Benchmark: Difference between revisions

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__NOTOC__
__NOTOC__
== Bessel function ==
== Benchmark Table ==


; Gold ID : 1
{| class="wikitable sortable"
; Link : https://sigir21.wmflabs.org/wiki/Bessel_function#math.51.18
|-
; Formula : <math>\begin{align}J_{-(m+\frac{1}{2})}(x) &= (-1)^{m+1} Y_{m+\frac{1}{2}}(x), \\Y_{-(m+\frac{1}{2})}(x) &= (-1)^m J_{m+\frac{1}{2}}(x).\end{align}</math>
! colspan="4" | Translation Results
; TeX Source : <syntaxhighlight lang="tex" inline>\begin{align}J_{-(m+\frac{1}{2})}(x) &= (-1)^{m+1} Y_{m+\frac{1}{2}}(x), \\Y_{-(m+\frac{1}{2})}(x) &= (-1)^m J_{m+\frac{1}{2}}(x).\end{align}</syntaxhighlight>
|-
! ID Link !! Semantic LaTeX !! Mathematica Translation !! Maple Translations


{| class="wikitable"
|-
|-
! colspan="3" | Translation Results
| [[Gold 1]] || {{ya}} || {{ya}} || {{ya}}
|-
| [[Gold 2]] || {{na}} || {{na}} || {{na}}
|-
| [[Gold 3]] || {{na}} || {{na}} || {{na}}
|-
| [[Gold 4]] || {{ya}} || - || -
|-
| [[Gold 5]] || {{ya}} || {{ya}} || {{ya}}
|-
| [[Gold 6]] || {{ya}} || {{ya}} || {{ya}}
|-
| [[Gold 7]] || {{ya}} || {{ya}} || {{ya}}
|-
| [[Gold 8]] || {{ya}} || {{na}} || -
|-
| [[Gold 9]] || {{na}} || {{na}} || {{na}}
|-
| [[Gold 10]] || {{ya}} || {{na}} || -
|-
| [[Gold 11]] || {{ya}} || {{na}} || {{ya}}
|-
| [[Gold 12]] || {{ya}} || {{ya}} || {{ya}}
|-
| [[Gold 13]] || {{ya}} || {{ya}} || {{ya}}
|-
| [[Gold 14]] || {{ya}} || {{ya}} || {{ya}}
|-
| [[Gold 15]] || {{na}} || {{na}} || {{na}}
|-
| [[Gold 16]] || {{na}} || {{na}} || {{ya}}
|-
| [[Gold 17]] || {{na}} || {{na}} || {{na}}
|-
| [[Gold 18]] || {{na}} || {{na}} || {{na}}
|-
| [[Gold 19]] || {{na}} || {{na}} || {{na}}
|-
| [[Gold 20]] || {{na}} || {{na}} || {{na}}
|-
| [[Gold 21]] || {{ya}} || {{na}} || -
|-
| [[Gold 22]] || {{na}} || - || -
|-
| [[Gold 23]] || {{na}} || {{na}} || {{na}}
|-
| [[Gold 24]] || {{ya}} || {{ya}} || {{ya}}
|-
| [[Gold 25]] || {{ya}} || {{ya}} || {{ya}}
|-
| [[Gold 26]] || {{ya}} || {{ya}} || {{ya}}
|-
| [[Gold 27]] || {{ya}} || {{na}} || {{ya}}
|-
| [[Gold 28]] || {{na}} || {{na}} || {{na}}
|-
| [[Gold 29]] || {{ya}} || {{na}} || {{ya}}
|-
| [[Gold 30]] || {{ya}} || {{ya}} || {{ya}}
|-
| [[Gold 31]] || {{na}} || {{na}} || {{na}}
|-
| [[Gold 32]] || {{ya}} || {{ya}} || {{ya}}
|-
| [[Gold 33]] || {{ya}} || {{ya}} || {{ya}}
|-
| [[Gold 34]] || {{na}} || {{na}} || -
|-
| [[Gold 35]] || {{na}} || {{na}} || -
|-
| [[Gold 36]] || {{ya}} || {{ya}} || {{ya}}
|-
| [[Gold 37]] || {{ya}} || {{ya}} || {{ya}}
|-
| [[Gold 38]] || {{ya}} || {{na}} || -
|-
| [[Gold 39]] || {{ya}} || {{ya}} || {{ya}}
|-
| [[Gold 40]] || {{ya}} || {{ya}} || {{na}}
|-
| [[Gold 41]] || {{ya}} || {{ya}} || {{ya}}
|-
|-
! Semantic LaTeX !! Mathematica Translation !! Maple Translations
| [[Gold 42]] || {{ya}} || {{ya}} || {{ya}}
|-
| [[Gold 43]] || {{na}} || {{na}} || {{na}}
|-
| [[Gold 44]] || {{na}} || - || -
|-
| [[Gold 45]] || {{ya}} || {{ya}} || {{ya}}
|-
| [[Gold 46]] || {{ya}} || {{na}} || {{na}}
|-
| [[Gold 47]] || {{ya}} || {{ya}} || {{ya}}
|-
| [[Gold 48]] || {{na}} || {{na}} || -
|-
| [[Gold 49]] || {{na}} || - || -
|-
| [[Gold 50]] || {{na}} || - || -
|-
| [[Gold 51]] || {{na}} || {{na}} || -
|-
| [[Gold 52]] || {{ya}} || {{na}} || {{na}}
|-
| [[Gold 53]] || {{na}} || {{na}} || {{na}}
|-
| [[Gold 54]] || {{na}} || {{na}} || {{na}}
|-
| [[Gold 55]] || {{ya}} || {{ya}} || {{ya}}
|-
| [[Gold 56]] || {{na}} || {{na}} || {{na}}
|-
| [[Gold 57]] || {{ya}} || - || -
|-
| [[Gold 58]] || {{ya}} || - || -
|-
| [[Gold 59]] || {{na}} || {{na}} || -
|-
| [[Gold 60]] || {{ya}} || {{na}} || -
|-
| [[Gold 61]] || {{na}} || {{na}} || -
|-
| [[Gold 62]] || {{na}} || - || -
|-
| [[Gold 63]] || {{ya}} || - || -
|-
| [[Gold 64]] || {{na}} || {{na}} || -
|-
| [[Gold 65]] || {{na}} || {{na}} || -
|-
| [[Gold 66]] || {{na}} || {{na}} || -
|-
| [[Gold 67]] || {{na}} || - || -
|-
| [[Gold 68]] || {{ya}} || {{na}} || {{na}}
|-
| [[Gold 69]] || {{ya}} || {{ya}} || {{ya}}
|-
| [[Gold 70]] || {{ya}} || - || -
|-
| [[Gold 71]] || {{ya}} || {{ya}} || {{ya}}
|-
| [[Gold 72]] || {{ya}} || - || -
|-
| [[Gold 73]] || {{na}} || {{na}} || -
|-
| [[Gold 74]] || {{na}} || - || -
|-
| [[Gold 75]] || {{na}} || {{na}} || -
|-
| [[Gold 76]] || {{na}} || {{na}} || -
|-
| [[Gold 77]] || {{na}} || {{na}} || -
|-
| [[Gold 78]] || {{na}} || {{na}} || {{na}}
|-
| [[Gold 79]] || {{na}} || {{na}} || -
|-
| [[Gold 80]] || {{ya}} || - || -
|-
| [[Gold 81]] || {{ya}} || {{na}} || -
|-
| [[Gold 82]] || {{ya}} || {{na}} || -
|-
| [[Gold 83]] || {{na}} || {{na}} || -
|-
| [[Gold 84]] || {{na}} || - || -
|-
| [[Gold 85]] || {{na}} || {{na}} || -
|-
| [[Gold 86]] || {{na}} || {{na}} || -
|-
| [[Gold 87]] || {{na}} || {{na}} || -
|-
| [[Gold 88]] || {{na}} || - || -
|-
| [[Gold 89]] || {{na}} || {{na}} || -
|-
| [[Gold 90]] || {{ya}} || {{na}} || -
|-
| [[Gold 91]] || {{na}} || - || -
|-
| [[Gold 92]] || {{ya}} || {{na}} || -
|-
| [[Gold 93]] || {{na}} || {{na}} || {{na}}
|-
| [[Gold 94]] || {{ya}} || - || -
|-
| [[Gold 95]] || {{ya}} || {{na}} || -
|-
|-
| {{ya}}
| {{ya}}
| {{ya}}
|}
|}
=== Semantic LaTeX ===
; Translation : <syntaxhighlight lang="tex" inline>\begin{align}\BesselJ{-(m+\frac{1}{2})}@{x} &=(- 1)^{m+1} \BesselY{m+\frac{1}{2}}@{x} , \\ \BesselY{-(m+\frac{1}{2})}@{x} &=(- 1)^m \BesselJ{m+\frac{1}{2}}@{x} .\end{align}</syntaxhighlight>
; Expected (Gold Entry) : <syntaxhighlight lang="tex" inline>\begin{align}\BesselJ{- (m + \frac{1}{2})}@{x} &= (- 1)^{m+1} \BesselY{m+\frac{1}{2}}@{x} , \\ \BesselY{- (m + \frac{1}{2})}@{x} &= (-1)^m \BesselJ{m+\frac{1}{2}}@{x} .\end{align}</syntaxhighlight>
=== Mathematica ===
; Translation : <syntaxhighlight lang="mathematica" inline>BesselJ[-(m +Divide[1,2]), x] == (- 1)^(m + 1)* BesselY[m +Divide[1,2], x]
BesselY[-(m +Divide[1,2]), x] == (- 1)^(m)* BesselJ[m +Divide[1,2], x]</syntaxhighlight>
; Expected (Gold Entry) : <syntaxhighlight lang="mathematica" inline>BesselJ[- (m +Divide[1,2]), x] == (- 1)^(m + 1)* BesselY[m +Divide[1,2], x] BesselY[- (m +Divide[1,2]), x] == (- 1)^(m)* BesselJ[m +Divide[1,2], x]</syntaxhighlight>
=== Maple ===
; Translation : <syntaxhighlight lang="mathematica" inline>BesselJ(-(m +(1)/(2)), x) = (- 1)^(m + 1)* BesselY(m +(1)/(2), x); BesselY(-(m +(1)/(2)), x) = (- 1)^(m)* BesselJ(m +(1)/(2), x)</syntaxhighlight>
; Expected (Gold Entry) : <syntaxhighlight lang="mathematica" inline>BesselJ(- (m +(1)/(2)), x) = (- 1)^(m + 1)* BesselY(m +(1)/(2), x); BesselY(- (m +(1)/(2)), x) = (- 1)^(m)* BesselJ(m +(1)/(2), x)</syntaxhighlight>

Latest revision as of 14:43, 1 September 2021

Benchmark Table

Translation Results
ID Link Semantic LaTeX Mathematica Translation Maple Translations
Gold 1 Yes Yes Yes
Gold 2 No No No
Gold 3 No No No
Gold 4 Yes - -
Gold 5 Yes Yes Yes
Gold 6 Yes Yes Yes
Gold 7 Yes Yes Yes
Gold 8 Yes No -
Gold 9 No No No
Gold 10 Yes No -
Gold 11 Yes No Yes
Gold 12 Yes Yes Yes
Gold 13 Yes Yes Yes
Gold 14 Yes Yes Yes
Gold 15 No No No
Gold 16 No No Yes
Gold 17 No No No
Gold 18 No No No
Gold 19 No No No
Gold 20 No No No
Gold 21 Yes No -
Gold 22 No - -
Gold 23 No No No
Gold 24 Yes Yes Yes
Gold 25 Yes Yes Yes
Gold 26 Yes Yes Yes
Gold 27 Yes No Yes
Gold 28 No No No
Gold 29 Yes No Yes
Gold 30 Yes Yes Yes
Gold 31 No No No
Gold 32 Yes Yes Yes
Gold 33 Yes Yes Yes
Gold 34 No No -
Gold 35 No No -
Gold 36 Yes Yes Yes
Gold 37 Yes Yes Yes
Gold 38 Yes No -
Gold 39 Yes Yes Yes
Gold 40 Yes Yes No
Gold 41 Yes Yes Yes
Gold 42 Yes Yes Yes
Gold 43 No No No
Gold 44 No - -
Gold 45 Yes Yes Yes
Gold 46 Yes No No
Gold 47 Yes Yes Yes
Gold 48 No No -
Gold 49 No - -
Gold 50 No - -
Gold 51 No No -
Gold 52 Yes No No
Gold 53 No No No
Gold 54 No No No
Gold 55 Yes Yes Yes
Gold 56 No No No
Gold 57 Yes - -
Gold 58 Yes - -
Gold 59 No No -
Gold 60 Yes No -
Gold 61 No No -
Gold 62 No - -
Gold 63 Yes - -
Gold 64 No No -
Gold 65 No No -
Gold 66 No No -
Gold 67 No - -
Gold 68 Yes No No
Gold 69 Yes Yes Yes
Gold 70 Yes - -
Gold 71 Yes Yes Yes
Gold 72 Yes - -
Gold 73 No No -
Gold 74 No - -
Gold 75 No No -
Gold 76 No No -
Gold 77 No No -
Gold 78 No No No
Gold 79 No No -
Gold 80 Yes - -
Gold 81 Yes No -
Gold 82 Yes No -
Gold 83 No No -
Gold 84 No - -
Gold 85 No No -
Gold 86 No No -
Gold 87 No No -
Gold 88 No - -
Gold 89 No No -
Gold 90 Yes No -
Gold 91 No - -
Gold 92 Yes No -
Gold 93 No No No
Gold 94 Yes - -
Gold 95 Yes No -
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