Task: Arithmetic-Relationship (source dataset: Auto-Relate)

You are given a table with numerical values in multiple columns. Your task is to analyze the data and identify semantic relationships, expressed in arithmetic relationships, that exist between columns.

These relationships may involve any combination of the following operations: addition (+), subtraction (−), multiplication (*), and division (/). The expressions can involve two or more columns and may be nested (e.g., B = (A + C) / D).

Please only identify arithmetic relationships that hold semantically based on the data, and do not return relationships that are likely spurious, e.g., (A = B * 0), where A is an all 0 column. Please only return minimal atomic relationships, e.g., if A = B + C and D = E + F, then there is no need to return A = B + C + E + F - D.

No explanation, return all the formula(s) in JSON format: {"Arithmetic-Relationship": [<list-of-formulas>]}. If no relationship is found, return {"Arithmetic-Relationship": []}.

Input Table:
|     A |        B |        C |        D |         E |      F |        G |      H |
|------:|---------:|---------:|---------:|----------:|-------:|---------:|-------:|
| 37622 |  74980.4 |  21954.3 |  96934.7 |  10695    | 107630 |  77572.3 | 185202 |
| 37653 |  75523   |  22351   |  97874   |   9978    | 107852 |  77582   | 185434 |
| 37681 |  74801   |  20608.3 |  95409.3 |  11158    | 106567 |  76774.3 | 183342 |
| 37712 |  73890   |  23499.3 |  97389.3 |  11239    | 108628 |  81543.3 | 190172 |
| 37742 |  76892   |  25103.3 | 101995   |  13824    | 115819 |  79924.3 | 195744 |
| 37773 |  76479.3 |  23734.2 | 100214   |  13840    | 114054 |  80789   | 194842 |
| 37803 |  83187   |  23758   | 106945   |  12464    | 119409 |  83578.4 | 202987 |
| 37834 |  84965   |  23311   | 108276   |  13009    | 121285 |  86825   | 208110 |
| 37865 |  81184   |  27884   | 109068   |  13294    | 122362 |  89691   | 212053 |
| 37895 |  81670   |  27327   | 108997   |  12209    | 121206 |  89018   | 210224 |
| 37926 |  80639   |  26865   | 107504   |  12354    | 119858 |  91300   | 211158 |
| 37956 |  91997   |  31275   | 123272   |  10138    | 133410 | 100408   | 233818 |
| 37987 |  79128   |  27057   | 106185   |  13936    | 120121 | 100846   | 220967 |
| 38018 |  79685.4 |  26791   | 106476   |  12629.3  | 119106 | 102820   | 221926 |
| 38047 |  79535   |  26812   | 106347   |  13459    | 119806 | 106808   | 226614 |
| 38078 |  79166   |  28561   | 107727   |  12963.2  | 120690 | 105400   | 226091 |
| 38108 |  78757   |  29147   | 107904   |  14406    | 122310 | 105883   | 228193 |
| 38139 |  82252.7 |  28855   | 111108   |  12252.8  | 123360 | 109341   | 232702 |
| 38169 |  85967.7 |  29079.9 | 115048   |   9651.75 | 124699 | 118394   | 243093 |
| 38200 |  86831.2 |  27778.3 | 114610   |   8784.67 | 123394 | 123606   | 247000 |
| 38231 |  86345.3 |  30996.9 | 117342   |   8792.17 | 126134 | 127229   | 253363 |
| 38261 |  87637.7 |  32235.2 | 119873   |   9340.83 | 129214 | 128376   | 257590 |
| 38292 |  86275.5 |  37285.1 | 123561   |   9899.64 | 133460 | 131458   | 264918 |
| 38322 |  98568.7 |  33844.8 | 132414   |  13304.4  | 145718 | 140226   | 285943 |
| 38353 |  82130.9 |  32778.3 | 114909   |  15588    | 130497 | 139331   | 269828 |
| 38384 |  85019.5 |  36136.1 | 121156   |  14082.7  | 135238 | 133163   | 268401 |
| 38412 |  91414.7 |  37263.2 | 128678   |  16802.2  | 145480 | 133316   | 278796 |
| 38443 |  98540.9 |  38781.4 | 137322   |  17864.4  | 155187 | 128088   | 283275 |
| 38473 | 102027   |  40609.5 | 142636   |  18127.5  | 160764 | 129636   | 290399 |
| 38504 | 105294   |  41808.5 | 147103   |  17374.6  | 164477 | 138819   | 303296 |
| 38534 | 116563   |  48026   | 164589   |  17597    | 182186 | 144499   | 326685 |
| 38565 | 123825   |  45661.7 | 169487   |  17822.2  | 187309 | 158657   | 345966 |
| 38596 | 122942   |  48092   | 171034   |  18818    | 189852 | 142591   | 332443 |
| 38626 | 128048   |  49831.5 | 177879   |  19970.7  | 197850 | 140174   | 338024 |
| 38657 | 130028   |  50391.4 | 180419   |  21759.4  | 202179 | 134938   | 337117 |
| 38687 | 144311   |  57749.9 | 202061   |  22741    | 224802 | 140757   | 365559 |
| 38718 | 130758   |  53935.2 | 184693   |  22496.3  | 207189 | 147459   | 354648 |
| 38749 | 131039   |  54401.7 | 185441   |  23367.9  | 208809 | 143900   | 352709 |
| 38777 | 130268   |  56500.1 | 186768   |  24142.1  | 210910 | 147560   | 358470 |
| 38808 | 132579   |  56208.4 | 188787   |  23908.8  | 212696 | 145117   | 357813 |
| 38838 | 135356   |  57329.9 | 192686   |  23283.6  | 215970 | 142636   | 358606 |
| 38869 | 144270   |  61770.4 | 206041   |  23425    | 229466 | 141294   | 370759 |
| 38899 | 153647   |  63734.1 | 217381   |  24121.6  | 241503 | 139189   | 380692 |
| 38930 | 162132   |  64760.5 | 226893   |  26000.2  | 252893 | 143969   | 396862 |
| 38961 | 172716   |  74702.3 | 247418   |  29457.5  | 276876 | 128520   | 405395 |
| 38991 | 178824   |  74377.2 | 253201   |  32148.3  | 285349 | 124658   | 410007 |
| 39022 | 183727   |  83283.5 | 267010   |  33934.1  | 300944 | 156028   | 456972 |
| 39052 | 211469   |  83858.5 | 295328   |  46998.4  | 342326 | 143411   | 485737 |
| 39083 | 193161   |  82119.5 | 275280   |  52515.4  | 327795 | 132179   | 459975 |
| 39114 | 197260   |  91925.4 | 289185   |  49826    | 339011 | 130634   | 469645 |
| 39142 | 201674   |  94002.5 | 295676   |  51429.6  | 347106 | 135822   | 482928 |
| 39173 | 214137   |  88316.3 | 302453   |  52258.4  | 354712 | 140135   | 494847 |
| 39203 | 216514   |  88335.6 | 304849   |  54387.7  | 359237 | 134701   | 493938 |
| 39234 | 227010   |  91924.7 | 318935   |  66481.2  | 385416 | 137620   | 523036 |
| 39264 | 248882   |  99585.6 | 348468   |  74238.9  | 422707 | 131572   | 554279 |
| 39295 | 260229   |  99665.3 | 359894   |  78412    | 438306 | 132169   | 570475 |
| 39326 | 260268   | 110669   | 370936   |  75626.4  | 446563 | 135328   | 581891 |
| 39356 | 273820   | 116566   | 390386   |  77243.5  | 467630 | 132526   | 600156 |
| 39387 | 304718   | 121936   | 426655   |  96553.1  | 523208 | 128426   | 651634 |
| 39417 | 326016   | 132542   | 458558   | 102465    | 561024 | 130320   | 691343 |
| 39448 | 306085   | 123637   | 429722   | 108271    | 537993 | 126398   | 664391 |
| 39479 | 311377   | 126176   | 437553   | 110002    | 547554 | 127532   | 675086 |
| 39508 | 302378   | 118282   | 420660   | 119281    | 539941 | 140331   | 680272 |
| 39539 | 306720   | 119598   | 426318   | 119950    | 546268 | 146649   | 692918 |
| 39569 | 309883   | 115949   | 425832   | 132304    | 558137 | 139529   | 697665 |
| 39600 | 320378   | 112784   | 433162   | 134685    | 567846 | 143258   | 711104 |
| 39630 | 333922   | 113484   | 447407   | 140327    | 587734 | 152610   | 740344 |
| 39661 | 339814   | 118743   | 458557   | 140076    | 598633 | 154778   | 753412 |
| 39692 | 334007   | 128041   | 462048   | 144248    | 606296 | 147263   | 753559 |
| 39722 | 335056   | 118684   | 453740   | 144322    | 598062 | 156691   | 754753 |
| 39753 | 322098   | 107992   | 430089   | 145286    | 575375 | 145955   | 721330 |
| 39783 | 315949   |  99692.2 | 415641   | 122317    | 537958 | 169830   | 707788 |
| 39814 | 275237   |  89958.3 | 365196   | 108922    | 474117 | 186891   | 661008 |
| 39845 | 229423   |  81094.8 | 310518   |  76329.7  | 386848 | 241884   | 628731 |
| 39873 | 212197   |  87099.7 | 299297   |  58512.4  | 357809 | 280090   | 637899 |
| 39904 | 217476   |  77325.2 | 294801   |  66648.4  | 361450 | 281152   | 642602 |
| 39934 | 226684   |  82172.9 | 308856   |  60593.2  | 369450 | 285470   | 654920 |
| 39965 | 236203   |  86999.6 | 323203   |  56210.6  | 379413 | 283312   | 662726 |
| 39995 | 254583   | 101918   | 356501   |  63017    | 419518 | 303182   | 722700 |
| 40026 | 262200   |  96212.4 | 358412   |  64852.8  | 423265 | 317131   | 740395 |
| 40057 | 254213   | 102663   | 356876   |  64461.1  | 421338 | 322355   | 743693 |
| 40087 | 265279   | 103900   | 369179   |  62519.6  | 431699 | 331370   | 763069 |
| 40118 | 266309   | 104531   | 370840   |  62799.7  | 433640 | 342002   | 775643 |
| 40148 | 282441   | 104354   | 386795   |  64082.2  | 450878 | 364113   | 814990 |
| 40179 | 252619   |  97377.7 | 349997   |  62706.6  | 412704 | 367122   | 779825 |



label: D=B+C
F=D+E
H=F+G
labeled_formulas: D=B+C
F=D+E
H=F+G
output: {"Arithmetic-Relationship": ["D=B+C", "F=D+E", "H=F+G"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_227521___xlsx_99d269543db96211d8432e35bed5e81a2166474e.xlsx___line_642