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 |                 I |                J |                 K |
|------:|:-----------------------------|:-----------|-----------------:|-----------------:|-----------------:|-----------------:|-----------------:|------------------:|-----------------:|------------------:|
| 48207 | Anthony Wayne Local SD       | Lucas      |      8.08032e+06 |      1.08028e+06 |      7.00003e+06 | 310150           | 285315           | -338331           |      0           |  -53016.3         |
| 49171 | Aurora City SD               | Portage    |      4.83272e+06 | 746524           |      4.0862e+06  | 115369           | 341192           | -207454           |      0           |  133738           |
| 48124 | Avon Lake City SD            | Lorain     |      3.37915e+06 | 898278           |      2.48087e+06 | 136282           | 559247           | -591423           | 591423           |  559247           |
| 48116 | Avon Local SD                | Lorain     |      4.91185e+06 | 808286           |      4.10356e+06 | 158062           | 355513           | -283510           | 283510           |  355513           |
| 43547 | Bay Village City SD          | Cuyahoga   |      4.48442e+06 | 631473           |      3.85295e+06 | 107931           | 254477           | -157517           |      0           |   96959.5         |
| 43554 | Beachwood City SD            | Cuyahoga   |      1.02987e+06 | 455391           | 574481           |  85302.6         | 308296           | -406238           |      0           |  -97942.5         |
| 47241 | Beavercreek City SD          | Greene     |      1.36075e+07 |      2.07292e+06 |      1.15345e+07 | 367800           | 888672           |      -1.26063e+06 |      1.26063e+06 |  888672           |
| 48926 | Benton Carroll Salem Local S | Ottawa     |      3.59553e+06 | 360721           |      3.23481e+06 | 144673           |    316.298       |   -1081.64        |      0           |    -765.342       |
| 43620 | Bexley City SD               | Franklin   |      4.38435e+06 | 635140           |      3.74921e+06 | 148885           | 223193           | -156370           |      0           |   66823           |
| 46748 | Big Walnut Local SD          | Delaware   |      6.35783e+06 | 935803           |      5.42202e+06 | 179127           | 375206           | -429104           | 429104           |  375206           |
| 46862 | Bloom Carroll Local SD       | Fairfield  |      5.15701e+06 | 430744           |      4.72626e+06 |  87386.1         |  33937.8         |       0           |      0           |   33937.8         |
| 43646 | Brecksville-Broadview Height | Cuyahoga   |      4.72128e+06 |      1.10636e+06 |      3.61492e+06 | 245258           | 577828           | -693027           |      0           | -115199           |
| 48470 | Buckeye Local SD             | Medina     |      4.86706e+06 | 515059           |      4.352e+06   | 151496           |  71539           |       0           |      0           |   71539           |
| 46755 | Buckeye Valley Local SD      | Delaware   |      4.65904e+06 | 643659           |      4.01538e+06 | 183341           | 180775           | -188104           |      0           |   -7328.84        |
| 48314 | Canfield Local SD            | Mahoning   |      6.04812e+06 | 683280           |      5.36484e+06 | 164248           | 156145           | -282340           |      0           | -126195           |
| 43737 | Centerville City SD          | Montgomery |      1.31671e+07 |      2.11939e+06 |      1.10477e+07 | 588343           | 741016           | -646900           |      0           |   94115.5         |
| 45286 | Chagrin Falls Ex Vill SD     | Cuyahoga   |      1.68236e+06 | 533732           |      1.14863e+06 |  44235.9         | 388554           | -342134           |      0           |   46420.5         |
| 47183 | Chardon Local SD             | Geauga     |      5.45263e+06 | 719967           |      4.73266e+06 | 200056           | 192753           | -211274           |      0           |  -18521           |
| 48140 | Columbia Local SD            | Lorain     |      2.13264e+06 | 222718           |      1.90992e+06 |  91335.5         |   3423.94        |       0           |      0           |    3423.94        |
| 49981 | Copley-Fairlawn City SD      | Summit     |      2.37676e+06 | 867231           |      1.50953e+06 | 226580           | 498045           | -741309           |      0           | -243264           |
| 46557 | Cuyahoga Heights Local SD    | Cuyahoga   | 542339           | 231630           | 310709           |  61034.4         | 138055           | -187507           |      0           |  -49452           |
| 47027 | Dublin City SD               | Franklin   |      2.15547e+07 |      3.46104e+06 |      1.80937e+07 |      1.11304e+06 |      1.05472e+06 |      -1.2042e+06  |      0           | -149483           |
| 50328 | Fairbanks Local SD           | Union      |      2.64465e+06 | 266898           |      2.37775e+06 |  59772.4         |  48446.9         |       0           |      0           |   48446.9         |
| 43976 | Fairview Park City SD        | Cuyahoga   |      2.70423e+06 | 375716           |      2.32851e+06 | 203067           |  10395.1         |  -95310           |      0           |  -84914.9         |
| 44073 | Grandview Heights City SD    | Franklin   |      1.48406e+06 | 320495           |      1.16356e+06 |  54934.2         | 176517           | -166261           |      0           |   10255.7         |
| 45393 | Granville Ex Vill SD         | Licking    |      6.47818e+06 | 574458           |      5.90372e+06 | 103222           |  82545.5         |       0           |      0           |   82545.5         |
| 48496 | Highland Local SD            | Medina     |      4.8669e+06  | 913303           |      3.9536e+06  | 136209           | 485080           | -467884           |      0           |   17196           |
| 50021 | Hudson City SD               | Summit     |      1.0705e+07  |      1.1455e+06  |      9.5595e+06  | 170144           | 333056           |       0           |      0           |  333056           |
| 44131 | Huron City SD                | Erie       |      2.29499e+06 | 340528           |      1.95446e+06 | 193664           |   9165.43        |  -91566.7         |  91566.7         |    9165.43        |
| 46565 | Independence Local SD        | Cuyahoga   | 612123           | 314843           | 297280           |  69161.4         | 208955           | -253977           | 253977           |  208955           |
| 45435 | Indian Hill Ex Vill SD       | Hamilton   |      1.29752e+06 | 621835           | 675684           | 125546           | 418439           | -497892           |      0           |  -79453.4         |
| 49858 | Jackson Local SD             | Stark      |      7.57985e+06 |      1.42662e+06 |      6.15323e+06 | 372104           | 599724           | -877879           |      0           | -278155           |
| 46797 | Kelleys Island Local SD      | Erie       |  11813.6         |   1785.64        |  10028           |      0           |   1076.82        |    -329           |      0           |     747.823       |
| 47191 | Kenston Local SD             | Geauga     |      3.69141e+06 | 791418           |      2.89999e+06 | 109739           | 460194           | -380946           |      0           |   79247.5         |
| 50435 | Kings Local SD               | Warren     |      9.46105e+06 | 875587           |      8.58547e+06 | 198209           | 109714           |       0           |      0           |  109714           |
| 47878 | Kirtland Local SD            | Lake       |      1.00946e+06 | 362387           | 647068           |  66087.6         | 235732           | -308175           |      0           |  -72442.3         |
| 50443 | Little Miami Local SD        | Warren     |      1.33001e+07 |      1.12175e+06 |      1.21783e+07 | 212646           | 111101           |       0           |      0           |  111101           |
| 44289 | Madeira City SD              | Hamilton   |      2.6527e+06  | 404142           |      2.24856e+06 |  66378.9         | 178601           | -125222           |      0           |   53378.5         |
| 44313 | Mariemont City SD            | Hamilton   |      3.09525e+06 | 422155           |      2.6731e+06  | 165174           |  71266           | -114908           | 114908           |   71266           |
| 44370 | Mayfield City SD             | Cuyahoga   |      2.66397e+06 |      1.21295e+06 |      1.45102e+06 | 285185           | 767923           | -634481           |      0           |  133442           |
| 44388 | Medina City SD               | Medina     |      1.83665e+07 |      1.53599e+06 |      1.68305e+07 | 407348           |  26653           |       0           |      0           |   26653           |
| 45492 | Mentor Ex Vill SD            | Lake       |      1.57722e+07 |      1.97612e+06 |      1.37961e+07 | 587147           | 442639           | -203814           |      0           |  238825           |
| 46995 | New Albany-Plain Local SD    | Franklin   |      3.63612e+06 | 865122           |      2.771e+06   | 262507           | 384448           | -541743           |      0           | -157295           |
| 47217 | Newbury Local SD             | Geauga     |      1.04813e+06 | 133670           | 914463           |  57750.6         |  13031           | -387543           |      0           | -374512           |
| 50047 | Nordonia Hills City SD       | Summit     |      4.58664e+06 |      1.0194e+06  |      3.56724e+06 | 252098           | 492106           | -635205           | 635205           |  492106           |
| 44537 | North Ridgeville City SD     | Lorain     |      1.18034e+07 | 969276           |      1.08341e+07 | 257459           |   3611.42        |       0           |      0           |    3611.42        |
| 44545 | North Royalton City SD       | Cuyahoga   |      5.7987e+06  |      1.11658e+06 |      4.68212e+06 | 311103           | 457554           | -747890           | 747890           |  457554           |
| 46763 | Olentangy Local SD           | Delaware   |      1.22913e+07 |      2.98836e+06 |      9.30297e+06 | 247030           |      2.00385e+06 |      -1.77198e+06 |      1.77198e+06 |       2.00385e+06 |
| 46581 | Orange City SD               | Cuyahoga   |      1.57554e+06 | 611190           | 964345           | 178137           | 338521           | -514851           |      0           | -176330           |
| 46813 | Perkins Local SD             | Erie       |      3.57299e+06 | 453226           |      3.11976e+06 | 147514           |  91332.2         |  -49867.7         |  49867.7         |   91332.2         |
| 47902 | Perry Local SD               | Lake       |      3.69363e+06 | 375004           |      3.31862e+06 | 142297           |  11089.5         |   -3676.49        |      0           |    7413           |
| 45583 | Perrysburg Ex Vill SD        | Wood       |      1.17948e+07 | 972953           |      1.08218e+07 |  96901.8         | 168364           |       0           |      0           |  168364           |
| 48975 | Put-In-Bay Local SD          | Ottawa     |  72912.2         |  19967.2         |  52945           |      0           |  15592.5         |  -19924.7         |      0           |   -4332.18        |
| 50054 | Revere Local SD              | Summit     |      2.17173e+06 | 821901           |      1.34983e+06 | 100642           | 590956           | -699964           |      0           | -109008           |
| 47894 | Riverside Local SD           | Lake       |      8.35171e+06 |      1.11905e+06 |      7.23265e+06 | 436472           | 181480           | -302728           |      0           | -121248           |
| 44701 | Rocky River City SD          | Cuyahoga   |      1.45736e+06 | 805051           | 652312           | 178370           | 539239           | -697113           |      0           | -157874           |
| 46607 | Solon City SD                | Cuyahoga   |      3.50089e+06 |      1.33814e+06 |      2.16276e+06 | 308495           | 819591           |      -1.10776e+06 |      0           | -288170           |
| 50427 | Springboro Community City SD | Warren     |      1.5672e+07  |      1.28363e+06 |      1.43884e+07 |  97312           | 246000           |       0           |      0           |  246000           |
| 45997 | St Clairsville-Richland City | Belmont    |      3.3718e+06  | 437305           |      2.9345e+06  | 157607           |  77389.4         |  -96892.1         |      0           |  -19502.7         |
| 44834 | Stow-Munroe Falls City SD    | Summit     |      1.37027e+07 |      1.17828e+06 |      1.25244e+07 | 340092           |  16024.9         |       0           |      0           |   16024.9         |
| 44842 | Strongsville City SD         | Cuyahoga   |      9.07432e+06 |      1.57511e+06 |      7.49921e+06 | 407128           | 623520           | -754532           |      0           | -131012           |
| 47274 | Sugarcreek Local SD          | Greene     |      5.88545e+06 | 659088           |      5.22636e+06 | 163234           | 142728           |    -778.21        |      0           |  141949           |
| 44867 | Sycamore Community City SD   | Hamilton   |      3.43116e+06 |      1.60693e+06 |      1.82423e+06 | 355853           |      1.04521e+06 |      -1.28077e+06 |      1.28077e+06 |       1.04521e+06 |
| 50070 | Twinsburg City SD            | Summit     |      5.94369e+06 | 874253           |      5.06944e+06 | 313019           | 204613           | -316892           |      0           | -112280           |
| 44933 | Upper Arlington City SD      | Franklin   |      3.40812e+06 |      1.82608e+06 |      1.58204e+06 | 304439           |      1.31715e+06 |      -1.5648e+06  |      0           | -247643           |
| 47464 | Van Buren Local SD           | Hancock    |      1.06633e+06 | 273690           | 792644           |  46699           | 163011           | -363589           |      0           | -200578           |
| 47225 | West Geauga Local SD         | Geauga     |      3.41408e+06 | 541854           |      2.87223e+06 |  79328.5         | 257681           | -165250           |      0           |   92430.6         |
| 45062 | Westlake City SD             | Cuyahoga   |      2.50882e+06 |      1.02509e+06 |      1.48373e+06 | 340763           | 533797           | -830449           | 830449           |  533797           |
| 45138 | Worthington City SD          | Franklin   |      2.09314e+07 |      2.19337e+06 |      1.87381e+07 | 749264           | 188224           | -201379           | 201379           |  188224           |



label: F=D-E
K=H+I+J
labeled_formulas: F=D-E
K=H+I+J
output: {"Arithmetic-Relationship": ["F=D-E", "K=H+I+J"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_132324___xlsx_4c6c07aac564a827394ffcfd05aac2851e1cb8ed.xlsx___line_267