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 |
|------:|------:|------:|:----------------------|----:|
| 34335 |   0   |   0   | #DIV/0!               | 100 |
| 34366 |   1.3 |   6   | 0.21666666666666667   | 100 |
| 34394 |  28.5 |  65.2 | 0.43711656441717789   | 100 |
| 34425 | 126.4 | 187.4 | 0.67449306296691569   | 100 |
| 34455 | 237.4 | 323   | 0.73498452012383908   | 100 |
| 34486 | 249.8 | 382.8 | 0.65256008359456641   | 100 |
| 34516 | 183.9 | 342   | 0.53771929824561404   | 100 |
| 34547 | 103.3 | 223.6 | 0.46198568872987478   |  75 |
| 34578 |  46.9 | 103.6 | 0.45270270270270269   |  92 |
| 34608 |   3.8 |  19.8 | 0.19191919191919191   | 100 |
| 34639 |   0   |   0   | #DIV/0!               | 100 |
| 34669 |   0   |   0   | #DIV/0!               | 100 |
| 34700 |   0   |   0   | #DIV/0!               | 100 |
| 34731 |   1.2 |   5.9 | 0.20338983050847456   | 100 |
| 34759 |  31.8 |  64.7 | 0.49149922720247297   | 100 |
| 34790 | 121.4 | 186.8 | 0.6498929336188437    | 100 |
| 34820 | 229.3 | 319.6 | 0.71745932415519398   | 100 |
| 34851 | 227.5 | 382.4 | 0.59492677824267781   |  99 |
| 34881 | 158.2 | 337.5 | 0.46874074074074068   |  80 |
| 34912 |  94.3 | 223   | 0.42286995515695064   |  75 |
| 34943 |  44.3 | 103.3 | 0.42884801548886736   |  74 |
| 34973 |   4.3 |  20.6 | 0.20873786407766989   |  89 |
| 35004 |   0   |   0   | #DIV/0!               |  99 |
| 35034 |   0   |   0   | #DIV/0!               | 100 |
| 35065 |   0   |   0   | #DIV/0!               | 100 |
| 35096 |   1.3 |   6.3 | 0.20634920634920637   | 100 |
| 35125 |  30   |  66.4 | 0.45180722891566261   | 100 |
| 35156 | 126   | 191.7 | 0.65727699530516437   | 100 |
| 35186 | 219.1 | 319   | 0.68683385579937306   |  99 |
| 35217 | 211   | 380.2 | 0.55497106785902162   |  99 |
| 35247 | 150.5 | 338.4 | 0.44473995271867617   |  83 |
| 35278 |  63.9 | 221.1 | 0.28900949796472186   |  58 |
| 35309 |  24.3 | 100.3 | 0.24227318045862414   |  61 |
| 35339 |   3.6 |  19.1 | 0.18848167539267013   |  99 |
| 35370 |   0   |   0   | #DIV/0!               |  97 |
| 35400 |   0   |   0   | #DIV/0!               | 100 |
| 35431 |   0   |   0   | #DIV/0!               | 100 |
| 35462 |   1.3 |   6.3 | 0.20634920634920637   | 100 |
| 35490 |  33.6 |  69.2 | 0.48554913294797686   | 100 |
| 35521 | 125.7 | 190   | 0.66157894736842104   | 100 |
| 35551 | 221.4 | 322.5 | 0.68651162790697673   | 100 |
| 35582 | 209.7 | 379.8 | 0.55213270142180093   |  97 |
| 35612 | 154.2 | 340   | 0.45352941176470585   |  86 |
| 35643 |  95.5 | 224.3 | 0.42576905929558623   |  58 |
| 35674 |  28   | 101.1 | 0.27695351137487639   |  33 |
| 35704 |   3.1 |  19   | 0.16315789473684211   |  41 |
| 35735 |   0   |   0   | #DIV/0!               |  80 |
| 35765 |   0   |   0   | #DIV/0!               |  99 |
| 35796 |   0   |   0   | #DIV/0!               | 100 |
| 35827 |   1.3 |   6   | 0.21666666666666667   | 100 |
| 35855 |  27.3 |  63.5 | 0.42992125984251972   | 100 |
| 35886 | 120.5 | 186.8 | 0.64507494646680941   | 100 |
| 35916 | 215.3 | 320.7 | 0.67134393514187718   | 100 |
| 35947 | 192.6 | 381.1 | 0.50537916557334028   | 100 |
| 35977 | 122.9 | 337.8 | 0.36382474837181766   |  71 |
| 36008 |  49.3 | 219.3 | 0.22480620155038758   |  15 |
| 36039 |  10   |  97.7 | 0.10235414534288638   |   0 |
| 36069 |   3   |  19   | 0.15789473684210525   |   2 |
| 36100 |   0   |   0   | #DIV/0!               |  71 |
| 36130 |   0   |   0   | #DIV/0!               | 100 |
| 36161 |   0   |   0   | #DIV/0!               | 100 |
| 36192 |   1.2 |   5.9 | 0.20338983050847456   | 100 |
| 36220 |  32.3 |  66.4 | 0.48644578313253006   | 100 |
| 36251 | 121.8 | 189.8 | 0.64172813487881974   | 100 |
| 36281 | 215.5 | 319.7 | 0.67406944010009384   | 100 |
| 36312 | 208.8 | 379.5 | 0.55019762845849807   | 100 |
| 36342 | 150.2 | 341   | 0.44046920821114366   |  88 |
| 36373 |  63.4 | 221   | 0.28687782805429862   |  42 |
| 36404 |  17.9 | 101.3 | 0.17670286278381045   |  14 |
| 36434 |   4.1 |  20.5 | 0.19999999999999998   |  70 |
| 36465 |   0   |   0   | #DIV/0!               | 100 |
| 36495 |   0   |   0   | #DIV/0!               |  97 |
| 36526 |   0   |   0   | #DIV/0!               | 100 |
| 36557 |   1.3 |   6.4 | 0.203125              | 100 |
| 36586 |  32.3 |  68.7 | 0.470160116448326     | 100 |
| 36617 | 124.3 | 192.6 | 0.64537902388369683   | 100 |
| 36647 | 223.4 | 325.4 | 0.68653964351567309   | 100 |
| 36678 | 220.7 | 380.8 | 0.57956932773109238   |  89 |
| 36708 | 165.3 | 341.3 | 0.48432464107823031   |  86 |
| 36739 |  95.1 | 221.9 | 0.42857142857142855   |  56 |
| 36770 |  26.8 |  99.6 | 0.26907630522088355   |  23 |
| 36800 |   3.6 |  19.1 | 0.18848167539267013   |  81 |
| 36831 |   0   |   0   | #DIV/0!               |  96 |
| 36861 |   0   |   0   | #DIV/0!               |  99 |
| 36892 |   0   |   0   | #DIV/0!               | 100 |
| 36923 |   1.3 |   6.3 | 0.20634920634920637   | 100 |
| 36951 |  30.5 |  67.2 | 0.45386904761904762   | 100 |
| 36982 | 129.7 | 192.5 | 0.67376623376623368   | 100 |
| 37012 | 238.2 | 326.5 | 0.72955589586523728   | 100 |
| 37043 | 234.6 | 383.6 | 0.61157455683003126   |  94 |
| 37073 | 172.6 | 342.3 | 0.50423605024832019   |  83 |
| 37104 |  67   | 220   | 0.30454545454545456   |  58 |
| 37135 |  26.3 |  99.6 | 0.2640562248995984    |  45 |
| 37165 |   4.3 |  19.8 | 0.21717171717171715   |  99 |
| 37196 |   0   |   0   | #DIV/0!               | 100 |
| 37226 |   0   |   0   | #DIV/0!               | 100 |
| 37257 |   0   |   0   | #DIV/0!               | 100 |
| 37288 |   1.3 |   6.1 | 0.21311475409836067   | 100 |
| 37316 |  31.4 |  64.7 | 0.48531684698608962   | 100 |
| 37347 | 124.1 | 190.8 | 0.65041928721174003   |  96 |
| 37377 | 233.6 | 318.5 | 0.73343799058084769   |  95 |
| 37408 | 242.2 | 382.9 | 0.63254113345521024   |  96 |
| 37438 | 145.1 | 337.7 | 0.42967130589280428   |  66 |
| 37469 |  58.7 | 219.6 | 0.26730418943533701   |  16 |
| 37500 |   4.1 |  97.8 | 4.1922290388548056E-2 |   0 |
| 37530 |   3.3 |  19.6 | 0.16836734693877548   |  52 |
| 37561 |   0   |   0   | #DIV/0!               |  98 |
| 37591 |   0   |   0   | #DIV/0!               | 100 |
| 37622 |   0   |   0   | #DIV/0!               | 100 |
| 37653 |   1.3 |   6.1 | 0.21311475409836067   | 100 |
| 37681 |  32.5 |  66.6 | 0.48798798798798804   | 100 |
| 37712 | 124.1 | 186.8 | 0.66434689507494638   |  99 |
| 37742 | 219.8 | 319.8 | 0.68730456535334583   |  94 |
| 37773 | 222.5 | 379.9 | 0.58568044222163729   |  97 |
| 37803 | 148.3 | 340.2 | 0.43592004703115816   |  63 |
| 37834 |  48.1 | 221   | 0.21764705882352942   |   8 |
| 37865 |   5.8 |  99.2 | 5.8467741935483868E-2 |   1 |
| 37895 |   3.3 |  19.4 | 0.17010309278350516   |  30 |
| 37926 |   0   |   0   | #DIV/0!               |  88 |
| 37956 |   0   |   0   | #DIV/0!               |  98 |
| 37987 |   0   |   0   | #DIV/0!               |  96 |
| 38018 |   1.4 |   6.5 | 0.21538461538461537   |  98 |
| 38047 |  35   |  69.4 | 0.50432276657060515   |  99 |
| 38078 | 129.9 | 192.5 | 0.67480519480519485   | 100 |
| 38108 | 234.2 | 324.3 | 0.72217082947887756   | 100 |
| 38139 | 217   | 378.7 | 0.57301293900184846   |  90 |
| 38169 | 142.6 | 336.3 | 0.42402616711269697   |  67 |
| 38200 |  34.7 | 214.1 | 0.16207379729098553   |   7 |
| 38231 |   7   |  98   | 7.1428571428571425E-2 |   1 |
| 38261 |   3.5 |  18.7 | 0.18716577540106952   |  30 |
| 38292 |   0   |   0   | #DIV/0!               |  96 |
| 38322 |   0   |   0   | #DIV/0!               |  99 |
| 38353 |   0   |   0   | #DIV/0!               |  86 |
| 38384 |   1.3 |   6.4 | 0.203125              |  88 |
| 38412 |  28.1 |  66.1 | 0.4251134644478064    |  88 |
| 38443 | 126.8 | 191.7 | 0.66145018257694321   |  88 |
| 38473 | 230.2 | 320.8 | 0.71758104738154604   |  84 |
| 38504 | 229.6 | 385.5 | 0.59559014267185473   |  84 |
| 38534 | 157.3 | 340.9 | 0.46142563801701386   |  70 |
| 38565 |  61.6 | 218.4 | 0.28205128205128205   |  36 |
| 38596 |  11.8 | 100.8 | 0.11706349206349208   |  32 |
| 38626 |   3.4 |  19.3 | 0.17616580310880828   |  55 |
| 38657 |   0   |   0   | #DIV/0!               |  84 |
| 38687 |   0   |   0   | #DIV/0!               |  88 |
| 38718 |   0   |   0   | #DIV/0!               | 100 |
| 38749 |   1.3 |   6   | 0.21666666666666667   | 100 |
| 38777 |  36.2 |  68.5 | 0.52846715328467153   | 100 |
| 38808 | 138   | 192.3 | 0.71762870514820587   | 100 |
| 38838 | 241.7 | 320.1 | 0.7550765385816931    | 100 |
| 38869 | 235.3 | 379.5 | 0.62002635046113308   | 100 |
| 38899 | 149.3 | 340.5 | 0.43847283406754778   |  88 |
| 38930 |  67.8 | 223.9 | 0.30281375614113443   |  78 |
| 38961 |  32   | 102.3 | 0.31280547409579668   |  60 |
| 38991 |   4.7 |  20.2 | 0.23267326732673269   |  47 |
| 39022 |   0   |   0   | #DIV/0!               |  89 |
| 39052 |   0   |   0   | #DIV/0!               | 100 |
| 39083 |   0   |   0   | #DIV/0!               | 100 |
| 39114 |   1.2 |   5.6 | 0.2142857142857143    |  99 |
| 39142 |  31.2 |  65.1 | 0.47926267281105994   |  99 |
| 39173 | 131.7 | 186.5 | 0.70616621983914207   |  99 |
| 39203 | 241.2 | 320.2 | 0.75327920049968766   | 100 |
| 39234 | 210.3 | 379.6 | 0.55400421496311902   |  90 |



label: D=B/C
labeled_formulas: D=B/C
output: {"Arithmetic-Relationship": ["D=B/C"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_653821___xlsx_6c2f3d1505d9cd9e1bcf6093444657a68049f5ae.xlsx___line_433