From c5d13ac48a5fc412b99717e23a39cf22976daec3 Mon Sep 17 00:00:00 2001 From: opelly27 <35671196+opelly27@users.noreply.github.com> Date: Thu, 11 Nov 2021 21:34:46 -0800 Subject: [PATCH] Add files via upload --- Custom Formulas/#README.txt | 363 ++++++++++ Custom Formulas/2^(1d5) - Native.cfg | 28 + Custom Formulas/2^(1d5) - Series.cfg | 32 + Custom Formulas/2^(1d7) - Native.cfg | 28 + Custom Formulas/2^(1d7) - Series.cfg | 32 + Custom Formulas/ArcCosh(e).cfg | 38 + Custom Formulas/ArcCoth(GoldenRatio).cfg | 37 + Custom Formulas/ArcSinh(e).cfg | 38 + Custom Formulas/ArcTanh(Pi^-1).cfg | 43 ++ Custom Formulas/ArcTanh(e^-1).cfg | 37 + Custom Formulas/BesselI(0,1) - Series.cfg | 31 + Custom Formulas/BesselJ(0,1) - Series.cfg | 31 + Custom Formulas/Catalan - Guillera (2008).cfg | 39 ++ Custom Formulas/Catalan - Guillera (2019).cfg | 33 + .../Catalan - Huvent (combined).cfg | 67 ++ .../Catalan - Huvent (optimized).cfg | 134 ++++ .../Catalan - Huvent (original).cfg | 95 +++ Custom Formulas/Catalan - LogPi.cfg | 49 ++ Custom Formulas/Catalan - Lupas.cfg | 38 + .../Catalan - Pilehrood (long).cfg | 39 ++ .../Catalan - Pilehrood (short).cfg | 39 ++ .../Catalan - Ramanujan (unoptimized).cfg | 48 ++ Custom Formulas/Catalan - Ramanujan.cfg | 58 ++ Custom Formulas/Cbrt(2) - Native.cfg | 28 + Custom Formulas/Cbrt(2) - Series.cfg | 32 + Custom Formulas/Cbrt(2) - Series2.cfg | 32 + Custom Formulas/Cbrt(3) - Native.cfg | 28 + Custom Formulas/Cbrt(3) - Series.cfg | 32 + .../Cos(1) - Half Angle Formula.cfg | 37 + Custom Formulas/Cos(1) - Series.cfg | 31 + Custom Formulas/Erf(1) - Series.cfg | 35 + Custom Formulas/Gamma(1d3) - AGM-Pi.cfg | 47 ++ Custom Formulas/Gamma(1d3) - Series-Pi.cfg | 45 ++ Custom Formulas/Gamma(1d4) - AGM-Pi.cfg | 44 ++ Custom Formulas/Gamma(1d4) - Lemniscate.cfg | 39 ++ Custom Formulas/Gamma(1d4) - Series-Pi.cfg | 49 ++ Custom Formulas/Gamma(1d6) - AGM-Pi.cfg | 51 ++ Custom Formulas/Gamma(1d6) - Series-Pi.cfg | 44 ++ Custom Formulas/Gamma(2d3) - AGM-Pi.cfg | 40 ++ Custom Formulas/Gamma(2d3) - Series-Pi.cfg | 44 ++ Custom Formulas/Gamma(3d4) - AGM-Pi.cfg | 39 ++ Custom Formulas/Gamma(3d4) - Lemniscate.cfg | 42 ++ Custom Formulas/Gamma(3d4) - Series-Pi.cfg | 45 ++ Custom Formulas/Gamma(5d6) - AGM-Pi.cfg | 51 ++ Custom Formulas/Gamma(5d6) - Series-Pi.cfg | 43 ++ Custom Formulas/Gauss - AGM.cfg | 30 + Custom Formulas/Gauss - Lemniscate.cfg | 33 + Custom Formulas/Gauss - Series.cfg | 43 ++ .../GoldenRatio - Native Invsqrt.cfg | 29 + Custom Formulas/GoldenRatio - Series.cfg | 30 + Custom Formulas/Khinchin-Levy Constant.cfg | 35 + Custom Formulas/Lemniscate - AGM-Pi.cfg | 30 + Custom Formulas/Lemniscate - Gauss.cfg | 32 + Custom Formulas/Lemniscate - Sebah.cfg | 32 + Custom Formulas/Lemniscate - Series-Pi.cfg | 40 ++ Custom Formulas/Log(2) - BBP.cfg | 61 ++ Custom Formulas/Log(2) - Lupas.cfg | 35 + Custom Formulas/Log(2) - Machin (3 terms).cfg | 29 + Custom Formulas/Log(2) - Machin (4 terms).cfg | 30 + Custom Formulas/Log(Pi) (unoptimized).cfg | 27 + Custom Formulas/Log(Pi).cfg | 37 + Custom Formulas/Log10(2).cfg | 36 + Custom Formulas/Pi - BBP (Original).cfg | 71 ++ Custom Formulas/Pi - Bellard.cfg | 100 +++ Custom Formulas/Pi - Brown.cfg | 37 + Custom Formulas/Pi - Chudnovsky.cfg | 38 + Custom Formulas/Pi - Hwang (1997).cfg | 79 +++ Custom Formulas/Pi - Machin.cfg | 46 ++ Custom Formulas/Pi - Ramanujan.cfg | 38 + Custom Formulas/Pi - Sharp.cfg | 38 + Custom Formulas/Pi - Stormer.cfg | 62 ++ Custom Formulas/Pi - Takano.cfg | 62 ++ Custom Formulas/Pi^-1 - Native.cfg | 25 + .../Sin(1) - Half Angle Formula.cfg | 40 ++ Custom Formulas/Sin(1) - Series.cfg | 31 + Custom Formulas/Sqrt(2) - Native Invsqrt.cfg | 26 + Custom Formulas/Sqrt(2) - Series.cfg | 30 + Custom Formulas/Sqrt(Pi).cfg | 25 + ...ersal Parabolic Constant (unoptimized).cfg | 35 + .../Universal Parabolic Constant.cfg | 45 ++ Custom Formulas/Unnormalized Fresnel C(1).cfg | 34 + Custom Formulas/Unnormalized Fresnel S(1).cfg | 34 + Custom Formulas/Zeta(2) - Chudnovsky.cfg | 43 ++ Custom Formulas/Zeta(2) - Direct.cfg | 34 + .../Zeta(3) - Amdeberhan-Zeilberger.cfg | 38 + Custom Formulas/Zeta(3) - Amdeberhan.cfg | 36 + Custom Formulas/Zeta(3) - Hjortnaes.cfg | 36 + Custom Formulas/Zeta(3) - Mohammed.cfg | 38 + Custom Formulas/Zeta(3) - Wedeniwski.cfg | 40 ++ Custom Formulas/Zeta(4) - Chudnovsky.cfg | 43 ++ Custom Formulas/Zeta(4) - Direct.cfg | 34 + Custom Formulas/Zeta(5) - BBP-Kruse.cfg | 118 ++++ .../Zeta(5) - Broadhurst (Huvent 2006).cfg | 305 ++++++++ .../Zeta(5) - Broadhurst (optimized).cfg | 655 ++++++++++++++++++ Custom Formulas/Zeta(5) - Broadhurst.cfg | 258 +++++++ Custom Formulas/e - exp(-1).cfg | 30 + Custom Formulas/e - exp(0.25)^4.cfg | 32 + Custom Formulas/e - exp(0.5)^2.cfg | 32 + Custom Formulas/e - exp(1).cfg | 29 + Custom Formulas/e^-1 - Native.cfg | 25 + 100 files changed, 5566 insertions(+) create mode 100644 Custom Formulas/#README.txt create mode 100644 Custom Formulas/2^(1d5) - Native.cfg create mode 100644 Custom Formulas/2^(1d5) - Series.cfg create mode 100644 Custom Formulas/2^(1d7) - Native.cfg create mode 100644 Custom Formulas/2^(1d7) - Series.cfg create mode 100644 Custom Formulas/ArcCosh(e).cfg create mode 100644 Custom Formulas/ArcCoth(GoldenRatio).cfg create mode 100644 Custom Formulas/ArcSinh(e).cfg create mode 100644 Custom Formulas/ArcTanh(Pi^-1).cfg create mode 100644 Custom Formulas/ArcTanh(e^-1).cfg create mode 100644 Custom Formulas/BesselI(0,1) - Series.cfg create mode 100644 Custom Formulas/BesselJ(0,1) - Series.cfg create mode 100644 Custom Formulas/Catalan - Guillera (2008).cfg create mode 100644 Custom Formulas/Catalan - Guillera (2019).cfg create mode 100644 Custom Formulas/Catalan - Huvent (combined).cfg create mode 100644 Custom Formulas/Catalan - Huvent (optimized).cfg create mode 100644 Custom Formulas/Catalan - Huvent (original).cfg create mode 100644 Custom Formulas/Catalan - LogPi.cfg create mode 100644 Custom Formulas/Catalan - Lupas.cfg create mode 100644 Custom Formulas/Catalan - Pilehrood (long).cfg create mode 100644 Custom Formulas/Catalan - Pilehrood (short).cfg create mode 100644 Custom Formulas/Catalan - Ramanujan (unoptimized).cfg create mode 100644 Custom Formulas/Catalan - Ramanujan.cfg create mode 100644 Custom Formulas/Cbrt(2) - Native.cfg create mode 100644 Custom Formulas/Cbrt(2) - Series.cfg create mode 100644 Custom Formulas/Cbrt(2) - Series2.cfg create mode 100644 Custom Formulas/Cbrt(3) - Native.cfg create mode 100644 Custom Formulas/Cbrt(3) - Series.cfg create mode 100644 Custom Formulas/Cos(1) - Half Angle Formula.cfg create mode 100644 Custom Formulas/Cos(1) - Series.cfg create mode 100644 Custom Formulas/Erf(1) - Series.cfg create mode 100644 Custom Formulas/Gamma(1d3) - AGM-Pi.cfg create mode 100644 Custom Formulas/Gamma(1d3) - Series-Pi.cfg create mode 100644 Custom Formulas/Gamma(1d4) - AGM-Pi.cfg create mode 100644 Custom Formulas/Gamma(1d4) - Lemniscate.cfg create mode 100644 Custom Formulas/Gamma(1d4) - Series-Pi.cfg create mode 100644 Custom Formulas/Gamma(1d6) - AGM-Pi.cfg create mode 100644 Custom Formulas/Gamma(1d6) - Series-Pi.cfg create mode 100644 Custom Formulas/Gamma(2d3) - AGM-Pi.cfg create mode 100644 Custom Formulas/Gamma(2d3) - Series-Pi.cfg create mode 100644 Custom Formulas/Gamma(3d4) - AGM-Pi.cfg create mode 100644 Custom Formulas/Gamma(3d4) - Lemniscate.cfg create mode 100644 Custom Formulas/Gamma(3d4) - Series-Pi.cfg create mode 100644 Custom Formulas/Gamma(5d6) - AGM-Pi.cfg create mode 100644 Custom Formulas/Gamma(5d6) - Series-Pi.cfg create mode 100644 Custom Formulas/Gauss - AGM.cfg create mode 100644 Custom Formulas/Gauss - Lemniscate.cfg create mode 100644 Custom Formulas/Gauss - Series.cfg create mode 100644 Custom Formulas/GoldenRatio - Native Invsqrt.cfg create mode 100644 Custom Formulas/GoldenRatio - Series.cfg create mode 100644 Custom Formulas/Khinchin-Levy Constant.cfg create mode 100644 Custom Formulas/Lemniscate - AGM-Pi.cfg create mode 100644 Custom Formulas/Lemniscate - Gauss.cfg create mode 100644 Custom Formulas/Lemniscate - Sebah.cfg create mode 100644 Custom Formulas/Lemniscate - Series-Pi.cfg create mode 100644 Custom Formulas/Log(2) - BBP.cfg create mode 100644 Custom Formulas/Log(2) - Lupas.cfg create mode 100644 Custom Formulas/Log(2) - Machin (3 terms).cfg create mode 100644 Custom Formulas/Log(2) - Machin (4 terms).cfg create mode 100644 Custom Formulas/Log(Pi) (unoptimized).cfg create mode 100644 Custom Formulas/Log(Pi).cfg create mode 100644 Custom Formulas/Log10(2).cfg create mode 100644 Custom Formulas/Pi - BBP (Original).cfg create mode 100644 Custom Formulas/Pi - Bellard.cfg create mode 100644 Custom Formulas/Pi - Brown.cfg create mode 100644 Custom Formulas/Pi - Chudnovsky.cfg create mode 100644 Custom Formulas/Pi - Hwang (1997).cfg create mode 100644 Custom Formulas/Pi - Machin.cfg create mode 100644 Custom Formulas/Pi - Ramanujan.cfg create mode 100644 Custom Formulas/Pi - Sharp.cfg create mode 100644 Custom Formulas/Pi - Stormer.cfg create mode 100644 Custom Formulas/Pi - Takano.cfg create mode 100644 Custom Formulas/Pi^-1 - Native.cfg create mode 100644 Custom Formulas/Sin(1) - Half Angle Formula.cfg create mode 100644 Custom Formulas/Sin(1) - Series.cfg create mode 100644 Custom Formulas/Sqrt(2) - Native Invsqrt.cfg create mode 100644 Custom Formulas/Sqrt(2) - Series.cfg create mode 100644 Custom Formulas/Sqrt(Pi).cfg create mode 100644 Custom Formulas/Universal Parabolic Constant (unoptimized).cfg create mode 100644 Custom Formulas/Universal Parabolic Constant.cfg create mode 100644 Custom Formulas/Unnormalized Fresnel C(1).cfg create mode 100644 Custom Formulas/Unnormalized Fresnel S(1).cfg create mode 100644 Custom Formulas/Zeta(2) - Chudnovsky.cfg create mode 100644 Custom Formulas/Zeta(2) - Direct.cfg create mode 100644 Custom Formulas/Zeta(3) - Amdeberhan-Zeilberger.cfg create mode 100644 Custom Formulas/Zeta(3) - Amdeberhan.cfg create mode 100644 Custom Formulas/Zeta(3) - Hjortnaes.cfg create mode 100644 Custom Formulas/Zeta(3) - Mohammed.cfg create mode 100644 Custom Formulas/Zeta(3) - Wedeniwski.cfg create mode 100644 Custom Formulas/Zeta(4) - Chudnovsky.cfg create mode 100644 Custom Formulas/Zeta(4) - Direct.cfg create mode 100644 Custom Formulas/Zeta(5) - BBP-Kruse.cfg create mode 100644 Custom Formulas/Zeta(5) - Broadhurst (Huvent 2006).cfg create mode 100644 Custom Formulas/Zeta(5) - Broadhurst (optimized).cfg create mode 100644 Custom Formulas/Zeta(5) - Broadhurst.cfg create mode 100644 Custom Formulas/e - exp(-1).cfg create mode 100644 Custom Formulas/e - exp(0.25)^4.cfg create mode 100644 Custom Formulas/e - exp(0.5)^2.cfg create mode 100644 Custom Formulas/e - exp(1).cfg create mode 100644 Custom Formulas/e^-1 - Native.cfg diff --git a/Custom Formulas/#README.txt b/Custom Formulas/#README.txt new file mode 100644 index 0000000..6458857 --- /dev/null +++ b/Custom Formulas/#README.txt @@ -0,0 +1,363 @@ +This folder contains a set of custom formulas you can play with. + +Formulas can be loaded directly from the Custom Compute menu or entered from the +command line as "custom:filename". + + y-cruncher custom custom:"constant - algorithm" + + +More formulas can be found here on the official GitHub repo: + + https://github.com/Mysticial/y-cruncher-Formulas + + +Documentation for writing custom formulas can be found here: + + http://www.numberworld.org/y-cruncher/guides/custom_formulas.html + + +-------------------------------------------------------------------------------- + +The rest of this file documents which pairs of formulas are approved for +compute/verify pairs for the purpose of setting a world record or simply having +verified digits. + +Legend: + + "Fastest Pair" indicates the fastest approved pair for formulas. + + "Dependent Set" indicates a set of similar formula. You cannot do a + compute/verify pair with 2 formulas in the same dependent set. + + +The term "same relative dependency" will be used several times here. This means +that two formulas are dependent on the same constant in such a way that if the +constant were changed, both formulas will evaluate to the same (incorrect) value. + +Formula pairs that fall into these category will use different algorithms for +that constant and are rearranged in a way to avoid any computational dependencies. + + +-------------------------------------------------------------------------------- + +2^(1/5): + +Fastest Pair: + 2^(1d5) - Native.cfg + 2^(1d5) - Series.cfg + +The series formula is very slow. Instead, just compute: 200000^(1/5). +The digits will be the same, but shifted over by 1. + +-------------------------------------------------------------------------------- + +2^(1/7): + +Fastest Pair: + 2^(1d7) - Native.cfg + 2^(1d7) - Series.cfg + +The series formula is very slow. Instead, just compute: 20000000^(1/7). +The digits will be the same, but shifted over by 1. + + +-------------------------------------------------------------------------------- + +Catalan's Constant: + +Fastest Pair: + Catalan - Pilehrood (short).cfg + Catalan - Guillera (2019).cfg + +This constant is supported natively in y-cruncher. So it's faster to use the +built-in implementations instead. + +Dependent Set: + Catalan - Huvent (combined).cfg + Catalan - Huvent (optimized).cfg + Catalan - Huvent (original).cfg + +Dependent Set: + Catalan - Ramanujan (unoptimized).cfg + Catalan - Ramanujan.cfg + + +-------------------------------------------------------------------------------- + +Cbrt(2): + +Fastest Pair: + - Cbrt(2) - Native.cfg + - Cbrt(2) - Series2.cfg + +The series formula is very slow. Instead, just compute: 2000^(1/3). +The digits will be the same, but shifted over by 1. + + +-------------------------------------------------------------------------------- + +Cbrt(3): + +Fastest Pair: + - Cbrt(3) - Native.cfg + - Cbrt(3) - Series.cfg + +The series formula is very slow. Instead, just compute: 3000^(1/3). +The digits will be the same, but shifted over by 1. + + +-------------------------------------------------------------------------------- + +Cos(1): + +Fastest Pair: + Cos(1) - Series.cfg + Cos(1) - Half Angle Formula.cfg + + +-------------------------------------------------------------------------------- + +e: + +Fastest Pair: + e - exp(1).cfg + e - exp(-1).cfg + +This constant is supported natively in y-cruncher. So it's faster to use the +built-in implementations instead. + +Dependent Set: + e^-1 - Native.cfg + e - exp(-1).cfg + + +-------------------------------------------------------------------------------- + +Gamma(1/3): + +Fastest Pair: + Gamma(1d3) - Series-Pi + Gamma(1d3) - AGM-Pi + +These two formulas have the same relative dependency on Pi. Therefore Pi is set +to use two different algorithms. + + +-------------------------------------------------------------------------------- + +Gamma(1/4): + +Fastest Pair: + Gamma(1d4) - AGM-Pi.cfg + Gamma(1d4) - Series-Pi.cfg + +These two formulas have the same relative dependency on Pi. Therefore Pi is set +to use two different algorithms. + + +-------------------------------------------------------------------------------- + +Gamma(1/6): + +Fastest Pair: + Gamma(1d6) - Series-Pi.cfg + Gamma(1d6) - AGM-Pi.cfg + +These two formulas have the same relative dependency on Pi. Therefore Pi is set +to use two different algorithms. + + +-------------------------------------------------------------------------------- + +Gamma(2/3): + +Fastest Pair: + Gamma(2d3) - Series-Pi + Gamma(2d3) - AGM-Pi + +These two formulas have the same relative dependency on Pi. Therefore Pi is set +to use two different algorithms. + + +-------------------------------------------------------------------------------- + +Gamma(3/4): + +Fastest Pair: + Gamma(3d4) - AGM-Pi.cfg + Gamma(3d4) - Series-Pi.cfg + +These two formulas have the same relative dependency on Pi. Therefore Pi is set +to use two different algorithms. + + +-------------------------------------------------------------------------------- + +Gamma(5/6): + +Fastest Pair: + Gamma(2d3) - Series-Pi.cfg + Gamma(2d3) - AGM-Pi.cfg + +These two formulas have the same relative dependency on Pi. Therefore Pi is set +to use two different algorithms. + + +-------------------------------------------------------------------------------- + +Gauss's Constant: + +Fastest Pair: + Gauss - AGM.cfg + Gauss - Series.cfg + + +-------------------------------------------------------------------------------- + +Golden Ratio: + +Fastest Pair: + GoldenRatio - Native Invsqrt.cfg + GoldenRatio - Series.cfg + +Note that you really don't want to use the series formula here. The fastest way +to compute+verify is to run the built-in function for this constant and +sqrt(125). The digits will be the same except for the 2nd digit and all the +digits will be shifted over by one. + + +-------------------------------------------------------------------------------- + +Lemniscate: + +Fastest Pair: + Lemniscate - AGM-Pi.cfg + Lemniscate - Series-Pi.cfg + +This is a built-in constant. But the 2nd formula here (Series-Pi) is actually +faster than both the built-in ArcSinlemn formulas. + +These two formulas have the same relative dependency on Pi. Therefore Pi is set +to use two different algorithms. + + +-------------------------------------------------------------------------------- + +Log(2): + +Fastest Pair: + Log(2) - Machin (3 terms).cfg + Log(2) - Machin (4 terms).cfg + +This constant is supported natively in y-cruncher. So it's faster to use the +built-in implementations instead. + + +-------------------------------------------------------------------------------- + +Log(Pi): + +Fastest Pair: none + +Dependent Set: + Log(Pi) (unoptimized).cfg + Log(Pi).cfg + + +-------------------------------------------------------------------------------- + +Pi: + +Fastest Pair: + Pi - Chudnovsky.cfg + Pi - Ramanujan.cfg + +This constant is supported natively in y-cruncher. So it's faster to use the +built-in implementations instead. + + +-------------------------------------------------------------------------------- + +Sin(1): + +Fastest Pair: + Sin(1) - Half Angle Formula.cfg + Sin(1) - Series.cfg + + +-------------------------------------------------------------------------------- + +Sqrt(2): + +Fastest Pair: + Sqrt(2) - Native Invsqrt.cfg + Sqrt(2) - Series.cfg + +The series formula is very slow. Instead, just compute: Sqrt(200). +The digits will be the same, but shifted over by 1. + + +-------------------------------------------------------------------------------- + +Universal Parabolic Constant: + +Fastest Pair: none + +Dependent Set: + Universal Parabolic Constant (unoptimized).cfg + Universal Parabolic Constant.cfg + + +-------------------------------------------------------------------------------- + +Zeta(2): + +Fastest Pair: + Zeta(2) - Chudnovsky.cfg + Zeta(2) - Direct.cfg + +These two formulas have the same relative dependency on Pi. Therefore Pi is set +to use two different algorithms. + + +-------------------------------------------------------------------------------- + +Zeta(3): + +Fastest Pair: + Zeta(3) - Wedeniwski.cfg + Zeta(3) - Amdeberhan-Zeilberger.cfg + +This constant is supported natively in y-cruncher. So it's faster to use the +built-in implementations instead. + + +-------------------------------------------------------------------------------- + +Zeta(4): + +Fastest Pair: + Zeta(4) - Chudnovsky.cfg + Zeta(4) - Direct.cfg + +These two formulas have the same relative dependency on Pi. Therefore Pi is set +to use two different algorithms. + + +-------------------------------------------------------------------------------- + +Zeta(5): + +Fastest Pair: + Zeta(5) - BBP-Kruse.cfg + Zeta(5) - Broadhurst (optimized).cfg + +Dependent Set: + Zeta(5) - Broadhurst.cfg + Zeta(5) - Broadhurst (Huvent 2006).cfg + Zeta(5) - Broadhurst (optimized).cfg + + + + + diff --git a/Custom Formulas/2^(1d5) - Native.cfg b/Custom Formulas/2^(1d5) - Native.cfg new file mode 100644 index 0000000..3d75935 --- /dev/null +++ b/Custom Formulas/2^(1d5) - Native.cfg @@ -0,0 +1,28 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: February 22, 2019 +// +// 5th root of 2. +// +// Value: 1.14869835499703500679862694677792758944385088909779... +// + +{ + NameShort : "2^(⅕)" + NameLong : "5th root of 2" + AlgorithmShort : "Native" + AlgorithmLong : "Native InvNthRoot" + Formula : { + Shift : [ + {InvNthRoot : [5 16]} + 1 + ] + } +} diff --git a/Custom Formulas/2^(1d5) - Series.cfg b/Custom Formulas/2^(1d5) - Series.cfg new file mode 100644 index 0000000..cd4390f --- /dev/null +++ b/Custom Formulas/2^(1d5) - Series.cfg @@ -0,0 +1,32 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: November 11, 2018 +// +// 5th root of 2. +// +// Value: 1.14869835499703500679862694677792758944385088909779... +// + +{ + NameShort : "2^(⅕)" + NameLong : "5th root of 2" + AlgorithmShort : "Series" + AlgorithmLong : "Hypergeometric Series" + Formula : { + SeriesHypergeometric : { + CoefficientP : 1 + CoefficientQ : 1 + CoefficientD : 1 + PolynomialP : [4 -5] + PolynomialQ : [0 -10] + PolynomialR : [4 -5] + } + } +} diff --git a/Custom Formulas/2^(1d7) - Native.cfg b/Custom Formulas/2^(1d7) - Native.cfg new file mode 100644 index 0000000..f808517 --- /dev/null +++ b/Custom Formulas/2^(1d7) - Native.cfg @@ -0,0 +1,28 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: February 22, 2019 +// +// 7th root of 2. +// +// Value: 1.10408951367381233764950538762334472132532660078012... +// + +{ + NameShort : "2^(⅐)" + NameLong : "7th root of 2" + AlgorithmShort : "Native" + AlgorithmLong : "Native InvNthRoot" + Formula : { + Shift : [ + {InvNthRoot : [7 64]} + 1 + ] + } +} diff --git a/Custom Formulas/2^(1d7) - Series.cfg b/Custom Formulas/2^(1d7) - Series.cfg new file mode 100644 index 0000000..51e030e --- /dev/null +++ b/Custom Formulas/2^(1d7) - Series.cfg @@ -0,0 +1,32 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: November 11, 2018 +// +// 7th root of 2. +// +// Value: 1.10408951367381233764950538762334472132532660078012... +// + +{ + NameShort : "2^(⅐)" + NameLong : "7th root of 2" + AlgorithmShort : "Series" + AlgorithmLong : "Hypergeometric Series" + Formula : { + SeriesHypergeometric : { + CoefficientP : 1 + CoefficientQ : 1 + CoefficientD : 1 + PolynomialP : [6 -7] + PolynomialQ : [0 -14] + PolynomialR : [6 -7] + } + } +} diff --git a/Custom Formulas/ArcCosh(e).cfg b/Custom Formulas/ArcCosh(e).cfg new file mode 100644 index 0000000..d96eef8 --- /dev/null +++ b/Custom Formulas/ArcCosh(e).cfg @@ -0,0 +1,38 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: November 30, 2018 +// +// Value: 1.65745445415307727259382874228053473915839276203367... +// + +{ + NameShort : "ArcCosh(e)" + NameLong : "ArcCosh(e)" + AlgorithmShort : "Log-Formula" + AlgorithmLong : "Log Expansion of ArcCosh(x)" + Formula : { + Log : {Scope : { + Locals : [ + {arg : {E : {}}} + ] + Formula : { + LinearCombination : [ + [1 "arg"] + [1 {Sqrt : { + LinearCombination : [ + [1 {Power : ["arg" 2]}] + [1 -1] + ] + }}] + ] + } + }} + } +} diff --git a/Custom Formulas/ArcCoth(GoldenRatio).cfg b/Custom Formulas/ArcCoth(GoldenRatio).cfg new file mode 100644 index 0000000..449507c --- /dev/null +++ b/Custom Formulas/ArcCoth(GoldenRatio).cfg @@ -0,0 +1,37 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: November 30, 2018 +// +// Value: 0.72181773758940517124663837013655263470277650157849... +// + +{ + NameShort : "ArcCoth(GoldenRatio)" + NameLong : "ArcCoth(GoldenRatio)" + AlgorithmShort : "Log-Formula" + AlgorithmLong : "Log Expansion of ArcCoth(x)" + Formula : { + Shift : [ + {Log : {Scope : { + Locals : [ + {arg : {GoldenRatio : {}}} + ] + Formula : { + Divide : [ + {LinearCombination : [[1 "arg"][1 1]]} + {LinearCombination : [[1 "arg"][1 -1]]} + ] + } + }}} + -1 + ] + } + +} diff --git a/Custom Formulas/ArcSinh(e).cfg b/Custom Formulas/ArcSinh(e).cfg new file mode 100644 index 0000000..ab49fbc --- /dev/null +++ b/Custom Formulas/ArcSinh(e).cfg @@ -0,0 +1,38 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: November 30, 2018 +// +// Value: 1.72538255885231509394509797040488875627455727467293... +// + +{ + NameShort : "ArcSinh(e)" + NameLong : "ArcSinh(e)" + AlgorithmShort : "Log-Formula" + AlgorithmLong : "Log Expansion of ArcSinh(x)" + Formula : { + Log : {Scope : { + Locals : [ + {arg : {E : {}}} + ] + Formula : { + LinearCombination : [ + [1 "arg"] + [1 {Sqrt : { + LinearCombination : [ + [1 {Power : ["arg" 2]}] + [1 1] + ] + }}] + ] + } + }} + } +} diff --git a/Custom Formulas/ArcTanh(Pi^-1).cfg b/Custom Formulas/ArcTanh(Pi^-1).cfg new file mode 100644 index 0000000..279915e --- /dev/null +++ b/Custom Formulas/ArcTanh(Pi^-1).cfg @@ -0,0 +1,43 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: November 30, 2018 +// +// Value: 0.32976531495669910761786341755521860427013739114069... +// + +{ + NameShort : "ArcTanh(Pi^-1)" + NameLong : "ArcTanh(Pi^-1)" + AlgorithmShort : "Log-Formula" + AlgorithmLong : "Log Expansion of ArcTanh(x)" + Formula : { + Shift : [ + {Scope : { + Locals : [ + {pi : {Pi : {}}} + {log2 : {Log : 2}} + ] + Formula : { + Log-AGM : { + Pi : "pi" + Log2 : "log2" + Argument : { + Divide : [ + {LinearCombination : [[1 "pi"][1 1]]} + {LinearCombination : [[1 "pi"][1 -1]]} + ] + } + } + } + }} + -1 + ] + } +} diff --git a/Custom Formulas/ArcTanh(e^-1).cfg b/Custom Formulas/ArcTanh(e^-1).cfg new file mode 100644 index 0000000..77f1787 --- /dev/null +++ b/Custom Formulas/ArcTanh(e^-1).cfg @@ -0,0 +1,37 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: November 30, 2018 +// +// Value: 0.38596841645265236253531957001759267189612899618127... +// + +{ + NameShort : "ArcTanh(e^-1)" + NameLong : "ArcTanh(e^-1)" + AlgorithmShort : "Log-Formula" + AlgorithmLong : "Log Expansion of ArcTanh(x)" + Formula : { + Shift : [ + {Log : {Scope : { + Locals : [ + {arg : {E : {Power : -1}}} + ] + Formula : { + Divide : [ + {LinearCombination : [[1 "arg"][1 1]]} + {LinearCombination : [[-1 "arg"][1 1]]} + ] + } + }}} + -1 + ] + } + +} diff --git a/Custom Formulas/BesselI(0,1) - Series.cfg b/Custom Formulas/BesselI(0,1) - Series.cfg new file mode 100644 index 0000000..3556f5e --- /dev/null +++ b/Custom Formulas/BesselI(0,1) - Series.cfg @@ -0,0 +1,31 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: October 21, 2018 +// +// Value: 1.26606587775200833559824462521471753760767031135496... +// +// Formula: Taylor Series of BesselI(0,x) +// + +{ + NameShort : "BesselI(0,1)" + NameLong : "BesselI(0,1)" + AlgorithmShort : "Series" + AlgorithmLong : "Taylor Series of BesselI(0,x)" + Formula : { + SeriesHyperdescent : { + CoefficientP : 1 + CoefficientQ : 1 + CoefficientD : 1 + PolynomialP : [1] + PolynomialQ : [0 0 4] + } + } +} diff --git a/Custom Formulas/BesselJ(0,1) - Series.cfg b/Custom Formulas/BesselJ(0,1) - Series.cfg new file mode 100644 index 0000000..b03a865 --- /dev/null +++ b/Custom Formulas/BesselJ(0,1) - Series.cfg @@ -0,0 +1,31 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: October 21, 2018 +// +// Value: 0.76519768655796655144971752610266322090927428975532... +// +// Formula: Taylor Series of BesselJ(0,x) +// + +{ + NameShort : "BesselJ(0,1)" + NameLong : "BesselJ(0,1)" + AlgorithmShort : "Series" + AlgorithmLong : "Taylor Series of BesselJ(0,x)" + Formula : { + SeriesHyperdescent : { + CoefficientP : 1 + CoefficientQ : 1 + CoefficientD : 1 + PolynomialP : [1] + PolynomialQ : [0 0 -4] + } + } +} diff --git a/Custom Formulas/Catalan - Guillera (2008).cfg b/Custom Formulas/Catalan - Guillera (2008).cfg new file mode 100644 index 0000000..c830b8a --- /dev/null +++ b/Custom Formulas/Catalan - Guillera (2008).cfg @@ -0,0 +1,39 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: September 29, 2018 +// +// Value: 0.91596559417721901505460351493238411077414937428167... +// +// Original formula by Guillera (2008). Optimized as follows: +// +// 1 inf ( (-8)^k (3k+2) k!^6 ) +// Catalan = --- SUM (--------------------) +// 2 k=0 ( (2k+1)!^3 ) +// +// https://arxiv.org/pdf/1104.0396.pdf +// http://www.numberworld.org/y-cruncher/internals/binary-splitting-library.html#catalan_guillera +// + +{ + NameShort : "Catalan" + NameLong : "Catalan's Constant" + AlgorithmShort : "Guillera (2008)" + AlgorithmLong : "Guillera (2008)" + Formula : { + SeriesHypergeometric : { + CoefficientP : 1 + CoefficientQ : 2 + CoefficientD : 2 + PolynomialP : [0 0 0 2 3] + PolynomialQ : [-1 -6 -12 -8] + PolynomialR : [0 0 0 1] + } + } +} diff --git a/Custom Formulas/Catalan - Guillera (2019).cfg b/Custom Formulas/Catalan - Guillera (2019).cfg new file mode 100644 index 0000000..c39c844 --- /dev/null +++ b/Custom Formulas/Catalan - Guillera (2019).cfg @@ -0,0 +1,33 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: May 8, 2019 +// +// Value: 0.91596559417721901505460351493238411077414937428167... +// +// https://drive.google.com/file/d/1KUALCj_8JMnKUcABXSkRhoZ2YyrF92Mh/view +// http://www.numberworld.org/y-cruncher/internals/binary-splitting-library.html#catalan_guillera2019 +// + +{ + NameShort : "Catalan" + NameLong : "Catalan's Constant" + AlgorithmShort : "Guillera (2019)" + AlgorithmLong : "Guillera (2019)" + Formula : { + SeriesHypergeometric : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 2 + PolynomialP : [165 -3160 21240 -57184 45136] + PolynomialQ : [3375 -72900 597780 -2309472 4304016 -3779136 1259712] + PolynomialR : [0 0 0 512 -3072 6144 -4096] + } + } +} diff --git a/Custom Formulas/Catalan - Huvent (combined).cfg b/Custom Formulas/Catalan - Huvent (combined).cfg new file mode 100644 index 0000000..6708ade --- /dev/null +++ b/Custom Formulas/Catalan - Huvent (combined).cfg @@ -0,0 +1,67 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename.cfg". +// y-cruncher custom custom:"filename.cfg" +// +// +// Author: Alexander J. Yee +// Date: October 2, 2018 +// +// Value = 0.91596559417721901505460351493238411077414937428167... +// +// Formula: G. Huvent (2006) +// +// 3 inf ( 1 ( 2 2 1 )) +// Catalan = --- SUM (-------- (---------- - ---------- + ----------)) +// 4 k=0 ( (-4)^k ( (4k+1)^2 (4k+2)^2 (4k+3)^2 )) +// +// 1 inf ( 1 ( 8 4 1 )) +// - ---- SUM (--------- (---------- + ---------- + ----------)) +// 32 k=0 ( (-64)^k ( (4k+1)^2 (4k+2)^2 (4k+3)^2 )) +// +// +// Optimized by Alex Yee (2013) to: +// +// 1 inf ( 1 ( 576 144 72 18 +// Catalan = ----- SUM (--------- (----------- - ----------- - ----------- - ------------ +// 384 k=0 ( (-64)^k ( (12k+1)^2 (12k+5)^2 (12k+7)^2 (12k+11)^2 +// +// 144 9 64 8 8 )) +// - ---------- - ---------- - ---------- - ---------- - ---------- )) +// (6k+1)^2 (6k+5)^2 (4k+1)^2 (4k+3)^2 (2k+1)^2 )) +// +// This implementation combines all the terms into a single massive one. +// This mirrors y-cruncher's native implementation. +// + +{ + NameShort : "Catalan" + NameLong : "Catalan's Constant" + AlgorithmShort : "Huvent (combined)" + AlgorithmLong : "Huvent (2006) (combined)" + Formula : { + SeriesBinaryBBP : { + CoefficientP : -1334025 + CoefficientQ : 469137217 + CoefficientD : 512265600 + Alternating : "true" + PowerCoef : -6 + PowerShift : 0 + PolynomialP : [ + -11728430425 -360406957080 -4419704161120 -24153149527360 + 5572409156528 1029713994232704 8098743309464448 36670081182465024 + 113872382317283328 256653109156773888 428868733241327616 532937589964406784 + 486920573914447872 318025249742389248 140614334152704000 37721048963088384 + 4636372233093120 + ] + PolynomialQ : [ + 33350625 2116999500 60083208700 1015899910560 + 11506397536624 93025165344960 558162678313024 2549178063839232 + 9008762620336128 24883108561207296 53971174016925696 91902035745570816 + 122177336673042432 125309104724901888 97123825191223296 54970731296980992 + 21422417343676416 5135673858195456 570630428688384 + ] + } + } +} diff --git a/Custom Formulas/Catalan - Huvent (optimized).cfg b/Custom Formulas/Catalan - Huvent (optimized).cfg new file mode 100644 index 0000000..729843d --- /dev/null +++ b/Custom Formulas/Catalan - Huvent (optimized).cfg @@ -0,0 +1,134 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename.cfg". +// y-cruncher custom custom:"filename.cfg" +// +// +// Author: Alexander J. Yee +// Date: October 2, 2018 +// +// Value = 0.91596559417721901505460351493238411077414937428167... +// +// Formula: G. Huvent (2006) +// +// 3 inf ( 1 ( 2 2 1 )) +// Catalan = --- SUM (-------- (---------- - ---------- + ----------)) +// 4 k=0 ( (-4)^k ( (4k+1)^2 (4k+2)^2 (4k+3)^2 )) +// +// 1 inf ( 1 ( 8 4 1 )) +// - ---- SUM (--------- (---------- + ---------- + ----------)) +// 32 k=0 ( (-64)^k ( (4k+1)^2 (4k+2)^2 (4k+3)^2 )) +// +// +// Optimized by Alex Yee (2013) to: +// +// 1 inf ( 1 ( 576 144 72 18 +// Catalan = ----- SUM (--------- (----------- - ----------- - ----------- - ------------ +// 384 k=0 ( (-64)^k ( (12k+1)^2 (12k+5)^2 (12k+7)^2 (12k+11)^2 +// +// 144 9 64 8 8 )) +// - ---------- - ---------- - ---------- - ---------- - ---------- )) +// (6k+1)^2 (6k+5)^2 (4k+1)^2 (4k+3)^2 (2k+1)^2 )) +// + +{ + NameShort : "Catalan" + NameLong : "Catalan's Constant" + AlgorithmShort : "Huvent (optimized)" + AlgorithmLong : "Huvent (2006) (optimized)" + Formula : { + LinearCombination : [ + [-1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 1 + Alternating : "true" + PowerCoef : -6 + PowerShift : 5 + PolynomialP : [3] + PolynomialQ : [121 -264 144] + }}] + [1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 1 + Alternating : "true" + PowerCoef : -6 + PowerShift : 3 + PolynomialP : [3] + PolynomialQ : [49 -168 144] + }}] + [1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 1 + Alternating : "true" + PowerCoef : -6 + PowerShift : 2 + PolynomialP : [3] + PolynomialQ : [25 -120 144] + }}] + [-1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 1 + Alternating : "true" + PowerCoef : -6 + PowerShift : 0 + PolynomialP : [3] + PolynomialQ : [1 -24 144] + }}] + [1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 1 + Alternating : "true" + PowerCoef : -6 + PowerShift : 3 + PolynomialP : [3] + PolynomialQ : [25 -60 36] + }}] + [1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 2 + Alternating : "true" + PowerCoef : -6 + PowerShift : 0 + PolynomialP : [3] + PolynomialQ : [1 -12 36] + }}] + [1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 3 + Alternating : "true" + PowerCoef : -6 + PowerShift : 5 + PolynomialP : [1] + PolynomialQ : [9 -24 16] + }}] + [1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 3 + Alternating : "true" + PowerCoef : -6 + PowerShift : 2 + PolynomialP : [1] + PolynomialQ : [1 -8 16] + }}] + [1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 3 + Alternating : "true" + PowerCoef : -6 + PowerShift : 2 + PolynomialP : [1] + PolynomialQ : [1 -4 4] + }}] + ] + } +} diff --git a/Custom Formulas/Catalan - Huvent (original).cfg b/Custom Formulas/Catalan - Huvent (original).cfg new file mode 100644 index 0000000..4db11d6 --- /dev/null +++ b/Custom Formulas/Catalan - Huvent (original).cfg @@ -0,0 +1,95 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename.cfg". +// y-cruncher custom custom:"filename.cfg" +// +// +// Author: Alexander J. Yee +// Date: October 2, 2018 +// +// Value = 0.91596559417721901505460351493238411077414937428167... +// +// Formula: G. Huvent (2006) +// +// 3 inf ( 1 ( 2 2 1 )) +// Catalan = --- SUM (-------- (---------- - ---------- + ----------)) +// 4 k=0 ( (-4)^k ( (4k+1)^2 (4k+2)^2 (4k+3)^2 )) +// +// 1 inf ( 1 ( 8 4 1 )) +// - ---- SUM (--------- (---------- + ---------- + ----------)) +// 32 k=0 ( (-64)^k ( (4k+1)^2 (4k+2)^2 (4k+3)^2 )) +// +// http://functions.wolfram.com/Constants/Catalan/06/01/0007/ +// + +{ + NameShort : "Catalan" + NameLong : "Catalan's Constant" + AlgorithmShort : "Huvent (original)" + AlgorithmLong : "Huvent (2006) (original)" + Formula : { + LinearCombination : [ + [-1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 1 + Alternating : "true" + PowerCoef : -2 + PowerShift : 1 + PolynomialP : [3] + PolynomialQ : [9 -24 16] + }}] + [1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 1 + Alternating : "true" + PowerCoef : -2 + PowerShift : 0 + PolynomialP : [3] + PolynomialQ : [2 -8 8] + }}] + [-1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 1 + Alternating : "true" + PowerCoef : -2 + PowerShift : 0 + PolynomialP : [3] + PolynomialQ : [1 -8 16] + }}] + [1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 1 + Alternating : "true" + PowerCoef : -6 + PowerShift : 4 + PolynomialP : [1] + PolynomialQ : [9 -24 16] + }}] + [1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 1 + Alternating : "true" + PowerCoef : -6 + PowerShift : 1 + PolynomialP : [1] + PolynomialQ : [1 -4 4] + }}] + [1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 1 + Alternating : "true" + PowerCoef : -6 + PowerShift : 1 + PolynomialP : [1] + PolynomialQ : [1 -8 16] + }}] + ] + } +} diff --git a/Custom Formulas/Catalan - LogPi.cfg b/Custom Formulas/Catalan - LogPi.cfg new file mode 100644 index 0000000..b03fea6 --- /dev/null +++ b/Custom Formulas/Catalan - LogPi.cfg @@ -0,0 +1,49 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename.cfg". +// y-cruncher custom custom:"filename.cfg" +// +// +// Author: Alexander J. Yee +// Date: October 4, 2018 +// +// Value: 0.91596559417721901505460351493238411077414937428167... +// +// Unknown formula: http://functions.wolfram.com/PDF/Catalan.pdf +// +// inf ( (2k)! ) Pi Log(2) +// Catalan = sqrt(2) SUM (-------------------) - ----------- +// k=0 ( 8^k k!^2 (2k+1)^2 ) 4 +// + +{ + NameShort : "Catalan" + NameLong : "Catalan's Constant" + AlgorithmShort : "LogPi" + AlgorithmLong : "Unknown Log-Pi Series" + Formula : { + LinearCombination : [ + [2 {Multiply : [ + {SeriesHypergeometric : { + CoefficientP : 1 + CoefficientQ : 1 + CoefficientD : 1 + PolynomialP : [-1 2] + PolynomialQ : [0 4 16 16] + PolynomialR : [-1 -2 4 8] + }} + {Invsqrt : 2} + ] + }] + [-1 {Shift : [ + {Multiply : [ + {Pi : {}} + {Log : 2} + ]} + -2 + ] + }] + ] + } +} diff --git a/Custom Formulas/Catalan - Lupas.cfg b/Custom Formulas/Catalan - Lupas.cfg new file mode 100644 index 0000000..03c14d3 --- /dev/null +++ b/Custom Formulas/Catalan - Lupas.cfg @@ -0,0 +1,38 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: September 29, 2018 +// +// Value: 0.91596559417721901505460351493238411077414937428167... +// +// Formula by A. Lupas (2000): +// +// 1 inf ( (-1)^(k-1) 256^k (40k^2 - 24k + 3) (2k)!^3 k!^2 ) +// Catalan = ---- SUM (-------------------------------------------------) +// 64 k=0 ( k^3 (2k-1) (4k)!^2 ) +// +// http://www.lacim.uqam.ca/~plouffe/articles/alupas1.pdf +// + +{ + NameShort : "Catalan" + NameLong : "Catalan's Constant" + AlgorithmShort : "Lupas" + AlgorithmLong : "Lupas (2000)" + Formula : { + SeriesHypergeometric : { + CoefficientP : 1 + CoefficientQ : 19 + CoefficientD : 18 + PolynomialP : [0 0 0 -608 -576 2304 2560] + PolynomialQ : [-9 -96 -352 -512 -256] + PolynomialR : [0 0 0 -32 64] + } + } +} diff --git a/Custom Formulas/Catalan - Pilehrood (long).cfg b/Custom Formulas/Catalan - Pilehrood (long).cfg new file mode 100644 index 0000000..06d121e --- /dev/null +++ b/Custom Formulas/Catalan - Pilehrood (long).cfg @@ -0,0 +1,39 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: September 29, 2018 +// +// Value: 0.91596559417721901505460351493238411077414937428167... +// +// Formula by Pilehrood (2010): +// +// 1 inf ( (-256)^k (419840k^6 - 915456k^5 + 782848k^4 - 332800k^3 + 73256k^2 - 7800k + 315) k!^2 (4k)!^4 ) +// Catalan = ---- SUM (------------------------------------------------------------------------------------------------) +// 64 k=0 ( k^3 (2k-1) (4k-1)^2 (4k-3)^2 (8k)!^2 (2k)! ) +// +// https://hal.inria.fr/hal-00990465/document +// http://www.numberworld.org/y-cruncher/internals/binary-splitting-library.html#catalan_pilehrood_long +// + +{ + NameShort : "Catalan" + NameLong : "Catalan's Constant" + AlgorithmShort : "Pilehrood (long)" + AlgorithmLong : "Pilehrood (2010) (long)" + Formula : { + SeriesHypergeometric : { + CoefficientP : -1 + CoefficientQ : 0 + CoefficientD : 2 + PolynomialP : [315 -7800 73256 -332800 782848 -915456 419840] + PolynomialQ : [-11025 295680 -3138304 17219584 -54222848 101711872 -112197632 67108864 -16777216] + PolynomialR : [0 0 0 -288 3648 -17408 38912 -40960 16384] + } + } +} diff --git a/Custom Formulas/Catalan - Pilehrood (short).cfg b/Custom Formulas/Catalan - Pilehrood (short).cfg new file mode 100644 index 0000000..3fa12a4 --- /dev/null +++ b/Custom Formulas/Catalan - Pilehrood (short).cfg @@ -0,0 +1,39 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: September 29, 2018 +// +// Value: 0.91596559417721901505460351493238411077414937428167... +// +// Formula by Pilehrood (2010): +// +// 1 inf ( 256^k (580k^2 - 184k + 15) (2k)!^3 (3k)!^2 ) +// Catalan = ---- SUM (--------------------------------------------) +// 64 k=0 ( k^3 (2k-1) (6k)!^2 ) +// +// https://hal.inria.fr/hal-00990465/document +// http://www.numberworld.org/y-cruncher/internals/binary-splitting-library.html#catalan_pilehrood_short +// + +{ + NameShort : "Catalan" + NameLong : "Catalan's Constant" + AlgorithmShort : "Pilehrood (short)" + AlgorithmLong : "Pilehrood (2010) (short)" + Formula : { + SeriesHypergeometric : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 2 + PolynomialP : [15 -184 580] + PolynomialQ : [225 -3240 14904 -23328 11664] + PolynomialR : [0 0 0 -32 64] + } + } +} diff --git a/Custom Formulas/Catalan - Ramanujan (unoptimized).cfg b/Custom Formulas/Catalan - Ramanujan (unoptimized).cfg new file mode 100644 index 0000000..e55348d --- /dev/null +++ b/Custom Formulas/Catalan - Ramanujan (unoptimized).cfg @@ -0,0 +1,48 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: November 1, 2018 +// +// Value: 0.91596559417721901505460351493238411077414937428167... +// +// Pi 3 inf ( k!^2 ) +// Catalan = ---- Log(2 + sqrt(3)) + --- SUM (----------------) +// 8 8 k=0 ( (2k+1)^2 (2k)! ) +// +// This is not efficient because it computes Pi twice. +// + +{ + NameShort : "Catalan" + NameLong : "Catalan's Constant" + AlgorithmShort : "Ramanujan" + AlgorithmLong : "Ramanujan's Formula" + Formula : { + LinearCombination : [ + [1 {SeriesHypergeometric : { + Power : 1 + CoefficientP : 3 + CoefficientQ : 3 + CoefficientD : 8 + PolynomialP : [0 1] + PolynomialQ : [-2 -4 8 16] + PolynomialR : [0 1 4 4] + }}] + [1 {Multiply : [ + {Log : { + LinearCombination : [ + [1 2] + [1 {Sqrt : 3}] + ] + }} + {Shift : [{Pi : {}} -3]} + ]}] + ] + } +} diff --git a/Custom Formulas/Catalan - Ramanujan.cfg b/Custom Formulas/Catalan - Ramanujan.cfg new file mode 100644 index 0000000..94ed800 --- /dev/null +++ b/Custom Formulas/Catalan - Ramanujan.cfg @@ -0,0 +1,58 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: November 1, 2018 +// +// Value: 0.91596559417721901505460351493238411077414937428167... +// +// Pi 3 inf ( k!^2 ) +// Catalan = ---- Log(2 + sqrt(3)) + --- SUM (----------------) +// 8 8 k=0 ( (2k+1)^2 (2k)! ) +// + +{ + NameShort : "Catalan" + NameLong : "Catalan's Constant" + AlgorithmShort : "Ramanujan" + AlgorithmLong : "Ramanujan's Formula" + Formula : { + LinearCombination : [ + [1 {SeriesHypergeometric : { + Power : 1 + CoefficientP : 3 + CoefficientQ : 3 + CoefficientD : 8 + PolynomialP : [0 1] + PolynomialQ : [-2 -4 8 16] + PolynomialR : [0 1 4 4] + }}] + [1 {Scope : { + Locals : [ + {pi : {Pi : {}}} + {log2 : {Log : 2}} + ] + Formula : { + Multiply : [ + {Log-AGM : { + Pi : "pi" + Log2 : "log2" + Argument : { + LinearCombination : [ + [1 2] + [1 {Sqrt : 3}] + ] + } + }} + {Shift : ["pi" -3]} + ] + } + }}] + ] + } +} diff --git a/Custom Formulas/Cbrt(2) - Native.cfg b/Custom Formulas/Cbrt(2) - Native.cfg new file mode 100644 index 0000000..b807a32 --- /dev/null +++ b/Custom Formulas/Cbrt(2) - Native.cfg @@ -0,0 +1,28 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: February 22, 2019 +// +// Cube root of 2. +// +// Value: 1.25992104989487316476721060727822835057025146470150... +// + +{ + NameShort : "Cbrt(2)" + NameLong : "Cube Root of 2" + AlgorithmShort : "Native" + AlgorithmLong : "Native InvNthRoot" + Formula : { + Shift : [ + {InvNthRoot : [3 4]} + 1 + ] + } +} diff --git a/Custom Formulas/Cbrt(2) - Series.cfg b/Custom Formulas/Cbrt(2) - Series.cfg new file mode 100644 index 0000000..451074b --- /dev/null +++ b/Custom Formulas/Cbrt(2) - Series.cfg @@ -0,0 +1,32 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: November 11, 2018 +// +// Cube root of 2. +// +// Value: 1.25992104989487316476721060727822835057025146470150... +// + +{ + NameShort : "Cbrt(2)" + NameLong : "Cube Root of 2" + AlgorithmShort : "Series" + AlgorithmLong : "Hypergeometric Series" + Formula : { + SeriesHypergeometric : { + CoefficientP : 1 + CoefficientQ : 1 + CoefficientD : 1 + PolynomialP : [2 -3] + PolynomialQ : [0 -6] + PolynomialR : [2 -3] + } + } +} diff --git a/Custom Formulas/Cbrt(2) - Series2.cfg b/Custom Formulas/Cbrt(2) - Series2.cfg new file mode 100644 index 0000000..b2f4bb5 --- /dev/null +++ b/Custom Formulas/Cbrt(2) - Series2.cfg @@ -0,0 +1,32 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: November 13, 2018 +// +// Cube root of 2. +// +// Value: 1.25992104989487316476721060727822835057025146470150... +// + +{ + NameShort : "Cbrt(2)" + NameLong : "Cube Root of 2" + AlgorithmShort : "Series 2" + AlgorithmLong : "Hypergeometric Series 2" + Formula : { + SeriesHypergeometric : { + CoefficientP : 5 + CoefficientQ : 5 + CoefficientD : 4 + PolynomialP : [2 -3] + PolynomialQ : [0 -128] + PolynomialR : [2 -3] + } + } +} diff --git a/Custom Formulas/Cbrt(3) - Native.cfg b/Custom Formulas/Cbrt(3) - Native.cfg new file mode 100644 index 0000000..13aa5e3 --- /dev/null +++ b/Custom Formulas/Cbrt(3) - Native.cfg @@ -0,0 +1,28 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: February 22, 2019 +// +// Cube root of 3. +// +// Value: 1.44224957030740838232163831078010958839186925349935... +// + +{ + NameShort : "Cbrt(3)" + NameLong : "Cube Root of 3" + AlgorithmShort : "Native" + AlgorithmLong : "Native InvNthRoot" + Formula : { + LinearCombination : [[ + 3 + {InvNthRoot : [3 9]} + ]] + } +} diff --git a/Custom Formulas/Cbrt(3) - Series.cfg b/Custom Formulas/Cbrt(3) - Series.cfg new file mode 100644 index 0000000..7fde475 --- /dev/null +++ b/Custom Formulas/Cbrt(3) - Series.cfg @@ -0,0 +1,32 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: November 13, 2018 +// +// Cube root of 3. +// +// Value: 1.44224957030740838232163831078010958839186925349935... +// + +{ + NameShort : "Cbrt(3)" + NameLong : "Cube Root of 3" + AlgorithmShort : "Series" + AlgorithmLong : "Hypergeometric Series" + Formula : { + SeriesHypergeometric : { + CoefficientP : 3 + CoefficientQ : 3 + CoefficientD : 2 + PolynomialP : [4 -3] + PolynomialQ : [0 -27] + PolynomialR : [4 -3] + } + } +} diff --git a/Custom Formulas/Cos(1) - Half Angle Formula.cfg b/Custom Formulas/Cos(1) - Half Angle Formula.cfg new file mode 100644 index 0000000..18c368e --- /dev/null +++ b/Custom Formulas/Cos(1) - Half Angle Formula.cfg @@ -0,0 +1,37 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: October 6, 2018 +// +// Value: 0.54030230586813971740093660744297660373231042061792... +// +// Formula: 2 Cos(1/2)^2 - 1 +// + +{ + NameShort : "Cos(1)" + NameLong : "Cosine of 1" + AlgorithmShort : "Half Angle Formula" + AlgorithmLong : "2 Cos(1/2)^2 - 1" + Formula : { + LinearCombination : [ + [2 {Power : [ + {SeriesHyperdescent : { + CoefficientP : 1 + CoefficientQ : 1 + CoefficientD : 1 + PolynomialP : [1] + PolynomialQ : [0 8 -16] + }} + 2 + ]}] + [-1 1] + ] + } +} diff --git a/Custom Formulas/Cos(1) - Series.cfg b/Custom Formulas/Cos(1) - Series.cfg new file mode 100644 index 0000000..f4ad1e0 --- /dev/null +++ b/Custom Formulas/Cos(1) - Series.cfg @@ -0,0 +1,31 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: October 6, 2018 +// +// Value: 0.54030230586813971740093660744297660373231042061792... +// +// Formula: Taylor Series of Cos(x) +// + +{ + NameShort : "Cos(1)" + NameLong : "Cosine of 1" + AlgorithmShort : "Series" + AlgorithmLong : "Taylor Series of cos(1)" + Formula : { + SeriesHyperdescent : { + CoefficientP : 1 + CoefficientQ : 1 + CoefficientD : 1 + PolynomialP : [1] + PolynomialQ : [0 2 -4] + } + } +} diff --git a/Custom Formulas/Erf(1) - Series.cfg b/Custom Formulas/Erf(1) - Series.cfg new file mode 100644 index 0000000..bac40bd --- /dev/null +++ b/Custom Formulas/Erf(1) - Series.cfg @@ -0,0 +1,35 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: October 24, 2018 +// +// Value: 0.84270079294971486934122063508260925929606699796630... +// + +{ + NameShort : "Erf(1)" + NameLong : "Erf(1)" + AlgorithmShort : "Series" + AlgorithmLong : "Taylor Series" + Formula : { + Multiply : [ + {SeriesHypergeometric : { + CoefficientP : -6 + CoefficientQ : 4 + CoefficientD : 3 + PolynomialP : [1] + PolynomialQ : [-3 -5 -2] + PolynomialR : [3 2] + }} + {Invsqrt : { + Pi : {} + }} + ] + } +} diff --git a/Custom Formulas/Gamma(1d3) - AGM-Pi.cfg b/Custom Formulas/Gamma(1d3) - AGM-Pi.cfg new file mode 100644 index 0000000..b0e2fd5 --- /dev/null +++ b/Custom Formulas/Gamma(1d3) - AGM-Pi.cfg @@ -0,0 +1,47 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: February 22, 2019 +// +// Value: 2.67893853470774763365569294097467764412868937795730... +// +// Source: http://arblib.org/gamma.html +// + +{ + NameShort : "Gamma(⅓)" + NameLong : "Gamma(1/3)" + AlgorithmShort : "AGM-Pi" + AlgorithmLong : "AGM-Pi" + Formula : { + Divide : [ + {Multiply : [ + {InvNthRoot : [ + 3 + {AGM : {Invsqrt : + {LinearCombination : [ + [1 8] + [-1 {Sqrt : 48}] + ]} + }} + ]} + {InvNthRoot : [12 3]} + ]} + {Multiply : [ + {InvNthRoot : [3 + {Power : [ + {Pi : {Algorithm : "ramanujan"}} + 2 + ]} + ]} + {InvNthRoot : [9 16]} + ]} + ] + } +} diff --git a/Custom Formulas/Gamma(1d3) - Series-Pi.cfg b/Custom Formulas/Gamma(1d3) - Series-Pi.cfg new file mode 100644 index 0000000..1674252 --- /dev/null +++ b/Custom Formulas/Gamma(1d3) - Series-Pi.cfg @@ -0,0 +1,45 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: February 22, 2019 +// +// Value: 2.67893853470774763365569294097467764412868937795730... +// +// Sources: +// http://iamned.com/math/infiniteseries.pdf +// http://arblib.org/gamma.html +// + +{ + NameShort : "Gamma(⅓)" + NameLong : "Gamma(1/3)" + AlgorithmShort : "Series-Pi (Brown)" + AlgorithmLong : "Series-Pi (Brown 2009)" + Formula : { + InvNthRoot : [ + 6 + {Multiply : [ + {SeriesHypergeometric : { + Power : -1 + CoefficientP : 1 + CoefficientQ : 1 + CoefficientD : 5 + PolynomialP : [-5 46 -108 72] + PolynomialQ : [0 0 0 -512000] + PolynomialR : [-5 46 -108 72] + }} + {Power : [ + {Pi : {Power : -1}} + 4 + ]} + {Invsqrt : 360} + ]} + ] + } +} diff --git a/Custom Formulas/Gamma(1d4) - AGM-Pi.cfg b/Custom Formulas/Gamma(1d4) - AGM-Pi.cfg new file mode 100644 index 0000000..9b1dde5 --- /dev/null +++ b/Custom Formulas/Gamma(1d4) - AGM-Pi.cfg @@ -0,0 +1,44 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: October 24, 2018 +// +// Value: 3.62560990822190831193068515586767200299516768288006... +// +// ( 1 ) 1 +// Gamma(---) = ---------------------------- +// ( 4 ) ( AGM(1, sqrt(2)) ) +// sqrt( ------------------ ) +// ( sqrt( (2 Pi)^3 ) ) +// +// Source: http://mathworld.wolfram.com/GausssConstant.html +// + +{ + NameShort : "Gamma(¼)" + NameLong : "Gamma(1/4)" + AlgorithmShort : "AGM-Pi" + AlgorithmLong : "AGM-Pi" + Formula : { + Invsqrt : { + Multiply : [ + {AGM : {Sqrt : 2}} + {Invsqrt : { + Power : [ + {Shift : [ + {Pi : {}} + 1 + ]} + 3 + ] + }} + ] + } + } +} diff --git a/Custom Formulas/Gamma(1d4) - Lemniscate.cfg b/Custom Formulas/Gamma(1d4) - Lemniscate.cfg new file mode 100644 index 0000000..6b5515a --- /dev/null +++ b/Custom Formulas/Gamma(1d4) - Lemniscate.cfg @@ -0,0 +1,39 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: October 24, 2018 +// +// Value: 3.62560990822190831193068515586767200299516768288006... +// +// ( 1 ) ( Lemniscate ) +// Gamma(---) = sqrt(---------------) +// ( 4 ) ( ( 1 ) ) +// ( sqrt(------) ) +// ( ( 2 Pi ) ) +// + +{ + NameShort : "Gamma(¼)" + NameLong : "Gamma(1/4)" + AlgorithmShort : "Lemniscate" + AlgorithmLong : "Lemniscate Formula" + Formula : { + Sqrt : { + Multiply : [ + {Lemniscate : {Algorithm : "gauss"}} + {Invsqrt : { + Shift : [ + {Pi : {Power : -1}} + -1 + ] + }} + ] + } + } +} diff --git a/Custom Formulas/Gamma(1d4) - Series-Pi.cfg b/Custom Formulas/Gamma(1d4) - Series-Pi.cfg new file mode 100644 index 0000000..ac33001 --- /dev/null +++ b/Custom Formulas/Gamma(1d4) - Series-Pi.cfg @@ -0,0 +1,49 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: February 26, 2019 +// +// Value: 3.62560990822190831193068515586767200299516768288006... +// +// Source: http://iamned.com/math/infiniteseries.pdf +// +// This file uses Ramanujan's formula for Pi to make it computationally +// independent from "Gamma(1d4) - AGM-Pi.cfg". +// + +{ + NameShort : "Gamma(¼)" + NameLong : "Gamma(1/4)" + AlgorithmShort : "Series-Pi (Brown)" + AlgorithmLong : "Series-Pi (Brown 2009)" + Formula : { + Invsqrt : { + Multiply : [ + {SeriesHypergeometric : { + Power : -1 + CoefficientP : 1 + CoefficientQ : 147 + CoefficientD : 108 + PolynomialP : [15435 -143136 20224 1241088 -856064 -2752512 2621440] + PolynomialQ : [0 0 82944 331776 331776] + PolynomialR : [105 -1408 5504 -8192 4096] + }} + {Invsqrt : { + LinearCombination : [[ + 3 + {Power : [ + {Pi : {Algorithm : "ramanujan"}} + 3 + ]} + ]] + }} + ] + } + } +} diff --git a/Custom Formulas/Gamma(1d6) - AGM-Pi.cfg b/Custom Formulas/Gamma(1d6) - AGM-Pi.cfg new file mode 100644 index 0000000..72d70bf --- /dev/null +++ b/Custom Formulas/Gamma(1d6) - AGM-Pi.cfg @@ -0,0 +1,51 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: February 22, 2019 +// +// Value: 5.56631600178023520425009689520772611139879911487285... +// +// Source: http://arblib.org/gamma.html +// + +{ + NameShort : "Gamma(⅙)" + NameLong : "Gamma(1/6)" + AlgorithmShort : "AGM-Pi" + AlgorithmLong : "AGM-Pi" + Formula : { + Scope : { + Locals : [ + {pi : {Pi : {Algorithm : "ramanujan"}}} + ] + Formula : {Multiply : [ + {InvNthRoot : [ + 6 + {Multiply : [ + {Power : [ + {AGM : {Invsqrt : + {LinearCombination : [ + [1 8] + [-1 {Sqrt : 48}] + ]} + }} + 4 + ]} + "pi" + ]} + ]} + "pi" + {LinearCombination : [[ + 6 + {InvNthRoot : [9 11664]} + ]]} + ]} + } + } +} diff --git a/Custom Formulas/Gamma(1d6) - Series-Pi.cfg b/Custom Formulas/Gamma(1d6) - Series-Pi.cfg new file mode 100644 index 0000000..7c34423 --- /dev/null +++ b/Custom Formulas/Gamma(1d6) - Series-Pi.cfg @@ -0,0 +1,44 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: February 22, 2019 +// +// Value: 5.56631600178023520425009689520772611139879911487285... +// +// Sources: +// http://arblib.org/gamma.html +// http://iamned.com/math/infiniteseries.pdf +// + +{ + NameShort : "Gamma(⅙)" + NameLong : "Gamma(1/6)" + AlgorithmShort : "Series-Pi (Brown)" + AlgorithmLong : "Series-Pi (Brown 2009)" + Formula : { + InvNthRoot : [ + 3 + {Multiply : [ + {SeriesHypergeometric : { + Power : -1 + CoefficientP : 1 + CoefficientQ : 1 + CoefficientD : 5 + PolynomialP : [-5 46 -108 72] + PolynomialQ : [0 0 0 -512000] + PolynomialR : [-5 46 -108 72] + }} + {Invsqrt : {LinearCombination : [[ + 2430 + {Power : [{Pi : {}} 5]} + ]]}} + ]} + ] + } +} diff --git a/Custom Formulas/Gamma(2d3) - AGM-Pi.cfg b/Custom Formulas/Gamma(2d3) - AGM-Pi.cfg new file mode 100644 index 0000000..917df29 --- /dev/null +++ b/Custom Formulas/Gamma(2d3) - AGM-Pi.cfg @@ -0,0 +1,40 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: February 22, 2019 +// +// Value: 1.35411793942640041694528802815451378551932726605679... +// +// Source: http://arblib.org/gamma.html +// + +{ + NameShort : "Gamma(⅔)" + NameLong : "Gamma(2/3)" + AlgorithmShort : "AGM-Pi" + AlgorithmLong : "AGM-Pi" + Formula : { + Divide : [ + {InvNthRoot : [12 243]} + {Multiply : [ + {InvNthRoot : [ + 3 + {AGM : {Invsqrt : + {LinearCombination : [ + [1 8] + [-1 {Sqrt : 48}] + ]} + }} + ]} + {InvNthRoot : [3 {Pi : {Algorithm : "ramanujan"}}]} + {InvNthRoot : [9 32]} + ]} + ] + } +} diff --git a/Custom Formulas/Gamma(2d3) - Series-Pi.cfg b/Custom Formulas/Gamma(2d3) - Series-Pi.cfg new file mode 100644 index 0000000..d3427d3 --- /dev/null +++ b/Custom Formulas/Gamma(2d3) - Series-Pi.cfg @@ -0,0 +1,44 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: February 22, 2019 +// +// Value: 1.35411793942640041694528802815451378551932726605679... +// +// Sources: +// http://arblib.org/gamma.html +// http://iamned.com/math/infiniteseries.pdf +// + +{ + NameShort : "Gamma(⅔)" + NameLong : "Gamma(2/3)" + AlgorithmShort : "Series-Pi (Brown)" + AlgorithmLong : "Series-Pi (Brown 2009)" + Formula : { + InvNthRoot : [ + 6 + {Multiply : [ + {SeriesHypergeometric : { + CoefficientP : 81 + CoefficientQ : 81 + CoefficientD : 1 + PolynomialP : [-5 46 -108 72] + PolynomialQ : [0 0 0 -512000] + PolynomialR : [-5 46 -108 72] + }} + {Power : [ + {Pi : {Power : -1}} + 2 + ]} + {Invsqrt : 2560} + ]} + ] + } +} diff --git a/Custom Formulas/Gamma(3d4) - AGM-Pi.cfg b/Custom Formulas/Gamma(3d4) - AGM-Pi.cfg new file mode 100644 index 0000000..0927812 --- /dev/null +++ b/Custom Formulas/Gamma(3d4) - AGM-Pi.cfg @@ -0,0 +1,39 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: October 24, 2018 +// +// Value: 1.22541670246517764512909830336289052685123924810807... +// +// ( 3 ) ( ( Pi )) +// Gamma(---) = sqrt( AGM(1, sqrt(2)) * sqrt(----)) +// ( 4 ) ( ( 2 )) +// +// Source: http://arblib.org/gamma.html +// + +{ + NameShort : "Gamma(¾)" + NameLong : "Gamma(3/4)" + AlgorithmShort : "AGM-Pi" + AlgorithmLong : "AGM-Pi" + Formula : { + Sqrt : { + Multiply : [ + {AGM : {Sqrt : 2}} + {Sqrt : { + Shift : [ + {Pi : {}} + -1 + ] + }} + ] + } + } +} diff --git a/Custom Formulas/Gamma(3d4) - Lemniscate.cfg b/Custom Formulas/Gamma(3d4) - Lemniscate.cfg new file mode 100644 index 0000000..59ba9b3 --- /dev/null +++ b/Custom Formulas/Gamma(3d4) - Lemniscate.cfg @@ -0,0 +1,42 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: October 24, 2018 +// +// Value: 1.22541670246517764512909830336289052685123924810807... +// +// ( 3 ) 1 +// Gamma(---) = ---------------------- +// ( 4 ) ( Lemniscate ) +// sqrt(--------------) +// ( sqrt(2 Pi^3) ) +// + +{ + NameShort : "Gamma(¾)" + NameLong : "Gamma(3/4)" + AlgorithmShort : "Lemniscate" + AlgorithmLong : "Lemniscate Formula" + Formula : { + Invsqrt : { + Multiply : [ + {Lemniscate : {Algorithm : "gauss"}} + {Invsqrt : { + Shift : [ + {Power : [ + {Pi : {}} + 3 + ]} + 1 + ] + }} + ] + } + } +} diff --git a/Custom Formulas/Gamma(3d4) - Series-Pi.cfg b/Custom Formulas/Gamma(3d4) - Series-Pi.cfg new file mode 100644 index 0000000..e169eb3 --- /dev/null +++ b/Custom Formulas/Gamma(3d4) - Series-Pi.cfg @@ -0,0 +1,45 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: February 26, 2019 +// +// Value: 1.22541670246517764512909830336289052685123924810807... +// +// Source: http://iamned.com/math/infiniteseries.pdf +// +// This file uses Ramanujan's formula for Pi to make it computationally +// independent from "Gamma(1d4) - AGM-Pi.cfg". +// + +{ + NameShort : "Gamma(¾)" + NameLong : "Gamma(3/4)" + AlgorithmShort : "Series-Pi (Brown)" + AlgorithmLong : "Series-Pi (Brown 2009)" + Formula : { + Invsqrt : { + Multiply : [ + {SeriesHypergeometric : { + CoefficientP : 1 + CoefficientQ : 1 + CoefficientD : 2 + PolynomialP : [9 -24 16] + PolynomialQ : [0 0 -128] + PolynomialR : [9 -24 16] + }} + {Invsqrt : { + Multiply : [ + {Pi : {Algorithm : "ramanujan"}} + {Invsqrt : 32} + ] + }} + ] + } + } +} diff --git a/Custom Formulas/Gamma(5d6) - AGM-Pi.cfg b/Custom Formulas/Gamma(5d6) - AGM-Pi.cfg new file mode 100644 index 0000000..a169fd5 --- /dev/null +++ b/Custom Formulas/Gamma(5d6) - AGM-Pi.cfg @@ -0,0 +1,51 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: February 22, 2019 +// +// Value: 1.12878702990812596126090109025884201332678744166475... +// +// Source: http://arblib.org/gamma.html +// + +{ + NameShort : "Gamma(⅚)" + NameLong : "Gamma(5/6)" + AlgorithmShort : "AGM-Pi" + AlgorithmLong : "AGM-Pi" + Formula : { + Multiply : [ + {InvNthRoot : [ + 6 + {LinearCombination : [[ + 9 + {Power : [ + {Multiply : [ + {Power : [ + {AGM : {Invsqrt : + {LinearCombination : [ + [1 8] + [-1 {Sqrt : 48}] + ]} + }} + 4 + ]} + {Pi : {Algorithm : "ramanujan"}} + ]} + -1 + ]} + ]]} + ]} + {Shift : [ + {InvNthRoot : [9 32]} + 1 + ]} + ] + } +} diff --git a/Custom Formulas/Gamma(5d6) - Series-Pi.cfg b/Custom Formulas/Gamma(5d6) - Series-Pi.cfg new file mode 100644 index 0000000..f48fd05 --- /dev/null +++ b/Custom Formulas/Gamma(5d6) - Series-Pi.cfg @@ -0,0 +1,43 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: February 22, 2019 +// +// Value: 1.12878702990812596126090109025884201332678744166475... +// +// Sources: +// http://arblib.org/gamma.html +// http://iamned.com/math/infiniteseries.pdf +// + +{ + NameShort : "Gamma(⅚)" + NameLong : "Gamma(5/6)" + AlgorithmShort : "Series-Pi (Brown)" + AlgorithmLong : "Series-Pi (Brown 2009)" + Formula : { + InvNthRoot : [ + 3 + {Multiply : [ + {SeriesHypergeometric : { + CoefficientP : 27 + CoefficientQ : 27 + CoefficientD : 1 + PolynomialP : [-5 46 -108 72] + PolynomialQ : [0 0 0 -512000] + PolynomialR : [-5 46 -108 72] + }} + {Invsqrt : {LinearCombination : [[ + 480 + {Pi : {}} + ]]}} + ]} + ] + } +} diff --git a/Custom Formulas/Gauss - AGM.cfg b/Custom Formulas/Gauss - AGM.cfg new file mode 100644 index 0000000..d18fcc6 --- /dev/null +++ b/Custom Formulas/Gauss - AGM.cfg @@ -0,0 +1,30 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: October 26, 2018 +// +// Value: 0.83462684167407318628142973279904680899399301349034... +// +// 1 +// Gauss's Constant = ----------------- +// AGM(1, sqrt(2)) +// + +{ + NameShort : "Gauss" + NameLong : "Gauss's Constant" + AlgorithmShort : "AGM" + AlgorithmLong : "1 / AGM(1, Sqrt(2))" + Formula : { + Power : [ + {AGM : {Sqrt : 2}} + -1 + ] + } +} diff --git a/Custom Formulas/Gauss - Lemniscate.cfg b/Custom Formulas/Gauss - Lemniscate.cfg new file mode 100644 index 0000000..ffb636e --- /dev/null +++ b/Custom Formulas/Gauss - Lemniscate.cfg @@ -0,0 +1,33 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: October 6, 2018 +// +// Value: 0.83462684167407318628142973279904680899399301349034... +// +// 1 +// Gauss's Constant = ----------------- +// AGM(1, sqrt(2)) +// + +{ + NameShort : "Gauss" + NameLong : "Gauss's Constant" + AlgorithmShort : "Lemniscate" + AlgorithmLong : "Lemniscate / (2 Pi)" + Formula : { + Shift : [ + {Multiply : [ + {Lemniscate : {Algorithm : "gauss"}} + {Pi : {Power : -1}} + ]} + -1 + ] + } +} diff --git a/Custom Formulas/Gauss - Series.cfg b/Custom Formulas/Gauss - Series.cfg new file mode 100644 index 0000000..ca3e634 --- /dev/null +++ b/Custom Formulas/Gauss - Series.cfg @@ -0,0 +1,43 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: February 26, 2018 +// +// Value: 0.83462684167407318628142973279904680899399301349034... +// +// 1 +// Gauss's Constant = ----------------- +// AGM(1, sqrt(2)) +// +// +// The formula used here is derived from Brown's 2009 formula +// for Gamma(1/4). +// +// Source: http://iamned.com/math/infiniteseries.pdf +// + +{ + NameShort : "Gauss" + NameLong : "Gauss's Constant" + AlgorithmShort : "Series" + AlgorithmLong : "Hypergeometric Series" + Formula : { + Multiply : [ + {SeriesHypergeometric : { + CoefficientP : 1 + CoefficientQ : 147 + CoefficientD : 1 + PolynomialP : [15435 -143136 20224 1241088 -856064 -2752512 2621440] + PolynomialQ : [0 0 82944 331776 331776] + PolynomialR : [105 -1408 5504 -8192 4096] + }} + {Invsqrt : 31104} + ] + } +} diff --git a/Custom Formulas/GoldenRatio - Native Invsqrt.cfg b/Custom Formulas/GoldenRatio - Native Invsqrt.cfg new file mode 100644 index 0000000..c079280 --- /dev/null +++ b/Custom Formulas/GoldenRatio - Native Invsqrt.cfg @@ -0,0 +1,29 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: October 6, 2018 +// +// Value: 1.61803398874989484820458683436563811772030917980576... +// + +{ + NameShort : "Golden Ratio" + NameLong : "Golden Ratio" + AlgorithmShort : "Invsqrt" + AlgorithmLong : "Native Invsqrt" + Formula : { + Shift : [ + {LinearCombination : [ + [5 {Invsqrt : 5}] + [1 1] + ]} + -1 + ] + } +} diff --git a/Custom Formulas/GoldenRatio - Series.cfg b/Custom Formulas/GoldenRatio - Series.cfg new file mode 100644 index 0000000..6d8cc11 --- /dev/null +++ b/Custom Formulas/GoldenRatio - Series.cfg @@ -0,0 +1,30 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: November 11, 2018 +// +// Value: 1.61803398874989484820458683436563811772030917980576... +// + +{ + NameShort : "Golden Ratio" + NameLong : "Golden Ratio" + AlgorithmShort : "Series" + AlgorithmLong : "Hypergeometric Series" + Formula : { + SeriesHypergeometric : { + CoefficientP : 1 + CoefficientQ : 3 + CoefficientD : 2 + PolynomialP : [6 -4] + PolynomialQ : [0 8] + PolynomialR : [3 -2] + } + } +} diff --git a/Custom Formulas/Khinchin-Levy Constant.cfg b/Custom Formulas/Khinchin-Levy Constant.cfg new file mode 100644 index 0000000..26f6da8 --- /dev/null +++ b/Custom Formulas/Khinchin-Levy Constant.cfg @@ -0,0 +1,35 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: October 24, 2018 +// +// Value: 1.18656911041562545282172297594723712056835653647205... +// +// Pi^2 +// Beta = ------------- +// 12 * log(2) +// + +{ + NameShort : "Khinchin-Levy" + NameLong : "Khinchin-Levy Constant" + AlgorithmShort : "Definition" + AlgorithmLong : "Direct Definition" + Formula : { + Divide : [ + {Power : [ + {Pi : {}} + 2 + ]} + {LinearCombination : [ + [12 {Log : 2}] + ]} + ] + } +} diff --git a/Custom Formulas/Lemniscate - AGM-Pi.cfg b/Custom Formulas/Lemniscate - AGM-Pi.cfg new file mode 100644 index 0000000..90bad8b --- /dev/null +++ b/Custom Formulas/Lemniscate - AGM-Pi.cfg @@ -0,0 +1,30 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: October 26, 2018 +// +// Value: 5.24411510858423962092967917978223882736550990286324... +// +// 2 Pi +// Lemniscate = ----------------- +// AGM(1, sqrt(2)) +// + +{ + NameShort : "Lemniscate" + NameLong : "Lemniscate Constant" + AlgorithmShort : "AGM-Pi" + AlgorithmLong : "AGM-Pi" + Formula : { + Divide : [ + {LinearCombination : [[2 {Pi : {}}]]} + {AGM : {Sqrt : 2}} + ] + } +} diff --git a/Custom Formulas/Lemniscate - Gauss.cfg b/Custom Formulas/Lemniscate - Gauss.cfg new file mode 100644 index 0000000..9e764c6 --- /dev/null +++ b/Custom Formulas/Lemniscate - Gauss.cfg @@ -0,0 +1,32 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: September 29, 2018 +// +// Value: 5.24411510858423962092967917978223882736550990286324... +// +// Gauss Formula: +// +// Lemniscate = 8 ArcSinlemn(1/2) + 4 ArcSinlemn(7/23) +// +// http://www.numberworld.org/y-cruncher/internals/formulas.html#lemniscate +// + +{ + NameShort : "Lemniscate" + NameLong : "Lemniscate Constant" + AlgorithmShort : "Gauss" + AlgorithmLong : "Gauss Formula" + Formula : { + LinearCombination : [ + [1 {ArcSinlemn : {Coefficient:8 x:1 y:2}}] + [1 {ArcSinlemn : {Coefficient:4 x:7 y:23}}] + ] + } +} diff --git a/Custom Formulas/Lemniscate - Sebah.cfg b/Custom Formulas/Lemniscate - Sebah.cfg new file mode 100644 index 0000000..70da472 --- /dev/null +++ b/Custom Formulas/Lemniscate - Sebah.cfg @@ -0,0 +1,32 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: September 29, 2018 +// +// Value: 5.24411510858423962092967917978223882736550990286324... +// +// Sebah's Formula: +// +// Lemniscate = 8 ArcSinlemn(2/3) - 4 ArcSinlemn(7/137) +// +// http://www.numberworld.org/y-cruncher/internals/formulas.html#lemniscate +// + +{ + NameShort : "Lemniscate" + NameLong : "Lemniscate Constant" + AlgorithmShort : "Sebah" + AlgorithmLong : "Sebah's Formula" + Formula : { + LinearCombination : [ + [1 {ArcSinlemn : {Coefficient:8 x:2 y:3}}] + [1 {ArcSinlemn : {Coefficient:-4 x:7 y:137}}] + ] + } +} diff --git a/Custom Formulas/Lemniscate - Series-Pi.cfg b/Custom Formulas/Lemniscate - Series-Pi.cfg new file mode 100644 index 0000000..751803a --- /dev/null +++ b/Custom Formulas/Lemniscate - Series-Pi.cfg @@ -0,0 +1,40 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: March 2, 2019 +// +// Value: 5.24411510858423962092967917978223882736550990286324... +// +// +// The formula used here is derived from Brown's 2009 formula +// for Gamma(1/4). +// +// Source: http://iamned.com/math/infiniteseries.pdf +// + +{ + NameShort : "Lemniscate" + NameLong : "Lemniscate Constant" + AlgorithmShort : "Series-Pi" + AlgorithmLong : "Series-Pi" + Formula : { + Multiply : [ + {SeriesHypergeometric : { + CoefficientP : 1 + CoefficientQ : 147 + CoefficientD : 1 + PolynomialP : [15435 -143136 20224 1241088 -856064 -2752512 2621440] + PolynomialQ : [0 0 82944 331776 331776] + PolynomialR : [105 -1408 5504 -8192 4096] + }} + {Pi : {Algorithm : "ramanujan"}} + {Invsqrt : 7776} + ] + } +} diff --git a/Custom Formulas/Log(2) - BBP.cfg b/Custom Formulas/Log(2) - BBP.cfg new file mode 100644 index 0000000..744edd6 --- /dev/null +++ b/Custom Formulas/Log(2) - BBP.cfg @@ -0,0 +1,61 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename.cfg". +// y-cruncher custom custom:"filename.cfg" +// +// +// Author: Alexander J. Yee +// Date: October 5, 2018 +// +// Value: 0.69314718055994530941723212145817656807550013436025... +// +// Formula: Unknown BBP Formula +// +// 1 inf ( 1 ( 8 4 1 )) +// Log(2) = --- SUM (-------- (------ - ------ - ------)) +// 8 k=0 ( (-8)^k ( 3k+1 3k+2 3k+3 )) +// +// http://mathworld.wolfram.com/NaturalLogarithmof2.html +// + +{ + NameShort : "Log(2)" + NameLong : "Log(2)" + AlgorithmShort : "BBP (3 terms)" + AlgorithmLong : "Unknown BBP Formula (3 terms)" + Formula : { + LinearCombination : [ + [-1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 1 + Alternating : "true" + PowerCoef : -3 + PowerShift : 3 + PolynomialP : [1] + PolynomialQ : [-2 3] + }}] + [1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 1 + Alternating : "true" + PowerCoef : -3 + PowerShift : 2 + PolynomialP : [1] + PolynomialQ : [-1 3] + }}] + [1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 1 + Alternating : "true" + PowerCoef : -3 + PowerShift : 0 + PolynomialP : [1] + PolynomialQ : [0 3] + }}] + ] + } +} diff --git a/Custom Formulas/Log(2) - Lupas.cfg b/Custom Formulas/Log(2) - Lupas.cfg new file mode 100644 index 0000000..77af91a --- /dev/null +++ b/Custom Formulas/Log(2) - Lupas.cfg @@ -0,0 +1,35 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename.cfg". +// y-cruncher custom custom:"filename.cfg" +// +// +// Author: Alexander J. Yee +// Date: October 5, 2018 +// +// Value: 0.69314718055994530941723212145817656807550013436025... +// +// Formula: A. Lupas (2000) +// +// 3 1 inf ( (5k + 1) (2k)! ) +// Log(2) = --- + --- SUM (-------------------------) +// 4 4 k=1 ( (-16)^k k (2k + 1) k!^2 ) +// + +{ + NameShort : "Log(2)" + NameLong : "Log(2)" + AlgorithmShort : "Lupas" + AlgorithmLong : "Lupas (2000)" + Formula : { + SeriesHypergeometric : { + CoefficientP : 1 + CoefficientQ : 3 + CoefficientD : 4 + PolynomialP : [-1 -3 10] + PolynomialQ : [0 0 -8 -16] + PolynomialR : [0 -1 0 4] + } + } +} diff --git a/Custom Formulas/Log(2) - Machin (3 terms).cfg b/Custom Formulas/Log(2) - Machin (3 terms).cfg new file mode 100644 index 0000000..5a4f0b6 --- /dev/null +++ b/Custom Formulas/Log(2) - Machin (3 terms).cfg @@ -0,0 +1,29 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: September 29, 2018 +// +// Value: 0.69314718055994530941723212145817656807550013436025... +// +// Log(2) = 18 ArcCoth(26) - 2 ArcCoth(4801) + 8 ArcCoth(8749) +// + +{ + NameShort : "Log(2)" + NameLong : "Log(2)" + AlgorithmShort : "Machin (3 terms)" + AlgorithmLong : "Machin-like Formula (3 terms)" + Formula : { + LinearCombination : [ + [1 {ArcCoth : {Coefficient:18 x:26}}] + [1 {ArcCoth : {Coefficient:-2 x:4801}}] + [1 {ArcCoth : {Coefficient:8 x:8749}}] + ] + } +} diff --git a/Custom Formulas/Log(2) - Machin (4 terms).cfg b/Custom Formulas/Log(2) - Machin (4 terms).cfg new file mode 100644 index 0000000..f0ec806 --- /dev/null +++ b/Custom Formulas/Log(2) - Machin (4 terms).cfg @@ -0,0 +1,30 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: September 29, 2018 +// +// Value: 0.69314718055994530941723212145817656807550013436025... +// +// Log(2) = 144 ArcCoth(251) + 54 ArcCoth(449) - 38 ArcCoth(4801) + 62 ArcCoth(8749) +// + +{ + NameShort : "Log(2)" + NameLong : "Log(2)" + AlgorithmShort : "Machin (4 terms)" + AlgorithmLong : "Machin-like Formula (4 terms)" + Formula : { + LinearCombination : [ + [1 {ArcCoth : {Coefficient:144 x:251}}] + [1 {ArcCoth : {Coefficient:54 x:449}}] + [1 {ArcCoth : {Coefficient:-38 x:4801}}] + [1 {ArcCoth : {Coefficient:62 x:8749}}] + ] + } +} diff --git a/Custom Formulas/Log(Pi) (unoptimized).cfg b/Custom Formulas/Log(Pi) (unoptimized).cfg new file mode 100644 index 0000000..d41cc00 --- /dev/null +++ b/Custom Formulas/Log(Pi) (unoptimized).cfg @@ -0,0 +1,27 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: November 2, 2018 +// +// Value: 1.14472988584940017414342735135305871164729481291531... +// +// This is not efficient because it computes Pi twice. +// + +{ + NameShort : "Log(Pi)" + NameLong : "Log(Pi)" + AlgorithmShort : "Definition" + AlgorithmLong : "Direct Definition" + Formula : { + Log: { + Pi : {} + } + } +} diff --git a/Custom Formulas/Log(Pi).cfg b/Custom Formulas/Log(Pi).cfg new file mode 100644 index 0000000..96ad000 --- /dev/null +++ b/Custom Formulas/Log(Pi).cfg @@ -0,0 +1,37 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: November 30, 2018 +// +// Value: 1.14472988584940017414342735135305871164729481291531... +// +// Same as "Log(Pi).cfg", but avoids computing Pi twice. +// + +{ + NameShort : "Log(Pi)" + NameLong : "Log(Pi)" + AlgorithmShort : "Definition" + AlgorithmLong : "Direct Definition" + Formula : { + Scope : { + Locals : [ + {pi : {Pi : {}}} + {log2 : {Log : 2}} + ] + Formula : { + Log-AGM : { + Pi : "pi" + Log2 : "log2" + Argument : "pi" + } + } + } + } +} diff --git a/Custom Formulas/Log10(2).cfg b/Custom Formulas/Log10(2).cfg new file mode 100644 index 0000000..1c495ed --- /dev/null +++ b/Custom Formulas/Log10(2).cfg @@ -0,0 +1,36 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Originally from 鲍东方 +// Date: February 8, 2019 +// +// Value: 0.30102999566398119521373889472449302676818988146210... +// + +{ + NameShort : "Log10(2)" + NameLong : "Log base 10 of 2" + AlgorithmShort : "Machin (4 terms)" + AlgorithmLong : "Machin-like Formula (4 terms)" + Formula : { + Scope : { + Locals : [ + {t0 : {ArcCoth : {x : 251}}} + {t1 : {ArcCoth : {x : 449}}} + {t2 : {ArcCoth : {x : 4801}}} + {t3 : {ArcCoth : {x : 8749}}} + ] + Formula : { + Divide : [ + {LinearCombination : [[144 "t0"][ 54 "t1"][ -38 "t2"][ 62 "t3"]]} + {LinearCombination : [[478 "t0"][180 "t1"][-126 "t2"][206 "t3"]]} + ] + } + } + } +} diff --git a/Custom Formulas/Pi - BBP (Original).cfg b/Custom Formulas/Pi - BBP (Original).cfg new file mode 100644 index 0000000..48af987 --- /dev/null +++ b/Custom Formulas/Pi - BBP (Original).cfg @@ -0,0 +1,71 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename.cfg". +// y-cruncher custom custom:"filename.cfg" +// +// +// Author: Alexander J. Yee +// Date: October 1, 2018 +// +// Value = 3.14159265358979323846264338327950288419716939937510... +// +// Formula: Original BBP Formula +// +// inf ( 1 ( 4 2 1 1 )) +// Pi = SUM (------ (------ - ------ - ------ - ------)) +// k=0 ( 16^k ( 8k+1 8k+4 8k+5 8k+6 )) +// +// https://en.wikipedia.org/wiki/Bailey%E2%80%93Borwein%E2%80%93Plouffe_formula +// + +{ + NameShort : "Pi" + NameLong : "Pi" + AlgorithmShort : "BBP (Original)" + AlgorithmLong : "Original BBP Formula" + Formula : { + LinearCombination : [ + [1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 1 + Alternating : "false" + PowerCoef : -4 + PowerShift : 6 + PolynomialP : [1] + PolynomialQ : [-7 8] + }}] + [-1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 1 + Alternating : "false" + PowerCoef : -4 + PowerShift : 3 + PolynomialP : [1] + PolynomialQ : [-1 2] + }}] + [-1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 1 + Alternating : "false" + PowerCoef : -4 + PowerShift : 4 + PolynomialP : [1] + PolynomialQ : [-3 8] + }}] + [-1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 1 + Alternating : "false" + PowerCoef : -4 + PowerShift : 3 + PolynomialP : [1] + PolynomialQ : [-1 4] + }}] + ] + } +} diff --git a/Custom Formulas/Pi - Bellard.cfg b/Custom Formulas/Pi - Bellard.cfg new file mode 100644 index 0000000..64d0f5f --- /dev/null +++ b/Custom Formulas/Pi - Bellard.cfg @@ -0,0 +1,100 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename.cfg". +// y-cruncher custom custom:"filename.cfg" +// +// +// Author: Alexander J. Yee +// Date: October 1, 2018 +// +// Value = 3.14159265358979323846264338327950288419716939937510... +// Formula: Fabrice Bellard's BBP Formula +// +// 1 inf ( (-1)^k ( 32 1 256 64 4 4 1 )) +// Pi = ---- SUM (-------- (- ------ - ------ + ------- - ------- - ------- - ------- + -------)) +// 64 k=0 ( 1024^k ( 4k+1 4k+3 10k+1 10k+3 10k+5 10k+7 10k+9 )) +// +// https://en.wikipedia.org/wiki/Bellard%27s_formula +// + +{ + NameShort : "Pi" + NameLong : "Pi" + AlgorithmShort : "Bellard" + AlgorithmLong : "Fabrice Bellard's BBP Formula" + Formula : { + LinearCombination : [ + [1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 1 + Alternating : "true" + PowerCoef : -10 + PowerShift : 9 + PolynomialP : [1] + PolynomialQ : [-3 4] + }}] + [1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 1 + Alternating : "true" + PowerCoef : -10 + PowerShift : 4 + PolynomialP : [1] + PolynomialQ : [-1 4] + }}] + [-1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 1 + Alternating : "true" + PowerCoef : -10 + PowerShift : 12 + PolynomialP : [1] + PolynomialQ : [-9 10] + }}] + [1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 1 + Alternating : "true" + PowerCoef : -10 + PowerShift : 10 + PolynomialP : [1] + PolynomialQ : [-7 10] + }}] + [1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 5 + Alternating : "true" + PowerCoef : -10 + PowerShift : 6 + PolynomialP : [1] + PolynomialQ : [-1 2] + }}] + [1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 1 + Alternating : "true" + PowerCoef : -10 + PowerShift : 6 + PolynomialP : [1] + PolynomialQ : [-3 10] + }}] + [-1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 1 + Alternating : "true" + PowerCoef : -10 + PowerShift : 4 + PolynomialP : [1] + PolynomialQ : [-1 10] + }}] + ] + } +} diff --git a/Custom Formulas/Pi - Brown.cfg b/Custom Formulas/Pi - Brown.cfg new file mode 100644 index 0000000..3799e15 --- /dev/null +++ b/Custom Formulas/Pi - Brown.cfg @@ -0,0 +1,37 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: February 26, 2019 +// +// Value: 3.14159265358979323846264338327950288419716939937510... +// +// Source: http://iamned.com/math/infiniteseries.pdf +// + +{ + NameShort : "Pi" + NameLong : "Pi" + AlgorithmShort : "Brown" + AlgorithmLong : "Brown (2009)" + Formula : { + Multiply : [ + { + SeriesHypergeometric : { + CoefficientP : 1 + CoefficientQ : 109 + CoefficientD : 1 + PolynomialP : [0 109 -88 -260] + PolynomialQ : [90 648 648] + PolynomialR : [0 1 -2] + } + } + {Invsqrt : 1200} + ] + } +} diff --git a/Custom Formulas/Pi - Chudnovsky.cfg b/Custom Formulas/Pi - Chudnovsky.cfg new file mode 100644 index 0000000..736c42f --- /dev/null +++ b/Custom Formulas/Pi - Chudnovsky.cfg @@ -0,0 +1,38 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: September 29, 2018 +// +// Value: 3.14159265358979323846264338327950288419716939937510... +// +// https://en.wikipedia.org/wiki/Chudnovsky_algorithm +// + +{ + NameShort : "Pi" + NameLong : "Pi" + AlgorithmShort : "Chudnovsky" + AlgorithmLong : "Chudnovsky (1988)" + Formula : { + Multiply : [ + { + SeriesHypergeometric : { + Power : -1 + CoefficientP : 1 + CoefficientQ : 13591409 + CoefficientD : 4270934400 + PolynomialP : [-67957045 -2100495856 23608573992 -57896553024 39250089648] + PolynomialQ : [0 0 0 -10939058860032000] + PolynomialR : [-5 46 -108 72] + } + } + {Invsqrt : 10005} + ] + } +} diff --git a/Custom Formulas/Pi - Hwang (1997).cfg b/Custom Formulas/Pi - Hwang (1997).cfg new file mode 100644 index 0000000..ade8076 --- /dev/null +++ b/Custom Formulas/Pi - Hwang (1997).cfg @@ -0,0 +1,79 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename.cfg". +// y-cruncher custom custom:"filename.cfg" +// +// +// Author: Alexander J. Yee +// Date: September 30, 2018 +// +// Value: 3.14159265358979323846264338327950288419716939937510... +// +// Formula: Chien-Lih Hwang's 6-term formula (1997) +// +// Pi = 732 ArcTan(1/239) + 128 ArcTan(1/1023) - 272 ArcTan(1/5832) +// + 48 ArcTan(1/110443) - 48 ArcTan(1/4841182) - 400 ArcTan(1/6826318) +// +// This uses Euler's ArcTan formula which is slightly faster +// than the usual Taylor series. +// + +{ + NameShort : "Pi" + NameLong : "Pi" + AlgorithmShort : "Hwang" + AlgorithmLong : "Hwang's 6-term Formula (1997)" + Formula : { + LinearCombination : [ + [87474 {SeriesHypergeometric : { + CoefficientP : 1 + CoefficientQ : 1 + CoefficientD : 28561 + PolynomialP : [0 1] + PolynomialQ : [28561 57122] + PolynomialR : [0 1] + }}] + [65472 {SeriesHypergeometric : { + CoefficientP : 1 + CoefficientQ : 1 + CoefficientD : 523265 + PolynomialP : [0 1] + PolynomialQ : [523265 1046530] + PolynomialR : [0 1] + }}] + [-1586304 {SeriesHypergeometric : { + CoefficientP : 1 + CoefficientQ : 1 + CoefficientD : 34012225 + PolynomialP : [0 2] + PolynomialQ : [34012225 68024450] + PolynomialR : [0 2] + }}] + [2650632 {SeriesHypergeometric : { + CoefficientP : 1 + CoefficientQ : 1 + CoefficientD : 6098828125 + PolynomialP : [0 1] + PolynomialQ : [6098828125 12197656250] + PolynomialR : [0 1] + }}] + [-232376736 {SeriesHypergeometric : { + CoefficientP : 1 + CoefficientQ : 1 + CoefficientD : 23437043157125 + PolynomialP : [0 2] + PolynomialQ : [23437043157125 46874086314250] + PolynomialR : [0 2] + }}] + [-109221088 {SeriesHypergeometric : { + CoefficientP : 1 + CoefficientQ : 1 + CoefficientD : 1863944697485 + PolynomialP : [0 2] + PolynomialQ : [46598617437125 93197234874250] + PolynomialR : [0 2] + }}] + ] + } +} diff --git a/Custom Formulas/Pi - Machin.cfg b/Custom Formulas/Pi - Machin.cfg new file mode 100644 index 0000000..c59b148 --- /dev/null +++ b/Custom Formulas/Pi - Machin.cfg @@ -0,0 +1,46 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename.cfg". +// y-cruncher custom custom:"filename.cfg" +// +// +// Author: Alexander J. Yee +// Date: September 30, 2018 +// +// Value: 3.14159265358979323846264338327950288419716939937510... +// +// Formula: Machin's original 2-term formula +// +// Pi = 16 ArcTan(1/5) - 4 ArcTan(1/239) +// +// This uses Euler's ArcTan formula which is slightly faster +// than the usual Taylor series. +// + +{ + NameShort : "Pi" + NameLong : "Pi" + AlgorithmShort : "Machin" + AlgorithmLong : "Machin's Formula" + Formula : { + LinearCombination : [ + [80 {SeriesHypergeometric : { + CoefficientP : 1 + CoefficientQ : 1 + CoefficientD : 26 + PolynomialP : [0 1] + PolynomialQ : [13 26] + PolynomialR : [0 1] + }}] + [-956 {SeriesHypergeometric : { + CoefficientP : 1 + CoefficientQ : 1 + CoefficientD : 57122 + PolynomialP : [0 1] + PolynomialQ : [28561 57122] + PolynomialR : [0 1] + }}] + ] + } +} diff --git a/Custom Formulas/Pi - Ramanujan.cfg b/Custom Formulas/Pi - Ramanujan.cfg new file mode 100644 index 0000000..2626ffd --- /dev/null +++ b/Custom Formulas/Pi - Ramanujan.cfg @@ -0,0 +1,38 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: September 29, 2018 +// +// Value: 3.14159265358979323846264338327950288419716939937510... +// +// http://www.numberworld.org/y-cruncher/internals/binary-splitting-library.html#pi_ramanujan +// + +{ + NameShort : "Pi" + NameLong : "Pi" + AlgorithmShort : "Ramanujan" + AlgorithmLong : "Ramanujan (1910)" + Formula : { + Multiply : [ + { + SeriesHypergeometric : { + Power : -1 + CoefficientP : 1 + CoefficientQ : 1103 + CoefficientD : 9801 + PolynomialP : [-3309 -54904 527636 -1231424 844480] + PolynomialQ : [0 0 0 3073907232] + PolynomialR : [-3 22 -48 32] + } + } + {Invsqrt : 8} + ] + } +} diff --git a/Custom Formulas/Pi - Sharp.cfg b/Custom Formulas/Pi - Sharp.cfg new file mode 100644 index 0000000..16b7f9e --- /dev/null +++ b/Custom Formulas/Pi - Sharp.cfg @@ -0,0 +1,38 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename.cfg". +// y-cruncher custom custom:"filename.cfg" +// +// +// Author: Alexander J. Yee +// Date: September 29, 2018 +// +// Value = 3.14159265358979323846264338327950288419716939937510... +// +// Formula: Abraham Sharp (1717) +// +// Which corresponds to ArcTan(1/sqrt(3)) +// + +{ + NameShort : "Pi" + NameLong : "Pi" + AlgorithmShort : "Sharp" + AlgorithmLong : "Abraham Sharp (1717)" + Formula : { + Multiply : [ + { + SeriesHypergeometric : { + CoefficientP : 6 + CoefficientQ : 6 + CoefficientD : 1 + PolynomialP : [1] + PolynomialQ : [-3 -6] + PolynomialR : [1 2] + } + } + {Invsqrt : 3} + ] + } +} diff --git a/Custom Formulas/Pi - Stormer.cfg b/Custom Formulas/Pi - Stormer.cfg new file mode 100644 index 0000000..e2945e1 --- /dev/null +++ b/Custom Formulas/Pi - Stormer.cfg @@ -0,0 +1,62 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename.cfg". +// y-cruncher custom custom:"filename.cfg" +// +// +// Author: Alexander J. Yee +// Date: September 30, 2018 +// +// Value: 3.14159265358979323846264338327950288419716939937510... +// +// Formula: Carl Stormer's 4-term formula +// +// Pi = 176 ArcTan(1/57) + 28 ArcTan(1/239) - 48 ArcTan(1/682) + 96 ArcTan(1/12943) +// +// This uses Euler's ArcTan formula which is slightly faster +// than the usual Taylor series. +// + +{ + NameShort : "Pi" + NameLong : "Pi" + AlgorithmShort : "Stormer" + AlgorithmLong : "Stormer's 4-term formula" + Formula : { + LinearCombination : [ + [5016 {SeriesHypergeometric : { + CoefficientP : 1 + CoefficientQ : 1 + CoefficientD : 1625 + PolynomialP : [0 1] + PolynomialQ : [1625 3250] + PolynomialR : [0 1] + }}] + [3346 {SeriesHypergeometric : { + CoefficientP : 1 + CoefficientQ : 1 + CoefficientD : 28561 + PolynomialP : [0 1] + PolynomialQ : [28561 57122] + PolynomialR : [0 1] + }}] + [-32736 {SeriesHypergeometric : { + CoefficientP : 1 + CoefficientQ : 1 + CoefficientD : 465125 + PolynomialP : [0 2] + PolynomialQ : [465125 930250] + PolynomialR : [0 2] + }}] + [621264 {SeriesHypergeometric : { + CoefficientP : 1 + CoefficientQ : 1 + CoefficientD : 83760625 + PolynomialP : [0 1] + PolynomialQ : [83760625 167521250] + PolynomialR : [0 1] + }}] + ] + } +} diff --git a/Custom Formulas/Pi - Takano.cfg b/Custom Formulas/Pi - Takano.cfg new file mode 100644 index 0000000..d5da960 --- /dev/null +++ b/Custom Formulas/Pi - Takano.cfg @@ -0,0 +1,62 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename.cfg". +// y-cruncher custom custom:"filename.cfg" +// +// +// Author: Alexander J. Yee +// Date: September 30, 2018 +// +// Value: 3.14159265358979323846264338327950288419716939937510... +// +// Formula: Kikuo Takano's 4-term formula +// +// Pi = 48 ArcTan(1/49) + 128 ArcTan(1/57) - 20 ArcTan(1/239) + 48 ArcTan(1/110443) +// +// This uses Euler's ArcTan formula which is slightly faster +// than the usual Taylor series. +// + +{ + NameShort : "Pi" + NameLong : "Pi" + AlgorithmShort : "Takano" + AlgorithmLong : "Takano's 4-term Formula" + Formula : { + LinearCombination : [ + [1176 {SeriesHypergeometric : { + CoefficientP : 1 + CoefficientQ : 1 + CoefficientD : 1201 + PolynomialP : [0 1] + PolynomialQ : [1201 2402] + PolynomialR : [0 1] + }}] + [3648 {SeriesHypergeometric : { + CoefficientP : 1 + CoefficientQ : 1 + CoefficientD : 1625 + PolynomialP : [0 1] + PolynomialQ : [1625 3250] + PolynomialR : [0 1] + }}] + [-2390 {SeriesHypergeometric : { + CoefficientP : 1 + CoefficientQ : 1 + CoefficientD : 28561 + PolynomialP : [0 1] + PolynomialQ : [28561 57122] + PolynomialR : [0 1] + }}] + [2650632 {SeriesHypergeometric : { + CoefficientP : 1 + CoefficientQ : 1 + CoefficientD : 6098828125 + PolynomialP : [0 1] + PolynomialQ : [6098828125 12197656250] + PolynomialR : [0 1] + }}] + ] + } +} diff --git a/Custom Formulas/Pi^-1 - Native.cfg b/Custom Formulas/Pi^-1 - Native.cfg new file mode 100644 index 0000000..8ef3fbe --- /dev/null +++ b/Custom Formulas/Pi^-1 - Native.cfg @@ -0,0 +1,25 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: October 2, 2018 +// +// Value: 0.31830988618379067153776752674502872406891929148091... +// + +{ + NameShort : "Pi^-1" + NameLong : "1 / Pi" + AlgorithmShort : "Native" + AlgorithmLong : "Native Implementation" + Formula : { + Pi : { + Power : -1 + } + } +} diff --git a/Custom Formulas/Sin(1) - Half Angle Formula.cfg b/Custom Formulas/Sin(1) - Half Angle Formula.cfg new file mode 100644 index 0000000..d47ef0f --- /dev/null +++ b/Custom Formulas/Sin(1) - Half Angle Formula.cfg @@ -0,0 +1,40 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: October 10, 2018 +// +// Value: 0.84147098480789650665250232163029899962256306079837... +// +// Formula: 2 Sin(1/2) Cos(1/2) +// + +{ + NameShort : "Sin(1)" + NameLong : "Sine of 1" + AlgorithmShort : "Half Angle Formula" + AlgorithmLong : "2 Sin(1/2) Cos(1/2)" + Formula : { + Multiply : [ + {SeriesHyperdescent : { + CoefficientP : 1 + CoefficientQ : 1 + CoefficientD : 1 + PolynomialP : [1] + PolynomialQ : [0 -8 -16] + }} + {SeriesHyperdescent : { + CoefficientP : 1 + CoefficientQ : 1 + CoefficientD : 1 + PolynomialP : [1] + PolynomialQ : [0 8 -16] + }} + ] + } +} diff --git a/Custom Formulas/Sin(1) - Series.cfg b/Custom Formulas/Sin(1) - Series.cfg new file mode 100644 index 0000000..ccfe067 --- /dev/null +++ b/Custom Formulas/Sin(1) - Series.cfg @@ -0,0 +1,31 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: September 30, 2018 +// +// Value: 0.84147098480789650665250232163029899962256306079837... +// +// Formula: Taylor Series of Sin(x) +// + +{ + NameShort : "Sin(1)" + NameLong : "Sine of 1" + AlgorithmShort : "Series" + AlgorithmLong : "Taylor Series of sin(1)" + Formula : { + SeriesHyperdescent : { + CoefficientP : 1 + CoefficientQ : 1 + CoefficientD : 1 + PolynomialP : [1] + PolynomialQ : [0 -2 -4] + } + } +} diff --git a/Custom Formulas/Sqrt(2) - Native Invsqrt.cfg b/Custom Formulas/Sqrt(2) - Native Invsqrt.cfg new file mode 100644 index 0000000..18a7114 --- /dev/null +++ b/Custom Formulas/Sqrt(2) - Native Invsqrt.cfg @@ -0,0 +1,26 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: October 6, 2018 +// +// Value: 1.41421356237309504880168872420969807856967187537694... +// + +{ + NameShort : "Sqrt(2)" + NameLong : "Sqrt(2)" + AlgorithmShort : "Invsqrt" + AlgorithmLong : "Native Invsqrt" + Formula : { + Shift : [ + {Invsqrt : 2} + 1 + ] + } +} diff --git a/Custom Formulas/Sqrt(2) - Series.cfg b/Custom Formulas/Sqrt(2) - Series.cfg new file mode 100644 index 0000000..957c8bd --- /dev/null +++ b/Custom Formulas/Sqrt(2) - Series.cfg @@ -0,0 +1,30 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: November 11, 2018 +// +// Value: 1.41421356237309504880168872420969807856967187537694... +// + +{ + NameShort : "Sqrt(2)" + NameLong : "Sqrt(2)" + AlgorithmShort : "Series" + AlgorithmLong : "Hypergeometric Series" + Formula : { + SeriesHypergeometric : { + CoefficientP : 1 + CoefficientQ : 1 + CoefficientD : 1 + PolynomialP : [1 -2] + PolynomialQ : [0 -4] + PolynomialR : [1 -2] + } + } +} diff --git a/Custom Formulas/Sqrt(Pi).cfg b/Custom Formulas/Sqrt(Pi).cfg new file mode 100644 index 0000000..e324249 --- /dev/null +++ b/Custom Formulas/Sqrt(Pi).cfg @@ -0,0 +1,25 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: October 24, 2018 +// +// Value: 1.77245385090551602729816748334114518279754945612238... +// + +{ + NameShort : "Sqrt(Pi)" + NameLong : "Sqrt(Pi)" + AlgorithmShort : "Simple" + AlgorithmLong : "Simple" + Formula : { + Invsqrt : { + Pi : { Power : -1 } + } + } +} diff --git a/Custom Formulas/Universal Parabolic Constant (unoptimized).cfg b/Custom Formulas/Universal Parabolic Constant (unoptimized).cfg new file mode 100644 index 0000000..b05b8fe --- /dev/null +++ b/Custom Formulas/Universal Parabolic Constant (unoptimized).cfg @@ -0,0 +1,35 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: November 4, 2018 +// +// Value: 2.29558714939263807403429804918949038759783220363858... +// +// P = Log(1 + sqrt(2)) + sqrt(2) +// +// https://en.wikipedia.org/wiki/Universal_parabolic_constant +// + +{ + NameShort : "Universal Parabolic Constant" + NameLong : "Universal Parabolic Constant" + AlgorithmShort : "Definition" + AlgorithmLong : "Direct Definition" + Formula : { + LinearCombination : [ + [1 {Log : { + LinearCombination : [ + [1 1] + [1 {Sqrt : 2}] + ] + }}] + [1 {Sqrt : 2}] + ] + } +} diff --git a/Custom Formulas/Universal Parabolic Constant.cfg b/Custom Formulas/Universal Parabolic Constant.cfg new file mode 100644 index 0000000..4bc31fd --- /dev/null +++ b/Custom Formulas/Universal Parabolic Constant.cfg @@ -0,0 +1,45 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: November 4, 2018 +// +// Value: 2.29558714939263807403429804918949038759783220363858... +// +// P = Log(1 + sqrt(2)) + sqrt(2) +// +// https://en.wikipedia.org/wiki/Universal_parabolic_constant +// +// Same as "Universal Parabolic Constant (unoptimized).cfg", +// but avoids computing sqrt(2) twice. +// + +{ + NameShort : "Universal Parabolic Constant" + NameLong : "Universal Parabolic Constant" + AlgorithmShort : "Definition" + AlgorithmLong : "Direct Definition" + Formula : { + Scope : { + Locals : [ + {sqrt2 : {Sqrt : 2}} + ] + Formula : { + LinearCombination : [ + [1 {Log : { + LinearCombination : [ + [1 1] + [1 "sqrt2"] + ] + }}] + [1 "sqrt2"] + ] + } + } + } +} diff --git a/Custom Formulas/Unnormalized Fresnel C(1).cfg b/Custom Formulas/Unnormalized Fresnel C(1).cfg new file mode 100644 index 0000000..d80a84d --- /dev/null +++ b/Custom Formulas/Unnormalized Fresnel C(1).cfg @@ -0,0 +1,34 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: November 24, 2018 +// +// Value: 0.90452423790027208147478836683255714580799182059550... +// +// 1 ( ) +// C(1) = Integrate( Cos(x^2) ) dx +// 0 ( ) +// + +{ + NameShort : "Unnormalized Fresnel C(1)" + NameLong : "Unnormalized Fresnel C(1)" + AlgorithmShort : "Series" + AlgorithmLong : "Taylor Series" + Formula : { + SeriesHypergeometric : { + CoefficientP : 1 + CoefficientQ : 1 + CoefficientD : 1 + PolynomialP : [1] + PolynomialQ : [0 2 4 -16] + PolynomialR : [1 4] + } + } +} diff --git a/Custom Formulas/Unnormalized Fresnel S(1).cfg b/Custom Formulas/Unnormalized Fresnel S(1).cfg new file mode 100644 index 0000000..dbc29d0 --- /dev/null +++ b/Custom Formulas/Unnormalized Fresnel S(1).cfg @@ -0,0 +1,34 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: November 24, 2018 +// +// Value: 0.31026830172338110180815242316539650757450938883244... +// +// 1 ( ) +// S(1) = Integrate( Sin(x^2) ) dx +// 0 ( ) +// + +{ + NameShort : "Unnormalized Fresnel S(1)" + NameLong : "Unnormalized Fresnel S(1)" + AlgorithmShort : "Series" + AlgorithmLong : "Taylor Series" + Formula : { + SeriesHypergeometric : { + CoefficientP : 1 + CoefficientQ : 1 + CoefficientD : 3 + PolynomialP : [3] + PolynomialQ : [0 -6 -20 -16] + PolynomialR : [3 4] + } + } +} diff --git a/Custom Formulas/Zeta(2) - Chudnovsky.cfg b/Custom Formulas/Zeta(2) - Chudnovsky.cfg new file mode 100644 index 0000000..189056f --- /dev/null +++ b/Custom Formulas/Zeta(2) - Chudnovsky.cfg @@ -0,0 +1,43 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: October 6, 2018 +// +// Value: 1.64493406684822643647241516664602518921894990120679... +// +// Zeta(2) = Pi^2 / 6 +// +// https://en.wikipedia.org/wiki/Chudnovsky_algorithm +// + +{ + NameShort : "Zeta(2)" + NameLong : "Zeta(2)" + AlgorithmShort : "Chudnovsky" + AlgorithmLong : "Chudnovsky (1988)" + Formula : { + LinearCombination : [ + [ + 303862746112000 + {Power : [ + {SeriesHypergeometric : { + Power : -1 + CoefficientP : 1 + CoefficientQ : 13591409 + CoefficientD : 1 + PolynomialP : [-67957045 -2100495856 23608573992 -57896553024 39250089648] + PolynomialQ : [0 0 0 -10939058860032000] + PolynomialR : [-5 46 -108 72] + }} + 2 + ]} + ] + ] + } +} diff --git a/Custom Formulas/Zeta(2) - Direct.cfg b/Custom Formulas/Zeta(2) - Direct.cfg new file mode 100644 index 0000000..5b30cf5 --- /dev/null +++ b/Custom Formulas/Zeta(2) - Direct.cfg @@ -0,0 +1,34 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: November 10, 2018 +// +// Value: 1.64493406684822643647241516664602518921894990120679... +// +// Zeta(2) = Pi^2 / 6 +// +// This uses Ramanujan's formula for Pi so that it's independent +// from the other implementation. +// + +{ + NameShort : "Zeta(2)" + NameLong : "Zeta(2)" + AlgorithmShort : "Direct" + AlgorithmLong : "Direct Formula" + Formula : { + Divide : [ + {Power : [ + {Pi : {Algorithm : "ramanujan"}} + 2 + ]} + 6 + ] + } +} diff --git a/Custom Formulas/Zeta(3) - Amdeberhan-Zeilberger.cfg b/Custom Formulas/Zeta(3) - Amdeberhan-Zeilberger.cfg new file mode 100644 index 0000000..1ba6e00 --- /dev/null +++ b/Custom Formulas/Zeta(3) - Amdeberhan-Zeilberger.cfg @@ -0,0 +1,38 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: September 29, 2018 +// +// Value: 1.20205690315959428539973816151144999076498629234049... +// +// Formula: Amdeberhan-Zeilberger (1997) +// +// 1 inf ( (-1)^k (205k^2 + 250k + 77) k!^10 ) +// Zeta(3) = ---- SUM (-----------------------------------) +// 64 k=0 ( (2k + 1)!^5 ) +// +// https://arxiv.org/pdf/math/9804121.pdf +// + +{ + NameShort : "Zeta(3)" + NameLong : "Zeta(3) - Apery's Constant" + AlgorithmShort : "AZ" + AlgorithmLong : "Amdeberhan-Zeilberger (1997)" + Formula : { + SeriesHypergeometric : { + CoefficientP : 1 + CoefficientQ : 77 + CoefficientD : 64 + PolynomialP : [0 0 0 0 0 77 250 205] + PolynomialQ : [-32 -320 -1280 -2560 -2560 -1024] + PolynomialR : [0 0 0 0 0 1] + } + } +} diff --git a/Custom Formulas/Zeta(3) - Amdeberhan.cfg b/Custom Formulas/Zeta(3) - Amdeberhan.cfg new file mode 100644 index 0000000..780f755 --- /dev/null +++ b/Custom Formulas/Zeta(3) - Amdeberhan.cfg @@ -0,0 +1,36 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: September 30, 2018 +// +// Value: 1.20205690315959428539973816151144999076498629234049... +// +// Formula: Amdeberhan (1996) +// +// 1 inf ( (-1)^k (56k^2 - 32k + 5) (k - 1)!^3 ) +// Zeta(3) = - --- SUM (-------------------------------------) +// 4 k=1 ( (2k - 1)^2 (3k)! ) +// + +{ + NameShort : "Zeta(3)" + NameLong : "Zeta(3) - Apery's Constant" + AlgorithmShort : "Amdeberhan" + AlgorithmLong : "Amdeberhan (1996)" + Formula : { + SeriesHypergeometric : { + CoefficientP : 1 + CoefficientQ : 29 + CoefficientD : 24 + PolynomialP : [0 0 0 29 80 56] + PolynomialQ : [-6 -57 -210 -375 -324 -108] + PolynomialR : [0 0 0 1 4 4] + } + } +} diff --git a/Custom Formulas/Zeta(3) - Hjortnaes.cfg b/Custom Formulas/Zeta(3) - Hjortnaes.cfg new file mode 100644 index 0000000..d4400ad --- /dev/null +++ b/Custom Formulas/Zeta(3) - Hjortnaes.cfg @@ -0,0 +1,36 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: September 30, 2018 +// +// Value: 1.20205690315959428539973816151144999076498629234049... +// +// Formula: Hjortnaes (1953), rediscovered by Apery (1979) +// +// 5 inf ( (-1)^k k!^2 ) +// Zeta(3) = - --- SUM (--------------) +// 2 k=0 ( (2k)! k^3 ) +// + +{ + NameShort : "Zeta(3)" + NameLong : "Zeta(3) - Apery's Constant" + AlgorithmShort : "Hjortnaes" + AlgorithmLong : "Hjortnaes (1953)" + Formula : { + SeriesHypergeometric : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 2 + PolynomialP : [-5] + PolynomialQ : [0 0 2 -4] + PolynomialR : [0 0 0 1] + } + } +} diff --git a/Custom Formulas/Zeta(3) - Mohammed.cfg b/Custom Formulas/Zeta(3) - Mohammed.cfg new file mode 100644 index 0000000..080f403 --- /dev/null +++ b/Custom Formulas/Zeta(3) - Mohammed.cfg @@ -0,0 +1,38 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: September 30, 2018 +// +// Value: 1.20205690315959428539973816151144999076498629234049... +// +// Formula: Mohamud Mohammed (2005) +// +// 1 inf ( (-1)^k (2k)!^3 (k + 1)!^6 P(k) ) +// Zeta(3) = --- SUM (--------------------------------) +// 2 k=0 ( (k + 1)^2 (3k + 3)!^4 ) +// +// P(k) = 40885k^5 + 124346k^4 + 150160k^3 + 89888k^2 + 26629k + 3116 +// + +{ + NameShort : "Zeta(3)" + NameLong : "Zeta(3) - Apery's Constant" + AlgorithmShort : "Mohammed" + AlgorithmLong : "Mohammed (2005)" + Formula : { + SeriesHypergeometric : { + CoefficientP : 1 + CoefficientQ : 3116 + CoefficientD : 2592 + PolynomialP : [0 0 0 -24928 -63464 259952 756384 -712080 -3021000 -364496 4033184 2616640] + PolynomialQ : [-1296 -23328 -180792 -787320 -2106081 -3542940 -3661038 -2125764 -531441] + PolynomialR : [0 0 0 -8 32 -8 -80 32 64] + } + } +} diff --git a/Custom Formulas/Zeta(3) - Wedeniwski.cfg b/Custom Formulas/Zeta(3) - Wedeniwski.cfg new file mode 100644 index 0000000..3280116 --- /dev/null +++ b/Custom Formulas/Zeta(3) - Wedeniwski.cfg @@ -0,0 +1,40 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: September 29, 2018 +// +// Value: 1.20205690315959428539973816151144999076498629234049... +// +// Formula: Wedeniwski (1998) +// +// 1 inf ( (-1)^k ((2k + 1)! (2k)! k!)^3 P(k) ) +// Zeta(3) = ---- SUM (------------------------------------) +// 24 k=0 ( (3k + 2)! (4k + 3)!^3 ) +// +// P(k) = 126392k^5 + 412708k^4 + 531578k^3 + 336367k^2 + 104000k + 12463 +// +// http://sites.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/Zeta3.txt +// + +{ + NameShort : "Zeta(3)" + NameLong : "Zeta(3) - Apery's Constant" + AlgorithmShort : "Wedeniwski" + AlgorithmLong : "Wedeniwski (1998)" + Formula : { + SeriesHypergeometric : { + CoefficientP : 1 + CoefficientQ : 12463 + CoefficientD : 10368 + PolynomialP : [0 0 0 0 0 -12463 -29222 138077 338328 -427644 -1338144 58480 1784960 1011136] + PolynomialQ : [-1296 -26568 -230472 -1102080 -3171456 -5621760 -6002688 -3538944 -884736] + PolynomialR : [0 0 0 0 0 -1 6 -12 8] + } + } +} diff --git a/Custom Formulas/Zeta(4) - Chudnovsky.cfg b/Custom Formulas/Zeta(4) - Chudnovsky.cfg new file mode 100644 index 0000000..373652e --- /dev/null +++ b/Custom Formulas/Zeta(4) - Chudnovsky.cfg @@ -0,0 +1,43 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: October 6, 2018 +// +// Value: 1.08232323371113819151600369654116790277475095191872... +// +// Zeta(2) = Pi^4 / 90 +// +// https://en.wikipedia.org/wiki/Chudnovsky_algorithm +// + +{ + NameShort : "Zeta(4)" + NameLong : "Zeta(4)" + AlgorithmShort : "Chudnovsky" + AlgorithmLong : "Chudnovsky (1988)" + Formula : { + LinearCombination : [ + [ + 17795560 + {Power : [ + {SeriesHypergeometric : { + Power : -1 + CoefficientP : 1 + CoefficientQ : 13591409 + CoefficientD : 213440 + PolynomialP : [-67957045 -2100495856 23608573992 -57896553024 39250089648] + PolynomialQ : [0 0 0 -10939058860032000] + PolynomialR : [-5 46 -108 72] + }} + 4 + ]} + ] + ] + } +} diff --git a/Custom Formulas/Zeta(4) - Direct.cfg b/Custom Formulas/Zeta(4) - Direct.cfg new file mode 100644 index 0000000..c059581 --- /dev/null +++ b/Custom Formulas/Zeta(4) - Direct.cfg @@ -0,0 +1,34 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: November 10, 2018 +// +// Value: 1.08232323371113819151600369654116790277475095191872... +// +// Zeta(4) = Pi^4 / 90 +// +// This uses Ramanujan's formula for Pi so that it's independent +// from the other implementation. +// + +{ + NameShort : "Zeta(4)" + NameLong : "Zeta(4)" + AlgorithmShort : "Direct" + AlgorithmLong : "Direct Formula" + Formula : { + Divide : [ + {Power : [ + {Pi : {Algorithm : "ramanujan"}} + 4 + ]} + 90 + ] + } +} diff --git a/Custom Formulas/Zeta(5) - BBP-Kruse.cfg b/Custom Formulas/Zeta(5) - BBP-Kruse.cfg new file mode 100644 index 0000000..b72e2fd --- /dev/null +++ b/Custom Formulas/Zeta(5) - BBP-Kruse.cfg @@ -0,0 +1,118 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename.cfg". +// y-cruncher custom custom:"filename.cfg" +// +// +// Author: Oliver Kruse // DSG +// Date: October 30, 2019 +// +// Value = 1.03692775514336992633136548645703416805708091950191... +// +// Formula: Bailey, Borwein and Plouffe (1998), [Kruse (2019)] +// https://www.davidhbailey.com/dhbpapers/digits.pdf +// +// Formula optimized by Alex Yee (2019). +// + +{ + NameShort : "Zeta(5)" + NameLong : "Zeta(5)" + AlgorithmShort : "BBP-Kruse" + AlgorithmLong : "BBP (1998), Kruse (2019)" + Formula : { + Divide : [ + {LinearCombination : [ + [-1 {SeriesBinaryBBP : { + Power : 1 + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 1 + Alternating : "false" + PowerCoef : -6 + PowerShift : 0 + PolynomialP : [5] + PolynomialQ : [0 0 0 0 0 1] + }}] + [-1 {SeriesBinaryBBP : { + Power : 1 + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 1 + Alternating : "false" + PowerCoef : -6 + PowerShift : 8 + PolynomialP : [23] + PolynomialQ : [-1 10 -40 80 -80 32] + }}] + [-1 {SeriesBinaryBBP : { + Power : 1 + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 1 + Alternating : "false" + PowerCoef : -6 + PowerShift : 7 + PolynomialP : [243] + PolynomialQ : [-1 15 -90 270 -405 243] + }}] + [-1 {SeriesBinaryBBP : { + Power : 1 + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 1 + Alternating : "false" + PowerCoef : -6 + PowerShift : 9 + PolynomialP : [243] + PolynomialQ : [-32 240 -720 1080 -810 243] + }}] + [1 {SeriesBinaryBBP : { + Power : 1 + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 1 + Alternating : "false" + PowerCoef : -6 + PowerShift : 8 + PolynomialP : [243] + PolynomialQ : [-1 30 -360 2160 -6480 7776] + }}] + [1 {SeriesBinaryBBP : { + Power : 1 + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 1 + Alternating : "false" + PowerCoef : -6 + PowerShift : 12 + PolynomialP : [243] + PolynomialQ : [-3125 18750 -45000 54000 -32400 7776] + }}] + [1 {Scope : { + Locals : [ + { log1 : {Log : 2}} + { log2 : {Power : ["log1" 2]}} + ] + Formula : { + Multiply : [ + {LinearCombination : [ + [1 {Power : [ + {LinearCombination : [ + [12 {Power : [{Pi : {}} 2]}] + [-9 "log2"] + ]} + 2 + ]}] + [243 {Power : ["log2" 2]}] + ]} + "log1" + ] + } + }}] + ]} + 21762 + ] + } +} diff --git a/Custom Formulas/Zeta(5) - Broadhurst (Huvent 2006).cfg b/Custom Formulas/Zeta(5) - Broadhurst (Huvent 2006).cfg new file mode 100644 index 0000000..da7823a --- /dev/null +++ b/Custom Formulas/Zeta(5) - Broadhurst (Huvent 2006).cfg @@ -0,0 +1,305 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename.cfg". +// y-cruncher custom custom:"filename.cfg" +// +// +// Author: Alexander J. Yee +// Date: February 19, 2019 +// +// Value = 1.03692775514336992633136548645703416805708091950191... +// +// Formula: Broadhurst (1998) rearranged as Huvent (2006) +// http://functions.wolfram.com/ZetaFunctionsandPolylogarithms/Zeta/06/05/0002/ +// +// Huvent's 2006 formula is mathematically the same as Broadhurst's 1998 formula. +// +// ***Therefore, Broadhurst's and Huvent's formulas cannot be used as a compute/verify pair.*** +// +// The use of the optimized 74-term rearrangement by Alex Yee (2018) to pair with either +// Broadhurst (1998) or Huvent (2006) is also questionable. But the reformulation is +// significant enough that it can be considered *computationally* independent, though +// still *mathematically* the same. +// + +{ + NameShort : "Zeta(5)" + NameLong : "Zeta(5)" + AlgorithmShort : "Broadhurst (Huvent 2006)" + AlgorithmLong : "Broadhurst (1998), Huvent (2006)" + Formula : { + LinearCombination : [ + [-1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 62651 + Alternating : "true" + PowerCoef : -10 + PowerShift : 12 + PolynomialP : [369] + PolynomialQ : [-1 20 -160 640 -1280 1024] + }}] + [-1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 62651 + Alternating : "true" + PowerCoef : -10 + PowerShift : 0 + PolynomialP : [369] + PolynomialQ : [0 0 0 0 0 1] + }}] + [1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 62651 + Alternating : "true" + PowerCoef : -10 + PowerShift : 17 + PolynomialP : [369] + PolynomialQ : [-243 1620 -4320 5760 -3840 1024] + }}] + [-1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 62651 + Alternating : "false" + PowerCoef : -12 + PowerShift : 18 + PolynomialP : [7263] + PolynomialQ : [-161051 878460 -1916640 2090880 -1140480 248832] + }}] + [1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 1691577 + Alternating : "false" + PowerCoef : -12 + PowerShift : 20 + PolynomialP : [32635] + PolynomialQ : [-16807 96040 -219520 250880 -143360 32768] + }}] + [-1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 62651 + Alternating : "false" + PowerCoef : -12 + PowerShift : 13 + PolynomialP : [13977] + PolynomialQ : [-3125 18750 -45000 54000 -32400 7776] + }}] + [-1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 2021 + Alternating : "false" + PowerCoef : -12 + PowerShift : 20 + PolynomialP : [9] + PolynomialQ : [-2476099 15638520 -39507840 49904640 -31518720 7962624] + }}] + [1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 563859 + Alternating : "false" + PowerCoef : -12 + PowerShift : 18 + PolynomialP : [1051] + PolynomialQ : [-243 1620 -4320 5760 -3840 1024] + }}] + [1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 2021 + Alternating : "false" + PowerCoef : -12 + PowerShift : 19 + PolynomialP : [9] + PolynomialQ : [-1419857 10022520 -28298880 39951360 -28200960 7962624] + }}] + [1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 62651 + Alternating : "false" + PowerCoef : -12 + PowerShift : 7 + PolynomialP : [83871] + PolynomialQ : [-32 240 -720 1080 -810 243] + }}] + [-1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 1691577 + Alternating : "false" + PowerCoef : -12 + PowerShift : 17 + PolynomialP : [32635] + PolynomialQ : [-3125 25000 -80000 128000 -102400 32768] + }}] + [-1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 62651 + Alternating : "false" + PowerCoef : -12 + PowerShift : 14 + PolynomialP : [7263] + PolynomialQ : [-16807 144060 -493920 846720 -725760 248832] + }}] + [-1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 2021 + Alternating : "false" + PowerCoef : -12 + PowerShift : 17 + PolynomialP : [9] + PolynomialQ : [-371293 3427320 -12654720 23362560 -21565440 7962624] + }}] + [-1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 54567 + Alternating : "false" + PowerCoef : -12 + PowerShift : 6 + PolynomialP : [3187] + PolynomialQ : [-1 10 -40 80 -80 32] + }}] + [-1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 2021 + Alternating : "false" + PowerCoef : -12 + PowerShift : 16 + PolynomialP : [9] + PolynomialQ : [-161051 1756920 -7666560 16727040 -18247680 7962624] + }}] + [-1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 62651 + Alternating : "false" + PowerCoef : -12 + PowerShift : 12 + PolynomialP : [7263] + PolynomialQ : [-3125 37500 -180000 432000 -518400 248832] + }}] + [-1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 1691577 + Alternating : "false" + PowerCoef : -12 + PowerShift : 14 + PolynomialP : [32635] + PolynomialQ : [-243 3240 -17280 46080 -61440 32768] + }}] + [1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 62651 + Alternating : "false" + PowerCoef : -12 + PowerShift : 3 + PolynomialP : [83871] + PolynomialQ : [-1 15 -90 270 -405 243] + }}] + [1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 2021 + Alternating : "false" + PowerCoef : -12 + PowerShift : 14 + PolynomialP : [9] + PolynomialQ : [-16807 288120 -1975680 6773760 -11612160 7962624] + }}] + [1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 563859 + Alternating : "false" + PowerCoef : -12 + PowerShift : 12 + PolynomialP : [1051] + PolynomialQ : [-1 20 -160 640 -1280 1024] + }}] + [-1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 2021 + Alternating : "false" + PowerCoef : -12 + PowerShift : 13 + PolynomialP : [9] + PolynomialQ : [-3125 75000 -720000 3456000 -8294400 7962624] + }}] + [-1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 62651 + Alternating : "false" + PowerCoef : -12 + PowerShift : 5 + PolynomialP : [13977] + PolynomialQ : [-1 30 -360 2160 -6480 7776] + }}] + [1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 1691577 + Alternating : "false" + PowerCoef : -12 + PowerShift : 11 + PolynomialP : [32635] + PolynomialQ : [-1 40 -640 5120 -20480 32768] + }}] + [-1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 62651 + Alternating : "false" + PowerCoef : -12 + PowerShift : 8 + PolynomialP : [7263] + PolynomialQ : [-1 60 -1440 17280 -103680 248832] + }}] + [1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 2021 + Alternating : "false" + PowerCoef : -12 + PowerShift : 11 + PolynomialP : [9] + PolynomialQ : [-1 120 -5760 138240 -1658880 7962624] + }}] + [1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 1691577 + Alternating : "false" + PowerCoef : -12 + PowerShift : -5 + PolynomialP : [128125] + PolynomialQ : [0 0 0 0 0 1] + }}] + [1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 2021 + Alternating : "false" + PowerCoef : -12 + PowerShift : 22 + PolynomialP : [9] + PolynomialQ : [-6436343 33580920 -70081920 73128960 -38154240 7962624] + }}] + ] + } +} diff --git a/Custom Formulas/Zeta(5) - Broadhurst (optimized).cfg b/Custom Formulas/Zeta(5) - Broadhurst (optimized).cfg new file mode 100644 index 0000000..563a20f --- /dev/null +++ b/Custom Formulas/Zeta(5) - Broadhurst (optimized).cfg @@ -0,0 +1,655 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename.cfg". +// y-cruncher custom custom:"filename.cfg" +// +// +// Author: Alexander J. Yee +// Date: October 4, 2018 +// +// Value = 1.03692775514336992633136548645703416805708091950191... +// +// Original Formula: Broadhurst (1998) +// https://arxiv.org/pdf/math/9803067.pdf +// +// 1152 inf 1 ( 248 12912 124 24848 62 3228 31 74552 ) +// Zeta(5) = ------- SUM ------ (---------- - ---------- - ---------- - ---------- - ---------- - ---------- + ---------- + ----------) +// 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 ) +// +// 7 inf 1 ( 177152 145408 22144 29248 2768 2272 346 111 ) +// + -------- SUM -------- (---------- + ---------- - ---------- - ---------- - ---------- + ---------- + ---------- - ----------) +// 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 ) +// +// 369 inf 1 ( 131072 4096 1024 128 4 1 ) +// + ---------- SUM --------- (- ---------- + ---------- + ---------- + ---------- - ---------- - ----------) +// 64154624 k=0 2^(20k) ( (8k+1)^5 (8k+3)^5 (8k+4)^5 (8k+5)^5 (8k+7)^5 (8k+8)^5 ) +// +// +// Optimized into a massive 74-term BBP formula by Alex Yee (2018). +// The following implementation groups the 74 terms into sets of 2 or 3 terms each. +// + +{ + NameShort : "Zeta(5)" + NameLong : "Zeta(5)" + AlgorithmShort : "Broadhurst (optimized)" + AlgorithmLong : "Broadhurst (1998) (optimized)" + Formula : { + LinearCombination : [ + [-1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 1762059375 + Alternating : "false" + PowerCoef : -30 + PowerShift : 12 + PolynomialP : [ + 55293739267 -2260658245680 40544723556900 -418475704423680 + 2743554653514720 -11903795644396032 34544269695818880 -66159912056279040 + 80125279389331200 -55550303705640960 16795225145889792 + ] + PolynomialQ : [ + -3125 143750 -2982500 36979000 + -306192400 1793303776 -7678751040 24504739200 + -58849079040 106537628160 -144464145408 144349931520 + -103061237760 49716633600 -14511882240 1934917632 + ] + }}] + [-1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 117470625 + Alternating : "true" + PowerCoef : -30 + PowerShift : 18 + PolynomialP : [ + -34509025 693618140 -5558112160 22244671360 -44497491200 35600165888 + ] + PolynomialQ : [ + 243 -6480 75600 -506880 + 2158080 -6086656 11509760 -14417920 + 11468800 -5242880 1048576 + ] + }}] + [1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 563859 + Alternating : "false" + PowerCoef : -30 + PowerShift : 30 + PolynomialP : [ + -1192566547 8419823750 -23837731000 33810670000 -24015350000 6831500000 + ] + PolynomialQ : [ + 992436543 -12602368800 71888512500 -242585280000 + 536262300000 -811465600000 851210000000 -611200000000 + 287500000000 -80000000000 10000000000 + ] + }}] + [1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 563859 + Alternating : "false" + PowerCoef : -30 + PowerShift : 12 + PolynomialP : [ + -322657 7619750 -95641000 767230000 -3520850000 6831500000 + ] + PolynomialQ : [ + 243 -16200 472500 -7920000 + 84300000 -594400000 2810000000 -8800000000 + 17500000000 -20000000000 10000000000 + ] + }}] + [1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 195784375 + Alternating : "true" + PowerCoef : -30 + PowerShift : 27 + PolynomialP : [ + -19669507184511 169174898363340 -581291762951520 997878572323200 + -856076349070080 293675932965888 + ] + PolynomialQ : [ + 2706784157 -37965284280 238310226000 -881506644480 + 2127741073920 -3501690310656 3979152138240 -3082968760320 + 1558683648000 -464380231680 61917364224 + ] + }}] + [1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 195784375 + Alternating : "true" + PowerCoef : -30 + PowerShift : 12 + PolynomialP : [ + 2423887983 27619171020 -1493511864480 19915706597760 + -121886516655360 293675932965888 + ] + PolynomialQ : [ + 3125 -225000 6930000 -119232000 + 1257638400 -8429432832 36219985920 -98895790080 + 165542952960 -154793410560 61917364224 + ] + }}] + [-1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 1691577 + Alternating : "true" + PowerCoef : -30 + PowerShift : 35 + PolynomialP : [ + -289888774695 1755263684500 -4235370300000 5093670800000 + -3054636000000 731024000000 + ] + PolynomialQ : [ + 3515706497843 -39184344867600 196460896610000 -583507923840000 + 1136939844800000 -1518525619200000 1407975040000000 -894873600000000 + 373120000000000 -92160000000000 10240000000000 + ] + }}] + [-1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 1691577 + Alternating : "true" + PowerCoef : -30 + PowerShift : 26 + PolynomialP : [ + -54164342135 475456051500 -1676786300000 2968479600000 + -2636908000000 939888000000 + ] + PolynomialQ : [ + 59797108943 -1003587842400 7573696130000 -33843912960000 + 99171300800000 -199112140800000 277402240000000 -264806400000000 + 165760000000000 -61440000000000 10240000000000 + ] + }}] + [1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 1691577 + Alternating : "true" + PowerCoef : -30 + PowerShift : 20 + PolynomialP : [ + -6315035675 84097131500 -453365420000 1234908400000 + -1697020000000 939888000000 + ] + PolynomialQ : [ + 992436543 -25204737600 287554050000 -1940682240000 + 8580196800000 -25966899200000 54477440000000 -78233600000000 + 73600000000000 -40960000000000 10240000000000 + ] + }}] + [-1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 1691577 + Alternating : "true" + PowerCoef : -30 + PowerShift : 11 + PolynomialP : [ + 7669225 -238235500 2480260000 -2610800000 + -130540000000 731024000000 + ] + PolynomialQ : [ + 243 -32400 1890000 -63360000 + 1348800000 -19020800000 179840000000 -1126400000000 + 4480000000000 -10240000000000 10240000000000 + ] + }}] + [-1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 62651 + Alternating : "false" + PowerCoef : -30 + PowerShift : 30 + PolynomialP : [ + -3140790664563 20282405042250 -52494734259000 68041163970000 + -44152140150000 11471908500000 + ] + PolynomialQ : [ + 132016790288107 -1543824534103800 8112156076012500 -25222323419280000 + 51387246182700000 -71683580685600000 69338113290000000 -45921751200000000 + 19929037500000000 -5117580000000000 590490000000000 + ] + }}] + [-1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 62651 + Alternating : "false" + PowerCoef : -30 + PowerShift : 24 + PolynomialP : [ + -59233592601 505946027250 -1732944537000 2974852170000 + -2559118050000 882454500000 + ] + PolynomialQ : [ + 3515706497843 -58776517301400 442037017372500 -1969339242960000 + 5755757964300000 -11531303920800000 16037715690000000 -15289754400000000 + 9562657500000000 -3542940000000000 590490000000000 + ] + }}] + [-1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 62651 + Alternating : "false" + PowerCoef : -30 + PowerShift : 18 + PolynomialP : [ + -7375554711 94918331250 -491625207000 1280539530000 + -1676663550000 882454500000 + ] + PolynomialQ : [ + 59797108943 -1505381763600 17040816292500 -114223206240000 + 502054710300000 -1512007819200000 3159784890000000 -4524465600000000 + 4248247500000000 -2361960000000000 590490000000000 + ] + }}] + [-1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 62651 + Alternating : "false" + PowerCoef : -30 + PowerShift : 8 + PolynomialP : [ + -122534073 2685494250 -26604369000 221594130000 + -2088475650000 11471908500000 + ] + PolynomialQ : [ + 16807 -2881200 208372500 -8255520000 + 195104700000 -2823854400000 25084890000000 -136468800000000 + 442867500000000 -787320000000000 590490000000000 + ] + }}] + [-1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 2021 + Alternating : "true" + PowerCoef : -30 + PowerShift : 11 + PolynomialP : [ + 1602480483 1416834587700 -173879632692000 10436702858640000 + -313103081469600000 3757237383542400000 + ] + PolynomialQ : [ + 714924299 -218112498000 26835230898000 -1677329596800000 + 54447575198400000 -807728734080000000 3322224927360000000 -6244812288000000000 + 6096166272000000000 -3023308800000000000 604661760000000000 + ] + }}] + [-1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 2021 + Alternating : "true" + PowerCoef : -30 + PowerShift : 14 + PolynomialP : [ + -1265122252467 54359524782900 -932194548108000 7990597829520000 + -34245622389600000 58706827228800000 + ] + PolynomialQ : [ + 7028611650851 -341010807858000 6959010313458000 -77453783971200000 + 510840122385600000 -2043590186880000000 4956939192960000000 -7292892672000000000 + 6358186368000000000 -3023308800000000000 604661760000000000 + ] + }}] + [1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 2021 + Alternating : "true" + PowerCoef : -30 + PowerShift : 16 + PolynomialP : [ + -757391682951 20709906678900 -226057935996000 1233204529680000 + -3363383800800000 3669170140800000 + ] + PolynomialQ : [ + 45492921326699 -1519244125938000 21813414268338000 -176133818044800000 + 879587115422400000 -2821924241280000000 5874793349760000000 -7857243648000000000 + 6499274112000000000 -3023308800000000000 604661760000000000 + ] + }}] + [1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 2021 + Alternating : "true" + PowerCoef : -30 + PowerShift : 17 + PolynomialP : [ + -435930939801 10094402819700 -93267080964000 430575762960000 + -993708064800000 917287286400000 + ] + PolynomialQ : [ + 85154195684051 -2508634242738000 32070281620338000 -233299940515200000 + 1065214272657600000 -3179682449280000000 6276221573760000000 -8099108352000000000 + 6559740288000000000 -3023308800000000000 604661760000000000 + ] + }}] + [-1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 2021 + Alternating : "true" + PowerCoef : -30 + PowerShift : 19 + PolynomialP : [ + -103360140909 1838120123700 -13014363636000 45988022160000 + -81193687200000 57323894400000 + ] + PolynomialQ : [ + 208730966852651 -5139750209778000 55763828883378000 -350559625507200000 + 1412458131153600000 -3808194756480000000 6956018156160000000 -8502216192000000000 + 6660517248000000000 -3023308800000000000 604661760000000000 + ] + }}] + [1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 2021 + Alternating : "true" + PowerCoef : -30 + PowerShift : 20 + PolynomialP : [ + -44596750959 712993446900 -4528972764000 14339857680000 + -22669567200000 14325724800000 + ] + PolynomialQ : [ + 286871423439899 -6628607987058000 67894304401458000 -405659129788800000 + 1564859339294400000 -4070886698880000000 7231699128960000000 -8663459328000000000 + 6700828032000000000 -3023308800000000000 604661760000000000 + ] + }}] + [-1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 2021 + Alternating : "true" + PowerCoef : -30 + PowerShift : 22 + PolynomialP : [ + -6790571523 91652814900 -488178252000 1289707920000 + -1695362400000 888796800000 + ] + PolynomialQ : [ + 446321492229251 -9440407591218000 89312246200818000 -497626895779200000 + 1808198102289600000 -4477017847680000000 7649251666560000000 -8905324032000000000 + 6761294208000000000 -3023308800000000000 604661760000000000 + ] + }}] + [1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 2021 + Alternating : "true" + PowerCoef : -30 + PowerShift : 25 + PolynomialP : [ + -111538323 1325810700 -6151788000 14016240000 + -15746400000 6998400000 + ] + PolynomialQ : [ + 587216781904499 -11757399415218000 105921221205618000 -565401902140800000 + 1980373989470400000 -4755834103680000000 7930307410560000000 -9066567168000000000 + 6801604992000000000 -3023308800000000000 604661760000000000 + ] + }}] + [1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 1762059375 + Alternating : "false" + PowerCoef : -60 + PowerShift : 15 + PolynomialP : [ + 1792149404768 -44777700090000 501230286187920 -3309939127338120 + 14279247817681230 -42049112536556325 85598494996790250 -118944360443668680 + 107976311014313520 -57826406256512400 13874549065109280 + ] + PolynomialQ : [ + -32 1040 -15680 145480 + -928930 4324093 -15159195 40757940 + -84738960 136242405 -168022107 156100770 + -105763320 49338720 -14171760 1889568 + ] + }}] + [1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 1691577 + Alternating : "false" + PowerCoef : -60 + PowerShift : 31 + PolynomialP : [ + -127657600000 1063540000000 -3544450000000 5906562500000 + -4921601562500 1640400390625 + ] + PolynomialQ : [ + 248832 -3628800 23760000 -91980000 + 233137500 -404271875 485703125 -399218750 + 214843750 -68359375 9765625 + ] + }}] + [1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 1691577 + Alternating : "false" + PowerCoef : -60 + PowerShift : 7 + PolynomialP : [ + -528900000 13171250000 -131456250000 656640625000 + -1640800781250 1640400390625 + ] + PolynomialQ : [ + 32 -1200 20000 -195000 + 1231250 -5259375 15390625 -30468750 + 39062500 -29296875 9765625 + ] + }}] + [1 {SeriesBinaryBBP : { + CoefficientP : 3123927 + CoefficientQ : 0 + 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 + ] + }}] + [-1 {SeriesBinaryBBP : { + CoefficientP : 1 + 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 + ] + }}] + [-1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + 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 + ] + }}] + [1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 62651 + Alternating : "false" + PowerCoef : -60 + PowerShift : 51 + PolynomialP : [ + -543359279952 3116176682400 -7151344686000 8208874125000 + -4713026006250 1082722190625 + ] + 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 + ] + 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 + ] + }}] + [-1 {SeriesBinaryBBP : { + CoefficientP : 1 + 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 + ] + }}] + ] + } +} diff --git a/Custom Formulas/Zeta(5) - Broadhurst.cfg b/Custom Formulas/Zeta(5) - Broadhurst.cfg new file mode 100644 index 0000000..43e882e --- /dev/null +++ b/Custom Formulas/Zeta(5) - Broadhurst.cfg @@ -0,0 +1,258 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename.cfg". +// y-cruncher custom custom:"filename.cfg" +// +// +// Author: Alexander J. Yee +// Date: October 2, 2018 +// +// Value = 1.03692775514336992633136548645703416805708091950191... +// +// Formula: Broadhurst (1998) +// https://arxiv.org/pdf/math/9803067.pdf +// +// 1152 inf 1 ( 248 12912 124 24848 62 3228 31 74552 ) +// Zeta(5) = ------- SUM ------ (---------- - ---------- - ---------- - ---------- - ---------- - ---------- + ---------- + ----------) +// 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 ) +// +// 7 inf 1 ( 177152 145408 22144 29248 2768 2272 346 111 ) +// + -------- SUM -------- (---------- + ---------- - ---------- - ---------- - ---------- + ---------- + ---------- - ----------) +// 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 ) +// +// 369 inf 1 ( 131072 4096 1024 128 4 1 ) +// + ---------- SUM --------- (- ---------- + ---------- + ---------- + ---------- - ---------- - ----------) +// 64154624 k=0 2^(20k) ( (8k+1)^5 (8k+3)^5 (8k+4)^5 (8k+5)^5 (8k+7)^5 (8k+8)^5 ) +// + +{ + NameShort : "Zeta(5)" + NameLong : "Zeta(5)" + AlgorithmShort : "Broadhurst" + AlgorithmLong : "Broadhurst (1998)" + Formula : { + LinearCombination : [ + [1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 2021 + Alternating : "false" + PowerCoef : -4 + PowerShift : 14 + PolynomialP : [9] + PolynomialQ : [-16807 96040 -219520 250880 -143360 32768] + }}] + [-1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 2021 + Alternating : "false" + PowerCoef : -4 + PowerShift : 13 + PolynomialP : [9] + PolynomialQ : [-3125 25000 -80000 128000 -102400 32768] + }}] + [-1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 2021 + Alternating : "false" + PowerCoef : -4 + PowerShift : 12 + PolynomialP : [9] + PolynomialQ : [-243 3240 -17280 46080 -61440 32768] + }}] + [1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 2021 + Alternating : "false" + PowerCoef : -4 + PowerShift : 11 + PolynomialP : [9] + PolynomialQ : [-1 40 -640 5120 -20480 32768] + }}] + [-1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 62651 + Alternating : "false" + PowerCoef : -4 + PowerShift : 10 + PolynomialP : [7263] + PolynomialQ : [-243 1620 -4320 5760 -3840 1024] + }}] + [-1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 62651 + Alternating : "false" + PowerCoef : -4 + PowerShift : 8 + PolynomialP : [7263] + PolynomialQ : [-1 20 -160 640 -1280 1024] + }}] + [-1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 62651 + Alternating : "false" + PowerCoef : -4 + PowerShift : 5 + PolynomialP : [13977] + PolynomialQ : [-1 10 -40 80 -80 32] + }}] + [1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 125302 + Alternating : "false" + PowerCoef : -4 + PowerShift : 0 + PolynomialP : [83871] + PolynomialQ : [0 0 0 0 0 1] + }}] + [1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 62651 + Alternating : "false" + PowerCoef : -12 + PowerShift : 20 + PolynomialP : [1211] + PolynomialQ : [-16807 96040 -219520 250880 -143360 32768] + }}] + [-1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 62651 + Alternating : "false" + PowerCoef : -12 + PowerShift : 17 + PolynomialP : [1211] + PolynomialQ : [-3125 25000 -80000 128000 -102400 32768] + }}] + [-1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 62651 + Alternating : "false" + PowerCoef : -12 + PowerShift : 14 + PolynomialP : [1211] + PolynomialQ : [-243 3240 -17280 46080 -61440 32768] + }}] + [1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 62651 + Alternating : "false" + PowerCoef : -12 + PowerShift : 11 + PolynomialP : [1211] + PolynomialQ : [-1 40 -640 5120 -20480 32768] + }}] + [1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 62651 + Alternating : "false" + PowerCoef : -12 + PowerShift : 16 + PolynomialP : [497] + PolynomialQ : [-243 1620 -4320 5760 -3840 1024] + }}] + [1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 62651 + Alternating : "false" + PowerCoef : -12 + PowerShift : 10 + PolynomialP : [497] + PolynomialQ : [-1 20 -160 640 -1280 1024] + }}] + [-1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 62651 + Alternating : "false" + PowerCoef : -12 + PowerShift : 6 + PolynomialP : [3199] + PolynomialQ : [-1 10 -40 80 -80 32] + }}] + [-1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 2004832 + Alternating : "false" + PowerCoef : -12 + PowerShift : 0 + PolynomialP : [777] + PolynomialQ : [0 0 0 0 0 1] + }}] + [-1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 62651 + Alternating : "false" + PowerCoef : -20 + PowerShift : 27 + PolynomialP : [369] + PolynomialQ : [-16807 96040 -219520 250880 -143360 32768] + }}] + [1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 62651 + Alternating : "false" + PowerCoef : -20 + PowerShift : 22 + PolynomialP : [369] + PolynomialQ : [-3125 25000 -80000 128000 -102400 32768] + }}] + [1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 62651 + Alternating : "false" + PowerCoef : -20 + PowerShift : 17 + PolynomialP : [369] + PolynomialQ : [-243 3240 -17280 46080 -61440 32768] + }}] + [-1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 62651 + Alternating : "false" + PowerCoef : -20 + PowerShift : 12 + PolynomialP : [369] + PolynomialQ : [-1 40 -640 5120 -20480 32768] + }}] + [1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 62651 + Alternating : "false" + PowerCoef : -20 + PowerShift : 10 + PolynomialP : [369] + PolynomialQ : [-1 10 -40 80 -80 32] + }}] + [-1 {SeriesBinaryBBP : { + CoefficientP : 1 + CoefficientQ : 0 + CoefficientD : 2004832 + Alternating : "false" + PowerCoef : -20 + PowerShift : 0 + PolynomialP : [369] + PolynomialQ : [0 0 0 0 0 1] + }}] + ] + } +} diff --git a/Custom Formulas/e - exp(-1).cfg b/Custom Formulas/e - exp(-1).cfg new file mode 100644 index 0000000..f14a6e5 --- /dev/null +++ b/Custom Formulas/e - exp(-1).cfg @@ -0,0 +1,30 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: September 29, 2018 +// +// Value: 2.71828182845904523536028747135266249775724709369995... +// + +{ + NameShort : "e" + NameLong : "e" + AlgorithmShort : "exp(-1)" + AlgorithmLong : "Taylor Series of exp(-1)" + Formula : { + SeriesHyperdescent : { + Power : -1 + CoefficientP : -1 + CoefficientQ : 0 + CoefficientD : 1 + PolynomialP : [1] + PolynomialQ : [-1 -1] + } + } +} diff --git a/Custom Formulas/e - exp(0.25)^4.cfg b/Custom Formulas/e - exp(0.25)^4.cfg new file mode 100644 index 0000000..5a75ecd --- /dev/null +++ b/Custom Formulas/e - exp(0.25)^4.cfg @@ -0,0 +1,32 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: September 29, 2018 +// +// Value: 2.71828182845904523536028747135266249775724709369995... +// + +{ + NameShort : "e" + NameLong : "e" + AlgorithmShort : "exp(¼)^4" + AlgorithmLong : "Taylor Series of exp(1/4)" + Formula : { + Power : [ + {SeriesHyperdescent : { + CoefficientP : 1 + CoefficientQ : 1 + CoefficientD : 1 + PolynomialP : [1] + PolynomialQ : [0 4] + }} + 4 + ] + } +} diff --git a/Custom Formulas/e - exp(0.5)^2.cfg b/Custom Formulas/e - exp(0.5)^2.cfg new file mode 100644 index 0000000..9db9b82 --- /dev/null +++ b/Custom Formulas/e - exp(0.5)^2.cfg @@ -0,0 +1,32 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: September 29, 2018 +// +// Value: 2.71828182845904523536028747135266249775724709369995... +// + +{ + NameShort : "e" + NameLong : "e" + AlgorithmShort : "exp(½)^2" + AlgorithmLong : "Taylor Series of exp(1/2)" + Formula : { + Power : [ + {SeriesHyperdescent : { + CoefficientP : 1 + CoefficientQ : 3 + CoefficientD : 2 + PolynomialP : [1] + PolynomialQ : [2 2] + }} + 2 + ] + } +} diff --git a/Custom Formulas/e - exp(1).cfg b/Custom Formulas/e - exp(1).cfg new file mode 100644 index 0000000..2f59dcb --- /dev/null +++ b/Custom Formulas/e - exp(1).cfg @@ -0,0 +1,29 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: September 29, 2018 +// +// Value: 2.71828182845904523536028747135266249775724709369995... +// + +{ + NameShort : "e" + NameLong : "e" + AlgorithmShort : "exp(1)" + AlgorithmLong : "Taylor Series of exp(1)" + Formula : { + SeriesHyperdescent : { + CoefficientP : 1 + CoefficientQ : 1 + CoefficientD : 1 + PolynomialP : [1] + PolynomialQ : [0 1] + } + } +} diff --git a/Custom Formulas/e^-1 - Native.cfg b/Custom Formulas/e^-1 - Native.cfg new file mode 100644 index 0000000..08b93d0 --- /dev/null +++ b/Custom Formulas/e^-1 - Native.cfg @@ -0,0 +1,25 @@ +// y-cruncher Custom Formula File +// +// This can be loaded directly from the Custom Compute menu or +// entered from the command line as "custom:filename". +// +// y-cruncher custom custom:"constant - algorithm" +// +// +// Author: Alexander J. Yee +// Date: October 2, 2018 +// +// Value: 0.36787944117144232159552377016146086744581113103176... +// + +{ + NameShort : "e^-1" + NameLong : "1 / e" + AlgorithmShort : "Native" + AlgorithmLong : "Native Implementation" + Formula : { + E : { + Power : -1 + } + } +}