mirror of
https://github.com/opelly27/Y-Cruncher.git
synced 2026-05-20 01:47:34 +00:00
opelly27
656 lines
30 KiB
INI
656 lines
30 KiB
INI
// y-cruncher Custom Formula File
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//
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// This can be loaded directly from the Custom Compute menu or
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// entered from the command line as "custom:filename.cfg".
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// y-cruncher custom custom:"filename.cfg"
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//
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//
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// Author: Alexander J. Yee
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// Date: October 4, 2018
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//
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// Value = 1.03692775514336992633136548645703416805708091950191...
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//
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// Original Formula: Broadhurst (1998)
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// https://arxiv.org/pdf/math/9803067.pdf
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//
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// 1152 inf 1 ( 248 12912 124 24848 62 3228 31 74552 )
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// Zeta(5) = ------- SUM ------ (---------- - ---------- - ---------- - ---------- - ---------- - ---------- + ---------- + ----------)
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// 62651 k=0 16^k ( (8k+1)^5 (8k+2)^5 (8k+3)^5 (8k+4)^5 (8k+5)^5 (8k+6)^5 (8k+7)^5 (8k+8)^5 )
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//
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// 7 inf 1 ( 177152 145408 22144 29248 2768 2272 346 111 )
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// + -------- SUM -------- (---------- + ---------- - ---------- - ---------- - ---------- + ---------- + ---------- - ----------)
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// 250604 k=0 4096^k ( (8k+1)^5 (8k+2)^5 (8k+3)^5 (8k+4)^5 (8k+5)^5 (8k+6)^5 (8k+7)^5 (8k+8)^5 )
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//
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// 369 inf 1 ( 131072 4096 1024 128 4 1 )
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// + ---------- SUM --------- (- ---------- + ---------- + ---------- + ---------- - ---------- - ----------)
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// 64154624 k=0 2^(20k) ( (8k+1)^5 (8k+3)^5 (8k+4)^5 (8k+5)^5 (8k+7)^5 (8k+8)^5 )
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//
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//
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// Optimized into a massive 74-term BBP formula by Alex Yee (2018).
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// The following implementation groups the 74 terms into sets of 2 or 3 terms each.
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//
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{
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NameShort : "Zeta(5)"
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NameLong : "Zeta(5)"
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AlgorithmShort : "Broadhurst (optimized)"
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AlgorithmLong : "Broadhurst (1998) (optimized)"
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Formula : {
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LinearCombination : [
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[-1 {SeriesBinaryBBP : {
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CoefficientP : 1
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CoefficientQ : 0
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CoefficientD : 1762059375
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Alternating : "false"
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PowerCoef : -30
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PowerShift : 12
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PolynomialP : [
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55293739267 -2260658245680 40544723556900 -418475704423680
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2743554653514720 -11903795644396032 34544269695818880 -66159912056279040
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80125279389331200 -55550303705640960 16795225145889792
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]
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PolynomialQ : [
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-3125 143750 -2982500 36979000
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-306192400 1793303776 -7678751040 24504739200
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-58849079040 106537628160 -144464145408 144349931520
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-103061237760 49716633600 -14511882240 1934917632
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]
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}}]
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[-1 {SeriesBinaryBBP : {
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CoefficientP : 1
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CoefficientQ : 0
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CoefficientD : 117470625
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Alternating : "true"
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PowerCoef : -30
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PowerShift : 18
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PolynomialP : [
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-34509025 693618140 -5558112160 22244671360 -44497491200 35600165888
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]
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PolynomialQ : [
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243 -6480 75600 -506880
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2158080 -6086656 11509760 -14417920
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11468800 -5242880 1048576
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]
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}}]
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[1 {SeriesBinaryBBP : {
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CoefficientP : 1
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CoefficientQ : 0
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CoefficientD : 563859
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Alternating : "false"
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PowerCoef : -30
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PowerShift : 30
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PolynomialP : [
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-1192566547 8419823750 -23837731000 33810670000 -24015350000 6831500000
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]
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PolynomialQ : [
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992436543 -12602368800 71888512500 -242585280000
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536262300000 -811465600000 851210000000 -611200000000
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287500000000 -80000000000 10000000000
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]
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}}]
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[1 {SeriesBinaryBBP : {
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CoefficientP : 1
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CoefficientQ : 0
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CoefficientD : 563859
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Alternating : "false"
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PowerCoef : -30
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PowerShift : 12
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PolynomialP : [
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-322657 7619750 -95641000 767230000 -3520850000 6831500000
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]
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PolynomialQ : [
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243 -16200 472500 -7920000
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84300000 -594400000 2810000000 -8800000000
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17500000000 -20000000000 10000000000
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]
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}}]
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[1 {SeriesBinaryBBP : {
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CoefficientP : 1
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CoefficientQ : 0
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CoefficientD : 195784375
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Alternating : "true"
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PowerCoef : -30
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PowerShift : 27
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PolynomialP : [
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-19669507184511 169174898363340 -581291762951520 997878572323200
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-856076349070080 293675932965888
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]
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PolynomialQ : [
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2706784157 -37965284280 238310226000 -881506644480
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2127741073920 -3501690310656 3979152138240 -3082968760320
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1558683648000 -464380231680 61917364224
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]
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}}]
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[1 {SeriesBinaryBBP : {
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CoefficientP : 1
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CoefficientQ : 0
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CoefficientD : 195784375
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Alternating : "true"
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PowerCoef : -30
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PowerShift : 12
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PolynomialP : [
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2423887983 27619171020 -1493511864480 19915706597760
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-121886516655360 293675932965888
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]
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PolynomialQ : [
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3125 -225000 6930000 -119232000
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1257638400 -8429432832 36219985920 -98895790080
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165542952960 -154793410560 61917364224
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]
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}}]
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[-1 {SeriesBinaryBBP : {
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CoefficientP : 1
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CoefficientQ : 0
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CoefficientD : 1691577
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Alternating : "true"
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PowerCoef : -30
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PowerShift : 35
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PolynomialP : [
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-289888774695 1755263684500 -4235370300000 5093670800000
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-3054636000000 731024000000
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]
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PolynomialQ : [
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3515706497843 -39184344867600 196460896610000 -583507923840000
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1136939844800000 -1518525619200000 1407975040000000 -894873600000000
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373120000000000 -92160000000000 10240000000000
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]
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}}]
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[-1 {SeriesBinaryBBP : {
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CoefficientP : 1
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CoefficientQ : 0
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CoefficientD : 1691577
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Alternating : "true"
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PowerCoef : -30
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PowerShift : 26
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PolynomialP : [
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-54164342135 475456051500 -1676786300000 2968479600000
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-2636908000000 939888000000
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]
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PolynomialQ : [
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59797108943 -1003587842400 7573696130000 -33843912960000
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99171300800000 -199112140800000 277402240000000 -264806400000000
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165760000000000 -61440000000000 10240000000000
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]
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}}]
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[1 {SeriesBinaryBBP : {
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CoefficientP : 1
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CoefficientQ : 0
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CoefficientD : 1691577
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Alternating : "true"
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PowerCoef : -30
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PowerShift : 20
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PolynomialP : [
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-6315035675 84097131500 -453365420000 1234908400000
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-1697020000000 939888000000
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]
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PolynomialQ : [
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992436543 -25204737600 287554050000 -1940682240000
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8580196800000 -25966899200000 54477440000000 -78233600000000
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73600000000000 -40960000000000 10240000000000
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]
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}}]
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[-1 {SeriesBinaryBBP : {
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CoefficientP : 1
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CoefficientQ : 0
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CoefficientD : 1691577
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Alternating : "true"
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PowerCoef : -30
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PowerShift : 11
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PolynomialP : [
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7669225 -238235500 2480260000 -2610800000
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-130540000000 731024000000
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]
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PolynomialQ : [
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243 -32400 1890000 -63360000
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1348800000 -19020800000 179840000000 -1126400000000
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4480000000000 -10240000000000 10240000000000
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]
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}}]
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[-1 {SeriesBinaryBBP : {
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CoefficientP : 1
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CoefficientQ : 0
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CoefficientD : 62651
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Alternating : "false"
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PowerCoef : -30
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PowerShift : 30
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PolynomialP : [
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-3140790664563 20282405042250 -52494734259000 68041163970000
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-44152140150000 11471908500000
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]
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PolynomialQ : [
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132016790288107 -1543824534103800 8112156076012500 -25222323419280000
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51387246182700000 -71683580685600000 69338113290000000 -45921751200000000
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19929037500000000 -5117580000000000 590490000000000
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]
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}}]
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[-1 {SeriesBinaryBBP : {
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CoefficientP : 1
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CoefficientQ : 0
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CoefficientD : 62651
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Alternating : "false"
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PowerCoef : -30
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PowerShift : 24
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PolynomialP : [
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-59233592601 505946027250 -1732944537000 2974852170000
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-2559118050000 882454500000
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]
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PolynomialQ : [
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3515706497843 -58776517301400 442037017372500 -1969339242960000
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5755757964300000 -11531303920800000 16037715690000000 -15289754400000000
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9562657500000000 -3542940000000000 590490000000000
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]
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}}]
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[-1 {SeriesBinaryBBP : {
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CoefficientP : 1
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CoefficientQ : 0
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CoefficientD : 62651
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Alternating : "false"
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PowerCoef : -30
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PowerShift : 18
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PolynomialP : [
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-7375554711 94918331250 -491625207000 1280539530000
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-1676663550000 882454500000
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]
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PolynomialQ : [
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59797108943 -1505381763600 17040816292500 -114223206240000
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502054710300000 -1512007819200000 3159784890000000 -4524465600000000
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4248247500000000 -2361960000000000 590490000000000
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]
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}}]
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[-1 {SeriesBinaryBBP : {
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CoefficientP : 1
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CoefficientQ : 0
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CoefficientD : 62651
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Alternating : "false"
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PowerCoef : -30
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PowerShift : 8
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PolynomialP : [
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-122534073 2685494250 -26604369000 221594130000
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-2088475650000 11471908500000
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]
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PolynomialQ : [
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16807 -2881200 208372500 -8255520000
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195104700000 -2823854400000 25084890000000 -136468800000000
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442867500000000 -787320000000000 590490000000000
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]
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}}]
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[-1 {SeriesBinaryBBP : {
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CoefficientP : 1
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CoefficientQ : 0
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CoefficientD : 2021
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Alternating : "true"
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PowerCoef : -30
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PowerShift : 11
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PolynomialP : [
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1602480483 1416834587700 -173879632692000 10436702858640000
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-313103081469600000 3757237383542400000
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]
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PolynomialQ : [
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714924299 -218112498000 26835230898000 -1677329596800000
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54447575198400000 -807728734080000000 3322224927360000000 -6244812288000000000
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6096166272000000000 -3023308800000000000 604661760000000000
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]
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}}]
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[-1 {SeriesBinaryBBP : {
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CoefficientP : 1
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CoefficientQ : 0
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CoefficientD : 2021
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Alternating : "true"
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PowerCoef : -30
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PowerShift : 14
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PolynomialP : [
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-1265122252467 54359524782900 -932194548108000 7990597829520000
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-34245622389600000 58706827228800000
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]
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PolynomialQ : [
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7028611650851 -341010807858000 6959010313458000 -77453783971200000
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510840122385600000 -2043590186880000000 4956939192960000000 -7292892672000000000
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6358186368000000000 -3023308800000000000 604661760000000000
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]
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}}]
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[1 {SeriesBinaryBBP : {
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CoefficientP : 1
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CoefficientQ : 0
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CoefficientD : 2021
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Alternating : "true"
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PowerCoef : -30
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PowerShift : 16
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PolynomialP : [
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-757391682951 20709906678900 -226057935996000 1233204529680000
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-3363383800800000 3669170140800000
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]
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PolynomialQ : [
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45492921326699 -1519244125938000 21813414268338000 -176133818044800000
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879587115422400000 -2821924241280000000 5874793349760000000 -7857243648000000000
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6499274112000000000 -3023308800000000000 604661760000000000
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]
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}}]
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[1 {SeriesBinaryBBP : {
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CoefficientP : 1
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CoefficientQ : 0
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CoefficientD : 2021
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Alternating : "true"
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PowerCoef : -30
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PowerShift : 17
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PolynomialP : [
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-435930939801 10094402819700 -93267080964000 430575762960000
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-993708064800000 917287286400000
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]
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PolynomialQ : [
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85154195684051 -2508634242738000 32070281620338000 -233299940515200000
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1065214272657600000 -3179682449280000000 6276221573760000000 -8099108352000000000
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6559740288000000000 -3023308800000000000 604661760000000000
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]
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}}]
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[-1 {SeriesBinaryBBP : {
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CoefficientP : 1
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CoefficientQ : 0
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CoefficientD : 2021
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Alternating : "true"
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PowerCoef : -30
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PowerShift : 19
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PolynomialP : [
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-103360140909 1838120123700 -13014363636000 45988022160000
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-81193687200000 57323894400000
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]
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PolynomialQ : [
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208730966852651 -5139750209778000 55763828883378000 -350559625507200000
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1412458131153600000 -3808194756480000000 6956018156160000000 -8502216192000000000
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6660517248000000000 -3023308800000000000 604661760000000000
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]
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}}]
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[1 {SeriesBinaryBBP : {
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CoefficientP : 1
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CoefficientQ : 0
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CoefficientD : 2021
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Alternating : "true"
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PowerCoef : -30
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PowerShift : 20
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PolynomialP : [
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-44596750959 712993446900 -4528972764000 14339857680000
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-22669567200000 14325724800000
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]
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PolynomialQ : [
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286871423439899 -6628607987058000 67894304401458000 -405659129788800000
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1564859339294400000 -4070886698880000000 7231699128960000000 -8663459328000000000
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6700828032000000000 -3023308800000000000 604661760000000000
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]
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}}]
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[-1 {SeriesBinaryBBP : {
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|
CoefficientP : 1
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|
CoefficientQ : 0
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CoefficientD : 2021
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Alternating : "true"
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PowerCoef : -30
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|
PowerShift : 22
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|
PolynomialP : [
|
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-6790571523 91652814900 -488178252000 1289707920000
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-1695362400000 888796800000
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]
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PolynomialQ : [
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|
446321492229251 -9440407591218000 89312246200818000 -497626895779200000
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1808198102289600000 -4477017847680000000 7649251666560000000 -8905324032000000000
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6761294208000000000 -3023308800000000000 604661760000000000
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]
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}}]
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|
[1 {SeriesBinaryBBP : {
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|
CoefficientP : 1
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|
CoefficientQ : 0
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|
CoefficientD : 2021
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|
Alternating : "true"
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PowerCoef : -30
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PowerShift : 25
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|
PolynomialP : [
|
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-111538323 1325810700 -6151788000 14016240000
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-15746400000 6998400000
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]
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PolynomialQ : [
|
|
587216781904499 -11757399415218000 105921221205618000 -565401902140800000
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1980373989470400000 -4755834103680000000 7930307410560000000 -9066567168000000000
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6801604992000000000 -3023308800000000000 604661760000000000
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]
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}}]
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|
[1 {SeriesBinaryBBP : {
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|
CoefficientP : 1
|
|
CoefficientQ : 0
|
|
CoefficientD : 1762059375
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|
Alternating : "false"
|
|
PowerCoef : -60
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|
PowerShift : 15
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|
PolynomialP : [
|
|
1792149404768 -44777700090000 501230286187920 -3309939127338120
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14279247817681230 -42049112536556325 85598494996790250 -118944360443668680
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107976311014313520 -57826406256512400 13874549065109280
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]
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PolynomialQ : [
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-32 1040 -15680 145480
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-928930 4324093 -15159195 40757940
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-84738960 136242405 -168022107 156100770
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-105763320 49338720 -14171760 1889568
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]
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}}]
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[1 {SeriesBinaryBBP : {
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|
CoefficientP : 1
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|
CoefficientQ : 0
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|
CoefficientD : 1691577
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|
Alternating : "false"
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PowerCoef : -60
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PowerShift : 31
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PolynomialP : [
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-127657600000 1063540000000 -3544450000000 5906562500000
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-4921601562500 1640400390625
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]
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PolynomialQ : [
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|
248832 -3628800 23760000 -91980000
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233137500 -404271875 485703125 -399218750
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214843750 -68359375 9765625
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]
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}}]
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|
[1 {SeriesBinaryBBP : {
|
|
CoefficientP : 1
|
|
CoefficientQ : 0
|
|
CoefficientD : 1691577
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|
Alternating : "false"
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PowerCoef : -60
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|
PowerShift : 7
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|
PolynomialP : [
|
|
-528900000 13171250000 -131456250000 656640625000
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-1640800781250 1640400390625
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]
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PolynomialQ : [
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32 -1200 20000 -195000
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1231250 -5259375 15390625 -30468750
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39062500 -29296875 9765625
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]
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}}]
|
|
[1 {SeriesBinaryBBP : {
|
|
CoefficientP : 3123927
|
|
CoefficientQ : 0
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|
CoefficientD : 195784375
|
|
Alternating : "false"
|
|
PowerCoef : -60
|
|
PowerShift : 10
|
|
PolynomialP : [
|
|
-366503876967 10995116284010 -131941395348120 791648372016720
|
|
-2374945116006960 2849934139197984
|
|
]
|
|
PolynomialQ : [
|
|
3125 -112500 1732500 -14904000
|
|
78602400 -263419776 565937280 -772623360
|
|
646652160 -302330880 60466176
|
|
]
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|
}}]
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|
[-1 {SeriesBinaryBBP : {
|
|
CoefficientP : 1
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|
CoefficientQ : 0
|
|
CoefficientD : 54567
|
|
Alternating : "false"
|
|
PowerCoef : -60
|
|
PowerShift : 42
|
|
PolynomialP : [
|
|
-219585960427 1568172432950 -4479828859000 6399017950000
|
|
-4570317350000 1305713900000
|
|
]
|
|
PolynomialQ : [
|
|
992436543 -12602368800 71888512500 -242585280000
|
|
536262300000 -811465600000 851210000000 -611200000000
|
|
287500000000 -80000000000 10000000000
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|
]
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|
}}]
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|
[-1 {SeriesBinaryBBP : {
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|
CoefficientP : 1
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|
CoefficientQ : 0
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|
CoefficientD : 54567
|
|
Alternating : "false"
|
|
PowerCoef : -60
|
|
PowerShift : 6
|
|
PolynomialP : [
|
|
-13828393 665604950 -13140001000 130826350000
|
|
-653175650000 1305713900000
|
|
]
|
|
PolynomialQ : [
|
|
243 -16200 472500 -7920000
|
|
84300000 -594400000 2810000000 -8800000000
|
|
17500000000 -20000000000 10000000000
|
|
]
|
|
}}]
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|
[1 {SeriesBinaryBBP : {
|
|
CoefficientP : 1
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|
CoefficientQ : 0
|
|
CoefficientD : 62651
|
|
Alternating : "false"
|
|
PowerCoef : -60
|
|
PowerShift : 51
|
|
PolynomialP : [
|
|
-543359279952 3116176682400 -7151344686000 8208874125000
|
|
-4713026006250 1082722190625
|
|
]
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|
PolynomialQ : [
|
|
199690286432 -2221828736400 11122707960000 -32991379785000
|
|
64208642793750 -85676839003125 79378816640625 -50422310156250
|
|
21015703125000 -5189853515625 576650390625
|
|
]
|
|
}}]
|
|
[1 {SeriesBinaryBBP : {
|
|
CoefficientP : 1
|
|
CoefficientQ : 0
|
|
CoefficientD : 62651
|
|
Alternating : "false"
|
|
PowerCoef : -60
|
|
PowerShift : 31
|
|
PolynomialP : [
|
|
-11270482573509 105626237883525 -396004202309250 742379438756250
|
|
-695893150715625 260936047940625
|
|
]
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|
PolynomialQ : [
|
|
5277319168 -85456588800 620991360000 -2666656080000
|
|
7493688675000 -14399283178125 19159999453125 -17432782031250
|
|
10379707031250 -3652119140625 576650390625
|
|
]
|
|
}}]
|
|
[1 {SeriesBinaryBBP : {
|
|
CoefficientP : 1
|
|
CoefficientQ : 0
|
|
CoefficientD : 62651
|
|
Alternating : "false"
|
|
PowerCoef : -60
|
|
PowerShift : 15
|
|
PolynomialP : [
|
|
-353190090681 6610986897525 -49533856148250 185647934306250
|
|
-347978420128125 260936047940625
|
|
]
|
|
PolynomialQ : [
|
|
17210368 -507091200 6667920000 -51517620000 258955987500
|
|
-884771353125 2080896328125 -3326632031250 3459902343750
|
|
-2114384765625 576650390625
|
|
]
|
|
}}]
|
|
[1 {SeriesBinaryBBP : {
|
|
CoefficientP : 1
|
|
CoefficientQ : 0
|
|
CoefficientD : 62651
|
|
Alternating : "false"
|
|
PowerCoef : -60
|
|
PowerShift : 3
|
|
PolynomialP : [
|
|
-4025808 201290400 -4529034000 56612925000
|
|
-382137243750 1082722190625
|
|
]
|
|
PolynomialQ : [
|
|
32 -3600 180000 -5265000
|
|
99731250 -1278028125 11219765625 -66635156250
|
|
256289062500 -576650390625 576650390625
|
|
]
|
|
}}]
|
|
[-1 {SeriesBinaryBBP : {
|
|
CoefficientP : 1
|
|
CoefficientQ : 0
|
|
CoefficientD : 62651
|
|
Alternating : "false"
|
|
PowerCoef : -60
|
|
PowerShift : 49
|
|
PolynomialP : [
|
|
-368765982320229 2404608706441350 -6272091938853000 8180161548750000
|
|
-5334459723450000 1391509586700000
|
|
]
|
|
PolynomialQ : [
|
|
132016790288107 -1543824534103800 8112156076012500 -25222323419280000
|
|
51387246182700000 -71683580685600000 69338113290000000 -45921751200000000
|
|
19929037500000000 -5117580000000000 590490000000000
|
|
]
|
|
}}]
|
|
[-1 {SeriesBinaryBBP : {
|
|
CoefficientP : 1
|
|
CoefficientQ : 0
|
|
CoefficientD : 62651
|
|
Alternating : "false"
|
|
PowerCoef : -60
|
|
PowerShift : 37
|
|
PolynomialP : [
|
|
-352133896347 3074919733350 -10751150331000 18812343150000
|
|
-16472593350000 5773898700000
|
|
]
|
|
PolynomialQ : [
|
|
3515706497843 -58776517301400 442037017372500 -1969339242960000
|
|
5755757964300000 -11531303920800000 16037715690000000 -15289754400000000
|
|
9562657500000000 -3542940000000000 590490000000000
|
|
]
|
|
}}]
|
|
[-1 {SeriesBinaryBBP : {
|
|
CoefficientP : 1
|
|
CoefficientQ : 0
|
|
CoefficientD : 62651
|
|
Alternating : "false"
|
|
PowerCoef : -60
|
|
PowerShift : 25
|
|
PolynomialP : [
|
|
-41205719493 551008981350 -2955254949000 7943827950000
|
|
-10698694650000 5773898700000
|
|
]
|
|
PolynomialQ : [
|
|
59797108943 -1505381763600 17040816292500 -114223206240000
|
|
502054710300000 -1512007819200000 3159784890000000 -4524465600000000
|
|
4248247500000000 -2361960000000000 590490000000000
|
|
]
|
|
}}]
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|
[-1 {SeriesBinaryBBP : {
|
|
CoefficientP : 1
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|
CoefficientQ : 0
|
|
CoefficientD : 62651
|
|
Alternating : "false"
|
|
PowerCoef : -60
|
|
PowerShift : 5
|
|
PolynomialP : [
|
|
-292161231 13621285350 -558395127000 15642359550000
|
|
-232257905550000 1391509586700000
|
|
]
|
|
PolynomialQ : [
|
|
16807 -2881200 208372500 -8255520000
|
|
195104700000 -2823854400000 25084890000000 -136468800000000
|
|
442867500000000 -787320000000000 590490000000000
|
|
]
|
|
}}]
|
|
]
|
|
}
|
|
}
|