13545095800000001,
0.13545095784912908,
-1.5087092686272285E-10]
[1.3100000000000001,   0.133372975,
0.13337297529345732,
2.9345731400454156E-10]
[1.3200000000000001,   0.131331314,
0.13133131417489974,
1.7489973358486566E-10]
[1.3300000000000001,   0.12932522399999999,
0.12932522360862764,
-3.9137235119390823E-10]
[1.3400000000000001,   0.12735397200000001,
0.12735397158504419,
-4.1495581970529827E-10]
[1.3500000000000001,   0.125416844,
0.12541684438866441,
3.8866440621454501E-10]
[1.3600000000000001,   0.123513146,
0.12351314603863212,
3.8632111398761992E-11]
[1.3700000000000001,   0.12164219800000001,

0.1216421977499248,
-2.5007521053943549E-10]
[1.3799999999999999,   0.119803337,
0.11980333741433752,
4.1433752262509671E-10]
[1.3899999999999999,   0.117995919,
0.11799591910039325,
1.0039324926935933E-10]
[1.3999999999999999,   0.116219313,
0.11621931257135804,
-4.2864196914127461E-10]
[1.4099999999999999,   0.114472903,
0.11447290282058709,
-1.7941291508005719E-10]
[1.4199999999999999,   0.11275609,
0.11275608962347,
-3.7653000162229944E-10]
[1.4299999999999999,   0.111068287,
0.11106828710526567,
1.0526567117974395E-10]
[1.4399999999999999,   0.10940892300000001,
0.10940892332417007,
3.2417006579077423E-10]
[1.45,                 0.10777744,
0.10777743986897642,
-1.3102358087380139E-10]
[1.46,                 0.106173291,
0.10617329147072579,
4.7072579167917183E-10]
[1.47,                 0.104595946,
0.10459594562777519,
-3.7222480653298362E-10]
[1.48,                 0.103044882,
0.10304488224373387,
2.4373386642295714E-10]
[1.49,                 0.10151959300000001,
0.10151959327774779,
2.7774778310618586E-10]
[1.5,                  0.100019582,
0.10001958240663256,
4.0663256095641032E-10]
[1.51,                 9.8544364999999995E-2,
9.85443646983854E-2,
-3.0161459441124805E-10]
[1.52,                 9.7093466000000003E-2,
9.7093466296618358E-2,
2.9661835487804211E-10]
[1.53,                 9.5666424E-2,
9.5666424115486592E-2,
1.1548659251126026E-10]

[1.54,                 9.4262786000000001E-2,
9.4262785544698136E-2,
-4.5530186565390096E-10]
[1.55,                 9.2882108000000005E-2,
9.2882108164209165E-2,
1.6420916015835729E-10]
[1.5600000000000001,   9.1523960000000001E-2,
9.152395946823666E-2,
-5.3176334169346973E-10]
[1.5700000000000001,   9.0187917000000006E-2,
9.0187916598222728E-2,
-4.0177727811396835E-10]
[1.5800000000000001,   8.8873566000000001E-2,
8.8873566084412048E-2,
8.441204679687786E-11]
[1.5900000000000001,   8.7580504000000003E-2,
8.7580503595714843E-2,
-4.0428516090429412E-10]
[1.6000000000000001,   8.6308334E-2,
8.6308333697539708E-2,
-3.0246029292246845E-10]
[1.6100000000000001,   8.5056670000000001E-2,
8.5056669617302794E-2,
-3.8269720725736533E-10]
[1.6200000000000001,   8.3825132999999996E-2,
8.3825133017319142E-2,
1.7319146117245054E-11]
[1.6299999999999999,   8.2613354E-2,
8.2613353774808662E-2,
-2.25191337799302E-10]
[1.6399999999999999,   8.1420969999999995E-2,
8.1420969768751517E-2,
-2.3124847869926413E-10]
[1.6499999999999999,   8.0247627000000002E-2,
8.0247626673343175E-2,
-3.266568265880565E-10]
[1.6599999999999999,   7.9092977999999994E-2,
7.9092977757806437E-2,
-2.4219355687638E-10]
[1.6699999999999999,   7.7956683999999998E-2,
7.7956683692333661E-2,
-3.0766633685175293E-10]
[1.6799999999999999,   7.6838411999999995E-2,
7.6838412359934938E-2,
3.5993494296171491E-10]
[1.6899999999999999,   7.5737839000000001E-2,
7.5737838673983093E-2,
-3.2601690791445037E-10]
[1.7,                  7.4654644000000006E-2,
7.4654644401252912E-2,

4.0125290590165008E-10]
[1.71,                 7.3588518000000006E-2,
7.358851799025623E-2,
-9.7437752311080317E-12]
[1.72,                 7.2539153999999995E-2,
7.2539154404693273E-2,
4.0469327888814632E-10]
[1.73,                 7.1506255000000005E-2,
7.150625496183538E-2,
-3.8164624238667955E-11]
[1.74,                 7.0489526999999996E-2,
7.0489527175668809E-2,
1.7566881282959912E-10]
[1.75,                 6.9488684999999994E-2,
6.9488684604638751E-2,
-3.9536124374350834E-10]
[1.76,                 6.8503446999999995E-2,
6.8503446703828352E-2,
-2.9617164276629637E-10]
[1.77,                 6.7533539000000004E-2,
6.7533538681429195E-2,
-3.1857080862174314E-10]
[1.78,                 6.6578690999999995E-2,
6.657869135934702E-2,
3.5934702435902466E-10]
[1.79,                 6.5638640999999998E-2,
6.5638641037815026E-2,
3.7815028886001301E-11]
[1.8,                  6.4713128999999994E-2,
6.4713129363868749E-2,
3.638687545715058E-10]
[1.8100000000000001,   6.3801902999999993E-2,
6.3801903203559385E-2,
2.0355939156502245E-10]
[1.8200000000000001,   6.2904715E-2,
6.2904714517779237E-2,
-4.8222076332038455E-10]
[1.8300000000000001,   6.2021319999999998E-2,
6.2021320241580469E-2,
2.4158047090550028E-10]
[1.8400000000000001,   6.1151482E-2,
6.1151482166870164E-2,
1.6687016352046058E-10]
[1.8500000000000001,   6.0294966999999998E-2,
6.0294966828373431E-2,
-1.7162656712477187E-10]
[1.8600000000000001,   5.9451545000000001E-2,
5.9451545392755656E-2,
3.9275565438812166E-10]
[1.8700000000000001,   5.8620994000000003E-2,

5.8620993550804079E-2,
-4.4919592351311266E-10]
[1.8799999999999999,   5.7803091000000001E-2,
5.7803091412567897E-2,
4.1256789651278325E-10]
[1.8899999999999999,   5.6997622999999997E-2,
5.6997623405359299E-2,
4.0535930168061896E-10]
[1.8999999999999999,   5.6204377999999999E-2,
5.6204378174534608E-2,
1.7453460898764206E-10]
[1.9099999999999999,   5.5423148999999998E-2,
5.5423148486950402E-2,
-5.1304959586273569E-10]
[1.9199999999999999,   5.4653730999999997E-2,
5.4653731137026984E-2,
1.3702698697937166E-10]
[1.9299999999999999,   5.3895927000000003E-2,
5.3895926855324849E-2,
-1.4467515380145457E-10]
[1.9399999999999999,   5.3149540000000002E-2,
5.3149540219563307E-2,
2.1956330503725141E-10]
[1.95,                 5.2414380000000003E-2,
5.2414379567998548E-2,
-4.3200145544153301E-10]
[1.96,                 5.1690257000000003E-2,
5.1690256915094213E-2,
-8.4905790731504283E-11]
[1.97,                 5.0976988000000001E-2,
5.0976987869409074E-2,
-1.3059092696110497E-10]
[1.98,                 5.0274392000000001E-2,
5.0274391553638775E-2,
-4.4636122575880677E-10]
[1.99,                 4.9582291000000001E-2,
4.9582290526736128E-2,
-4.732638725357674E-10]
[2.,                   4.8900511000000001E-2,
4.8900510708061007E-2,
-2.9193899381274591E-10]]

Now that we move into larger numbers we need a new scaling function. — * —

--S 5 of 7
g(x)==x * %e^x * E1(x)::DFLOAT
--R
--R                                                                   Type: Void

--E 5

———-

And we compute the scaled value of E1(x) in the range 2.0 to 10.0 from Abramowitz and Stegun,“Handbook of Mathematical Functions”, Dover Publications, Inc. New York 1965. pp242-243

— * —

--S 6 of 7
t6:List List Fraction Integer:=[[machineFraction (x::DFLOAT) for x in line]_
 for line in _
[[2.0,0.722657234,g(2.0),g(2.0)-0.722657234],_
[2.1,0.730791502,g(2.1),g(2.1)-0.730791502],_
[2.2,0.738431132,g(2.2),g(2.2)-0.738431132],_
[2.3,0.745622149,g(2.3),g(2.3)-0.745622149],_
[2.4,0.752404829,g(2.4),g(2.4)-0.752404829],_
[2.5,0.758814592,g(2.5),g(2.5)-0.758814592],_
[2.6,0.764882722,g(2.6),g(2.6)-0.764882722],_
[2.7,0.770636987,g(2.7),g(2.7)-0.770636987],_
[2.8,0.776102123,g(2.8),g(2.8)-0.776102123],_
[2.9,0.781300252,g(2.9),g(2.9)-0.781300252],_
[3.0,0.786251221,g(3.0),g(3.0)-0.786251221],_
[3.1,0.790972800,g(3.1),g(3.1)-0.790972800],_
[3.2,0.795481422,g(3.2),g(3.2)-0.795481422],_
[3.3,0.799791408,g(3.3),g(3.3)-0.799791408],_
[3.4,0.803916127,g(3.4),g(3.4)-0.803916127],_
[3.5,0.807867661,g(3.5),g(3.5)-0.807867661],_
[3.6,0.811657037,g(3.6),g(3.6)-0.811657037],_
[3.7,0.815294342,g(3.7),g(3.7)-0.815294342],_
[3.8,0.818788821,g(3.8),g(3.8)-0.818788821],_
[3.9,0.822148967,g(3.9),g(3.9)-0.822148967],_
[4.0,0.825382500,g(4.0),g(4.0)-0.825382500],_
[4.1,0.828496926,g(4.1),g(4.1)-0.828496926],_
[4.2,0.831498602,g(4.2),g(4.2)-0.831498602],_
[4.3,0.834393794,g(4.3),g(4.3)-0.834393794],_
[4.4,0.837188207,g(4.4),g(4.4)-0.837188207],_
[4.5,0.839887144,g(4.5),g(4.5)-0.839887144],_
[4.6,0.842495539,g(4.6),g(4.6)-0.842495539],_
[4.7,0.845017971,g(4.7),g(4.7)-0.845017971],_
[4.8,0.847458721,g(4.8),g(4.8)-0.847458721],_
[4.9,0.849821778,g(4.9),g(4.9)-0.849821778],_
[5.0,0.852110880,g(5.0),g(5.0)-0.852110880],_
[5.1,0.854329519,g(5.1),g(5.1)-0.854329519],_
[5.2,0.856480958,g(5.2),g(5.2)-0.856480958],_
[5.3,0.858568275,g(5.3),g(5.3)-0.858568275],_
[5.4,0.860594348,g(5.4),g(5.4)-0.860594348],_
[5.5,0.862561885,g(5.5),g(5.5)-0.862561885],_
[5.6,0.864473436,g(5.6),g(5.6)-0.864473436],_

[5.7,0.866331399,g(5.7),g(5.7)-0.866331399],_
[5.8,0.868138040,g(5.8),g(5.8)-0.868138040],_
[5.9,0.869895494,g(5.9),g(5.9)-0.869895494],_
[6.0,0.871605775,g(6.0),g(6.0)-0.871605775],_
[6.1,0.873270793,g(6.1),g(6.1)-0.873270793],_
[6.2,0.874892347,g(6.2),g(6.2)-0.874892347],_
[6.3,0.876472150,g(6.3),g(6.3)-0.876472150],_
[6.4,0.878011816,g(6.4),g(6.4)-0.878011816],_
[6.5,0.879512881,g(6.5),g(6.5)-0.879512881],_
[6.6,0.880976797,g(6.6),g(6.6)-0.880976797],_
[6.7,0.882404955,g(6.7),g(6.7)-0.882404955],_
[6.8,0.883798662,g(6.8),g(6.8)-0.883798662],_
[6.9,0.885159176,g(6.9),g(6.9)-0.885159176],_
[7.0,0.886487675,g(7.0),g(7.0)-0.886487675],_
[7.1,0.887785294,g(7.1),g(7.1)-0.887785294],_
[7.2,0.889053119,g(7.2),g(7.2)-0.889053119],_
[7.3,0.890292173,g(7.3),g(7.3)-0.890292173],_
[7.4,0.891503440,g(7.4),g(7.4)-0.891503440],_
[7.5,0.892687854,g(7.5),g(7.5)-0.892687854],_
[7.6,0.893846312,g(7.6),g(7.6)-0.893846312],_
[7.7,0.894979666,g(7.7),g(7.7)-0.894979666],_
[7.8,0.896088737,g(7.8),g(7.8)-0.896088737],_
[7.9,0.897174302,g(7.9),g(7.9)-0.897174302],_
[8.0,0.898237113,g(8.0),g(8.0)-0.898237113],_
[8.1,0.899277888,g(8.1),g(8.1)-0.899277888],_
[8.2,0.900297306,g(8.2),g(8.2)-0.900297306],_
[8.3,0.901296033,g(8.3),g(8.3)-0.901296033],_
[8.4,0.902274695,g(8.4),g(8.4)-0.902274695],_
[8.5,0.903233900,g(8.5),g(8.5)-0.903233900],_
[8.6,0.904174228,g(8.6),g(8.6)-0.904174228],_
[8.7,0.905096235,g(8.7),g(8.7)-0.905096235],_
[8.8,0.906000459,g(8.8),g(8.8)-0.906000459],_
[8.9,0.906887414,g(8.9),g(8.9)-0.906887414],_
[9.0,0.907757602,g(9.0),g(9.0)-0.907757602],_
[9.1,0.908611483,g(9.1),g(9.1)-0.908611483],_
[9.2,0.909449530,g(9.2),g(9.2)-0.909449530],_
[9.3,0.910272177,g(9.3),g(9.3)-0.910272177],_
[9.4,0.911079850,g(9.4),g(9.4)-0.911079850],_
[9.5,0.911872958,g(9.5),g(9.5)-0.911872958],_
[9.6,0.912651897,g(9.6),g(9.6)-0.912651897],_
[9.7,0.913417043,g(9.7),g(9.7)-0.913417043],_
[9.8,0.914168766,g(9.8),g(9.8)-0.914168766],_
[9.9,0.914907418,g(9.9),g(9.9)-0.914907418],_
[10.0,0.915633339,g(10.0),g(10.0)-0.915633339]]]
--R
--R   Compiling function g with type Float -> Expression(DoubleFloat)
--R
--R   (6)
--R       3254558849758993 6509117697504369        2013617
--R   [[2,----------------,----------------,- ----------------],

--R       4503599627370496 9007199254740992   9007199254740992
--R     1182194902184755 3291192336092725 6582384674784089      2598639
--R    [----------------,----------------,----------------,----------------],
--R      562949953421312 4503599627370496 9007199254740992 9007199254740992
--R     2476979795053773 6651196341827947  831399541260985       11740067
--R    [----------------,----------------,----------------,- ----------------],
--R     1125899906842624 9007199254740992 1125899906842624   9007199254740992
--R     2589569785738035  839495908098897 6715967263163031        1628145
--R    [----------------,----------------,----------------,- ----------------],
--R     1125899906842624 1125899906842624 9007199254740992   9007199254740992
--R     5404319552844595 1694265053758081  847132528293387      2828693
--R    [----------------,----------------,----------------,----------------],
--R     2251799813685248 2251799813685248 1125899906842624 2251799813685248
--R     5 3417397113774495 3417397110238951        441943
--R    [-,----------------,----------------,- ---------------],
--R     2 4503599627370496 4503599627370496   562949953421312
--R     1463669878895411 6889451083562661 6889451085181963      809651
--R    [----------------,----------------,----------------,----------------],
--R      562949953421312 9007199254740992 9007199254740992 4503599627370496
--R     3039929748475085 1735320223745561 433830056641961      2822283
--R    [----------------,----------------,---------------,----------------],
--R     1125899906842624 2251799813685248 562949953421312 2251799813685248
--R     3152519739159347 3495253231944251 6990506485130493     21241991
--R    [----------------,----------------,----------------,----------------],
--R     1125899906842624 4503599627370496 9007199254740992 9007199254740992
--R     6530219459687219 7037327047543349 1759331764469647     10335239
--R    [----------------,----------------,----------------,----------------],
--R     2251799813685248 9007199254740992 2251799813685248 9007199254740992
--R       3540960705915197 1770480352430547        1054103
--R    [3,----------------,----------------,- ----------------],
--R       4503599627370496 2251799813685248   4503599627370496
--R     1745144855606067 1781112403670099 7124450498128123     883447727
--R    [----------------,----------------,----------------,----------------],
--R      562949953421312 2251799813685248 9007199254740992 9007199254740992
--R     3602879701896397 447816229462419 1791264918587303      737627
--R    [----------------,---------------,----------------,----------------],
--R     1125899906842624 562949953421312 2251799813685248 2251799813685248
--R     3715469692580659  900485071760731 1800970143605021       83559
--R    [----------------,----------------,----------------,----------------],
--R     1125899906842624 1125899906842624 2251799813685248 2251799813685248
--R     7656119366529843  905129092498583 7241032736505429        3483235
--R    [----------------,----------------,----------------,- ----------------],
--R     2251799813685248 1125899906842624 9007199254740992   9007199254740992
--R     7 1819156248522137 1819156247605725        229103
--R    [-,----------------,----------------,- ---------------],
--R     2 2251799813685248 2251799813685248   562949953421312
--R     2026619832316723 3655378329385841  913844582061705        1139021
--R    [----------------,----------------,----------------,- ----------------],
--R      562949953421312 4503599627370496 1125899906842624   4503599627370496
--R     4165829655317709 7343518589656947 7343518584009017        2823965

--R    [----------------,----------------,----------------,- ----------------],
--R     1125899906842624 9007199254740992 9007199254740992   4503599627370496
--R     4278419646001971 460937128643841 7374994054164043        4137413
--R    [----------------,---------------,----------------,- ----------------],
--R     1125899906842624 562949953421312 9007199254740992   9007199254740992
--R     8782019273372467 1851314890712119 7405259567957195      5108719
--R    [----------------,----------------,----------------,----------------],
--R     2251799813685248 2251799813685248 9007199254740992 9007199254740992
--R       232324519964883 3717192768015601     448577473
--R    [4,---------------,----------------,----------------],
--R       281474976710656 4503599627370496 4503599627370496
--R     2308094809027379 3731218447211201 7462436884601849        9820553
--R    [----------------,----------------,----------------,- ----------------],
--R      562949953421312 4503599627370496 9007199254740992   9007199254740992
--R     1182194902184755 234046049632893 7489473589300961      1048385
--R    [----------------,---------------,----------------,----------------],
--R      281474976710656 281474976710656 9007199254740992 9007199254740992
--R     4841369599423283 1878887789869327 469721946680651        3146723
--R    [----------------,----------------,---------------,- ----------------],
--R     1125899906842624 2251799813685248 562949953421312   2251799813685248
--R     2476979795053773 7540720994168347 3770360496609591        949165
--R    [----------------,----------------,----------------,- ----------------],
--R      562949953421312 9007199254740992 4503599627370496   9007199254740992
--R     9 1891257714375835 236407214829209      4257837
--R    [-,----------------,---------------,----------------],
--R     2 2251799813685248 281474976710656 2251799813685248
--R     2589569785738035 3794262595501705 3794262589093149        1602139
--R    [----------------,----------------,----------------,- ----------------],
--R      562949953421312 4503599627370496 4503599627370496   1125899906842624
--R     1322932390540083 7611245238633945 1902811306968295       10760765
--R    [----------------,----------------,----------------,- ----------------],
--R      281474976710656 9007199254740992 2251799813685248   9007199254740992
--R     5404319552844595 3816614780107477 3816614773923689        1545947
--R    [----------------,----------------,----------------,- ----------------],
--R     1125899906842624 4503599627370496 4503599627370496   1125899906842624
--R     2758454771764429  956814260683033 7654514099860267     14396003
--R    [----------------,----------------,----------------,----------------],
--R      562949953421312 1125899906842624 9007199254740992 9007199254740992
--R       3837566241646345 7675132496115893     12823203
--R    [5,----------------,----------------,----------------],
--R       4503599627370496 9007199254740992 9007199254740992
--R     2871044762448691 3847558103420015 7695116191051275       15788755
--R    [----------------,----------------,----------------,- ----------------],
--R      562949953421312 4503599627370496 9007199254740992   9007199254740992
--R     1463669878895411 3857247323298725 3857247327193773      486881
--R    [----------------,----------------,----------------,---------------],
--R      281474976710656 4503599627370496 4503599627370496 562949953421312
--R     5967269506265907 7733295526724259 7733295527575265      425503
--R    [----------------,----------------,----------------,----------------],
--R     1125899906842624 9007199254740992 9007199254740992 4503599627370496

--R     3039929748475085 3875772384969955 3875772382742157        1113899
--R    [----------------,----------------,----------------,- ----------------],
--R      562949953421312 4503599627370496 4503599627370496   2251799813685248
--R     11 7769266767739985 7769266764954073        348239
--R    [--,----------------,----------------,- ----------------],
--R      2 9007199254740992 9007199254740992   1125899906842624
--R     3152519739159347  973310561060323  973310560202397        428963
--R    [----------------,----------------,----------------,- ---------------],
--R      562949953421312 1125899906842624 1125899906842624   562949953421312
--R     1604407367250739 243850610357235 487701221015787      301317
--R    [----------------,---------------,---------------,---------------],
--R      281474976710656 281474976710656 562949953421312 562949953421312
--R     6530219459687219 3909746153450153 7819492311718607      4818301
--R    [----------------,----------------,----------------,----------------],
--R     1125899906842624 4503599627370496 9007199254740992 9007199254740992
--R     3321404725185741 7835322045259347 7835322041498613        1880367
--R    [----------------,----------------,----------------,- ----------------],
--R      562949953421312 9007199254740992 9007199254740992   4503599627370496
--R        981340860875993  981340861330093      113525
--R    [6,----------------,----------------,---------------],
--R       1125899906842624 1125899906842624 281474976710656
--R     3433994715870003 7865724035896675 7865724029886543        1502533
--R    [----------------,----------------,----------------,- ----------------],
--R      562949953421312 9007199254740992 9007199254740992   2251799813685248
--R     1745144855606067 7880329695876997 3940164851821349      7765701
--R    [----------------,----------------,----------------,----------------],
--R      281474976710656 9007199254740992 4503599627370496 9007199254740992
--R     7093169413108531 3947279648140617 7894559292391669        3889565
--R    [----------------,----------------,----------------,- ----------------],
--R     1125899906842624 4503599627370496 9007199254740992   9007199254740992
--R     3602879701896397  988553421841123 1977106842517461        1164785
--R    [----------------,----------------,----------------,- ----------------],
--R      562949953421312 1125899906842624 2251799813685248   2251799813685248
--R     13 3960973883139151 495121734805295        4696791
--R    [--,----------------,---------------,- ----------------],
--R      2 4503599627370496 562949953421312   4503599627370496
--R     3715469692580659 3967566774691253 3967566783996147      4652447
--R    [----------------,----------------,----------------,----------------],
--R      562949953421312 4503599627370496 4503599627370496 2251799813685248
--R     1885882343961395 3973998626527879 3973998629205993      1339057
--R    [----------------,----------------,----------------,----------------],
--R      281474976710656 4503599627370496 4503599627370496 2251799813685248
--R     7656119366529843 3980275324853743 7960550664516793     14809307
--R    [----------------,----------------,----------------,----------------],
--R     1125899906842624 4503599627370496 9007199254740992 9007199254740992
--R     3884354678607053 3986402535197175 7972805042402257       27992093
--R    [----------------,----------------,----------------,- ----------------],
--R      562949953421312 4503599627370496 9007199254740992   9007199254740992
--R       3992385562798537 1996192775851801       11094935
--R    [7,----------------,----------------,- ----------------],

--R       4503599627370496 2251799813685248   4503599627370496
--R     3996944669291315 1999114759621703 7996459047031801      8544989
--R    [----------------,----------------,----------------,----------------],
--R      562949953421312 2251799813685248 9007199254740992 9007199254740992
--R     2026619832316723 4003939295440977 8007878591474863      592909
--R    [----------------,----------------,----------------,----------------],
--R      281474976710656 4503599627370496 9007199254740992 9007199254740992
--R     8219069319951155 4009519498573669 501189937624389      2421443
--R    [----------------,----------------,---------------,----------------],
--R     1125899906842624 4503599627370496 562949953421312 4503599627370496
--R     4165829655317709 4014974560183515 8029949117243575        3123455
--R    [----------------,----------------,----------------,- ----------------],
--R      562949953421312 4503599627370496 9007199254740992   9007199254740992
--R     15 8040617373265135 8040617373833349      284107
--R    [--,----------------,----------------,----------------],
--R      2 9007199254740992 9007199254740992 4503599627370496
--R     4278419646001971 1006381479412423 2012762957281121        1543725
--R    [----------------,----------------,----------------,- ----------------],
--R      562949953421312 1125899906842624 2251799813685248   2251799813685248
--R     2167357320672051 4030630090301771 8061260182530025      1926483
--R    [----------------,----------------,----------------,----------------],
--R      281474976710656 4503599627370496 9007199254740992 9007199254740992
--R     8782019273372467 2017812451022049 504453112210195        2181269
--R    [----------------,----------------,---------------,- ----------------],
--R     1125899906842624 2251799813685248 562949953421312   2251799813685248
--R     4447304632028365 4040513852173585 1010128463671393      2511987
--R    [----------------,----------------,----------------,----------------],
--R      562949953421312 4503599627370496 1125899906842624 4503599627370496
--R       2022650163698575 8090600664053663      9259363
--R    [8,----------------,----------------,----------------],
--R       2251799813685248 9007199254740992 9007199254740992
--R     4559894622712627 8099975122598653 8099975112856887        4870883
--R    [----------------,----------------,----------------,- ----------------],
--R      562949953421312 9007199254740992 9007199254740992   4503599627370496
--R     2308094809027379 4054578611824261 4054578619164799      3670269
--R    [----------------,----------------,----------------,----------------],
--R      281474976710656 4503599627370496 4503599627370496 2251799813685248
--R     2336242306698445 2029538239184653 8118152966317681      9579069
--R    [----------------,----------------,----------------,----------------],
--R      281474976710656 2251799813685248 9007199254740992 9007199254740992
--R     1182194902184755 1015870995046957 4063483989634285      9446457
--R    [----------------,----------------,----------------,----------------],
--R      140737488355328 1125899906842624 4503599627370496 4503599627370496
--R     17 254237740966775 4067803864354941      8886541
--R    [--,---------------,----------------,----------------],
--R      2 281474976710656 4503599627370496 4503599627370496
--R     4841369599423283 2036019358149403 2036019361740689      1795643
--R    [----------------,----------------,----------------,----------------],
--R      562949953421312 2251799813685248 2251799813685248 1125899906842624
--R     2448832297382707 4076191066680439 8152382158143441     24782563

--R    [----------------,----------------,----------------,----------------],
--R      281474976710656 4503599627370496 9007199254740992 9007199254740992
--R     2476979795053773 2040131664774949 8160526688504177     29404381
--R    [----------------,----------------,----------------,----------------],
--R      281474976710656 2251799813685248 9007199254740992 9007199254740992
--R     1252563646362419 8168515639514785 8168515676159353      4580571
--R    [----------------,----------------,----------------,----------------],
--R      140737488355328 9007199254740992 9007199254740992 1125899906842624
--R       4088176798109935 255511049382469        7990431
--R    [9,----------------,---------------,- ----------------],
--R       4503599627370496 281474976710656   4503599627370496
--R     5122844576133939 2046011168131677 8184044689509625     16982917
--R    [----------------,----------------,----------------,----------------],
--R      562949953421312 2251799813685248 9007199254740992 9007199254740992
--R     2589569785738035 8191593128840545 8191593130497493      414237
--R    [----------------,----------------,----------------,----------------],
--R      281474976710656 9007199254740992 9007199254740992 2251799813685248
--R     2617717283409101 2049750718571465 4099501437574337      431407
--R    [----------------,----------------,----------------,----------------],
--R      281474976710656 2251799813685248 4503599627370496 4503599627370496
--R     1322932390540083 4103138872964767 4103138874027955      265797
--R    [----------------,----------------,----------------,----------------],
--R      140737488355328 4503599627370496 4503599627370496 1125899906842624
--R     19 256669419616127 128334709895015      173903
--R    [--,---------------,---------------,---------------],
--R      2 281474976710656 140737488355328 281474976710656
--R     5404319552844595 256888671453011 64222167818743        178039
--R    [----------------,---------------,--------------,- ---------------],
--R      562949953421312 281474976710656 70368744177664   281474976710656
--R     2730307274093363 1028416163622165 8227329312589533      3612213
--R    [----------------,----------------,----------------,----------------],
--R      281474976710656 1125899906842624 9007199254740992 9007199254740992
--R     2758454771764429 2058525056955673 8234100228394759      572067
--R    [----------------,----------------,----------------,----------------],
--R      281474976710656 2251799813685248 9007199254740992 9007199254740992
--R     1393301134717747 8240753413566605 4120376705584929        2396747
--R    [----------------,----------------,----------------,- ----------------],
--R      140737488355328 9007199254740992 4503599627370496   9007199254740992
--R        4123645964328403 8247291932240601      3583795
--R    [10,----------------,----------------,----------------]]
--R        4503599627370496 9007199254740992 9007199254740992
--R                                          Type: List(List(Fraction(Integer)))
--E 6

———-

The actual table values from above are:

 [2.,                   0.72265723400000004,
                        0.72265723377644353,

-2.2355650663996585E-10]
[2.1000000000000001,   0.73079150199999998,
0.73079150228850298,
2.8850299926830303E-10]
[2.2000000000000002,   0.73843113199999999,
0.73843113069659072,
-1.3034092694041988E-9]
[2.2999999999999998,   0.74562214900000001,
0.74562214881923961,
-1.8076040664283255E-10]
[2.3999999999999999,   0.75240482900000005,
0.75240483025618621,
1.2561861550963727E-9]
[2.5,                  0.75881459200000001,
0.75881459121494477,
-7.850552430355151E-10]
[2.6000000000000001,   0.76488272199999996,
0.76488272217978248,
1.7978252220274271E-10]
[2.7000000000000002,   0.77063698700000005,
0.77063698825333671,
1.2533366566813697E-9]
[2.7999999999999998,   0.77610212300000003,
0.77610212535832457,
2.3583245356562088E-9]
[2.8999999999999999,   0.78130025199999997,
0.78130025314743023,
1.1474302619163268E-9]
[3.,                   0.786251221,
0.78625122076592868,
-2.3407131788388824E-10]
[3.1000000000000001,   0.79097280000000003,
0.79097289808240101,
9.8082400978860562E-8]
[3.2000000000000002,   0.79548142200000005,
0.7954814223275547,
3.2755465007028306E-10]
[3.2999999999999998,   0.79979140800000004,
0.79979140803702831,
3.7028269339600683E-11]
[3.3999999999999999,   0.80391612700000004,
0.80391612661323797,
-3.8676206681742542E-10]
[3.5,                  0.80786766099999996,
0.80786766059300552,
-4.0699443815128689E-10]
[3.6000000000000001,   0.81165703700000003,
0.81165703674711587,
-2.5288415805846398E-10]
[3.7000000000000002,   0.81529434199999995,

0.81529434137285406,
-6.2714589077472738E-10]
[3.7999999999999998,   0.81878882100000006,
0.81878882054050406,
-4.5949599680739084E-10]
[3.8999999999999999,   0.82214896699999995,
0.8221489675670105,
5.6701054962360331E-10]
[4.,                   0.82538250000000002,
0.82538259960411076,
9.9604110737061546E-8]
[4.0999999999999996,   0.82849692600000002,
0.82849692490970006,
-1.0902999614259556E-9]
[4.2000000000000002,   0.83149860200000003,
0.83149860211639337,
1.1639333941104724E-10]
[4.2999999999999998,   0.83439379400000002,
0.83439379260257418,
-1.397425841709321E-9]
[4.4000000000000004,   0.83718820699999996,
0.83718820689462137,
-1.0537859473913613E-10]
[4.5,                  0.83988714399999997,
0.83988714589085944,
1.8908594690003611E-9]
[4.5999999999999996,   0.84249553899999996,
0.84249553757701434,
-1.4229856182268463E-9]
[4.7000000000000002,   0.84501797099999998,
0.84501796980531307,
-1.1946869049594966E-9]
[4.7999999999999998,   0.84745872099999997,
0.84745871962692243,
-1.3730775405562667E-9]
[4.9000000000000004,   0.84982177800000003,
0.84982177959827732,
1.5982772882949803E-9]
[5.,                   0.85211088000000001,
0.85211088142366165,
1.4236616330265406E-9]
[5.0999999999999996,   0.85432951899999998,
0.85432951724709605,
-1.7529039331165563E-9]
[5.2000000000000002,   0.85648095800000001,
0.85648095886487274,
8.6487272898949641E-10]
[5.2999999999999998,   0.85856827499999999,
0.85856827509448064,
9.4480645529415597E-11]

[5.4000000000000004,   0.86059434800000001,
0.86059434750532948,
-4.946705267627749E-10]
[5.5,                  0.86256188499999997,
0.86256188469070161,
-3.0929836469795191E-10]
[5.5999999999999996,   0.86447343600000004,
0.86447343523800879,
-7.6199124787734718E-10]
[5.7000000000000002,   0.866331399,
0.8663313995352464,
5.3524640275526281E-10]
[5.7999999999999998,   0.86813804000000006,
0.86813804053493893,
5.3493887097744164E-10]
[5.9000000000000004,   0.86989549399999999,
0.86989549358247464,
-4.1752534762906635E-10]
[6.,                   0.87160577500000003,
0.87160577540332174,
4.0332170936352441E-10]
[6.0999999999999996,   0.87327079299999999,
0.8732707923327413,
-6.6725869274364413E-10]
[6.2000000000000002,   0.87489234699999996,
0.8748923478621643,
8.6216433992092334E-10]
[6.2999999999999998,   0.87647215000000001,
0.87647214956817143,
-4.3182857289991716E-10]
[6.4000000000000004,   0.878011816,
0.87801181548273155,
-5.1726845029520518E-10]
[6.5,                  0.87951288100000002,
0.87951287995710281,
-1.0428972130327452E-9]
[6.5999999999999996,   0.88097679699999998,
0.88097679906610149,
2.0661015120992943E-9]
[6.7000000000000002,   0.88240495500000005,
0.8824049555946607,
5.9466065405189283E-10]
[6.7999999999999998,   0.88379866200000001,
0.88379866364416337,
1.6441633610142503E-9]
[6.9000000000000004,   0.88515917600000005,
0.88515917289225332,
-3.1077467266271697E-9]
[7.,                   0.88648767500000003,
0.88648767253642946,

-2.4635705697662047E-9]
[7.0999999999999996,   0.88778529399999995,
0.8877852949486843,
9.4868435329686918E-10]
[7.2000000000000002,   0.88905311899999995,
0.88905311906582485,
6.5824901085420606E-11]
[7.2999999999999998,   0.89029217299999996,
0.89029217353766843,
5.3766846530578505E-10]
[7.4000000000000004,   0.89150344000000004,
0.89150343965322676,
-3.4677327676035929E-10]
[7.5,                  0.89268785399999995,
0.89268785406308437,
6.308442657143587E-11]
[7.5999999999999996,   0.89384631199999998,
0.89384631131444836,
-6.8555161547578791E-10]
[7.7000000000000002,   0.89497966600000001,
0.89497966621388148,
2.1388146809186992E-10]
[7.7999999999999998,   0.89608873700000002,
0.89608873603132189,
-9.686781377027387E-10]
[7.9000000000000004,   0.89717430200000003,
0.8971743025577732,
5.5777316099181462E-10]
[8.,                   0.89823711299999998,
0.89823711402799578,
1.0279957995962263E-9]
[8.0999999999999996,   0.89927788799999997,
0.89927788691844668,
-1.0815532913710513E-9]
[8.1999999999999993,   0.90029730600000002,
0.90029730762992677,
1.629926749124877E-9]
[8.3000000000000007,   0.90129603300000005,
0.90129603406349046,
1.0634904068496098E-9]
[8.4000000000000004,   0.90227469500000002,
0.90227469709753316,
2.0975331471717595E-9]
[8.5,                  0.90323390000000003,
0.90323390197320852,
1.9732084854950926E-9]
[8.5999999999999996,   0.90417422800000002,
0.9041742295948515,
1.5948514731078944E-9]
[8.6999999999999993,   0.90509623500000003,

0.90509623775141723,
2.7514172051823493E-9]
[8.8000000000000007,   0.90600045900000004,
0.90600046226454201,
3.264541970082746E-9]
[8.9000000000000004,   0.90688741399999995,
0.90688741806836271,
4.0683627577919879E-9]
[9.,                   0.907757602,
0.90775760022576812,
-1.7742318725311179E-9]
[9.0999999999999996,   0.90861148300000005,
0.90861148488548271,
1.8854826588921014E-9]
[9.1999999999999993,   0.90944952999999995,
0.90944953018395813,
1.8395818202066039E-10]
[9.3000000000000007,   0.91027217699999996,
0.91027217709579178,
9.5791818921497907E-11]
[9.4000000000000004,   0.91107985000000002,
0.91107985023607185,
2.3607182875196031E-10]
[9.5,                  0.91187295800000001,
0.91187295861782769,
6.1782767790674598E-10]
[9.5999999999999996,   0.91265189700000005,
0.91265189636747834,
-6.3252170168226485E-10]
[9.6999999999999993,   0.91341704300000004,
0.91341704340103613,
4.010360932227286E-10]
[9.8000000000000007,   0.91416876599999997,
0.91416876606351216,
6.3512195502823943E-11]
[9.9000000000000004,   0.91490741799999997,
0.9149074177339066,
-2.6609336956084917E-10]
[10.,                  0.91563333899999999,
0.91563333939788116,
3.9788117245365129E-10]]

— * —

--S 7 of 7
E1(0.0)
--R
--R

--R   (7)  infinity
--R                                        Type: OnePointCompletion(DoubleFloat)
--E 7
)spool
)lisp (bye)

———-

References

[1] Abramowitz and Stegun,“Handbook of Mathematical Functions”, Dover Publications, Inc. New York 1965. pp238-243

[2] Segletes, Steven, B., “A Compact Analytical Fit to the Exponential Integral E_{1}(x)”, Army Research Laboratory, ARL-TR-1758, September 1998

[3] Lund, Lars Erik, “Numlibc”, http://www.math.ntnu.no/num/nnm/Program/Numlibc

[4] Haavie, T. “expint.c”, http://www.math.ntnu.no/num/nnm/Program/Numlibc, June, 1988