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:
|   C | D                                     |   E |   F |   G |    H |    I |
|----:|:--------------------------------------|----:|----:|----:|-----:|-----:|
|  15 | Lihue (LIH)                           |   3 |   0 |   3 |    3 |    0 |
|  16 | Hilo (ITO) / Kona (KOA)               |   3 |   0 |   3 |    4 |    1 |
|  17 | Kahului (OGG)                         |   3 |   0 |   3 |    4 |    1 |
|  18 | Casper (CPR)                          |   3 |   0 |   3 |    5 |    2 |
|  19 | Elko (EKO)                            |   3 |   0 |   3 |    5 |    2 |
|  20 | Grand Junction (GJT)                  |   3 |   0 |   3 |    5 |    2 |
|  21 | Great Falls (GTF)                     |   3 |   0 |   3 |    5 |    2 |
|  22 | La Crosse (LSE)                       |   3 |   0 |   3 |    5 |    2 |
|  23 | Lewiston (LWS)                        |   3 |   0 |   3 |    5 |    2 |
|  24 | Pocatello (PIH)                       |   3 |   0 |   3 |    5 |    2 |
|  25 | Twin Falls (TWF)                      |   3 |   0 |   3 |    5 |    2 |
|  26 | San Juan Luis Muñoz Marin (SJU), PR   |   5 |   0 |   5 |    5 |    0 |
|  27 | Fort Wayne (FWA)                      |   5 |   0 |   5 |    5 |    0 |
|  28 | Albany, GA (ABY)                      |   3 |   0 |   3 |    6 |    3 |
|  29 | Ithaca (ITH)                          |   3 |   0 |   3 |    6 |    3 |
|  30 | Worcester (ORH)                       |   3 |   0 |   3 |    6 |    3 |
|  31 | Alexandria, LA (AEX)                  |   5 |   0 |   5 |    6 |    1 |
|  32 | Charlottesville (CHO)                 |   5 |   0 |   5 |    6 |    1 |
|  33 | Charleston, WV (CRW)                  |   5 |   0 |   5 |    6 |    1 |
|  34 | Wichita Eisenhower (ICT)              |   5 |   0 |   5 |    6 |    1 |
|  35 | Monroe Regional (MLU)                 |   5 |   0 |   5 |    6 |    1 |
|  36 | Wilkes-Barre/Scranton (AVP)           |   3 |   0 |   3 |    7 |    4 |
|  37 | Binghamton (BGM)                      |   3 |   0 |   3 |    7 |    4 |
|  38 | Bangor (BGR)                          |   3 |   0 |   3 |    7 |    4 |
|  39 | Bloomington/Normal (BMI)              |   3 |   0 |   3 |    7 |    4 |
|  40 | Brunswick (BQK)                       |   3 |   0 |   3 |    7 |    4 |
|  41 | Columbus, GA (CSG)                    |   3 |   0 |   3 |    7 |    4 |
|  42 | El Paso (ELP)                         |   3 |   0 |   3 |    7 |    4 |
|  43 | Erie (ERI)                            |   3 |   0 |   3 |    7 |    4 |
|  44 | New Bern (EWN)                        |   3 |   0 |   3 |    7 |    4 |
|  45 | Fairbanks Int'l (FAI)                 |   3 |   0 |   3 |    7 |    4 |
|  46 | Flint (FNT)                           |   3 |   0 |   3 |    7 |    4 |
|  47 | Fort Smith, AR (FSM)                  |   3 |   0 |   3 |    7 |    4 |
|  48 | Hilton Head (HHH)                     |   3 |   0 |   3 |    7 |    4 |
|  49 | Lafayette, LA (LFT)                   |   3 |   0 |   3 |    7 |    4 |
|  50 | Santa Barbara, CA (SBA)               |   3 |   0 |   3 |    7 |    4 |
|  51 | Sun Valley (SUN)                      |   3 |   0 |   3 |    7 |    4 |
|  52 | West Yellowstone (WYS)                |   3 |   0 |   3 |    7 |    4 |
|  53 | Williston (XWA)                       |   3 |   0 |   3 |    7 |    4 |
|  54 | Allentown (ABE)                       |   5 |   0 |   5 |    7 |    2 |
|  55 | Aspen (ASE)                           |   5 |   0 |   5 |    7 |    2 |
|  56 | Asheville (AVL)                       |   5 |   0 |   5 |    7 |    2 |
|  57 | Kalamazoo (AZO)                       |   5 |   0 |   5 |    7 |    2 |
|  58 | Baton Rouge (BTR)                     |   5 |   0 |   5 |    7 |    2 |
|  59 | Burlington, VT (BTV)                  |   5 |   0 |   5 |    7 |    2 |
|  60 | Bozeman (BZN)                         |   5 |   0 |   5 |    7 |    2 |
|  61 | Cedar Rapids (CID)                    |   5 |   0 |   5 |    7 |    2 |
|  62 | Wausau Mosinee (CWA)                  |   5 |   0 |   5 |    7 |    2 |
|  63 | Daytona Beach (DAB)                   |   5 |   0 |   5 |    7 |    2 |
|  64 | Dothan (DHN)                          |   5 |   0 |   5 |    7 |    2 |
|  65 | Duluth (DLH)                          |   5 |   0 |   5 |    7 |    2 |
|  66 | Key West Int'l (EYW)                  |   5 |   0 |   5 |    7 |    2 |
|  67 | Kalispell (FCA)                       |   5 |   0 |   5 |    7 |    2 |
|  68 | Grand Forks (GFK)                     |   5 |   0 |   5 |    7 |    2 |
|  69 | Green Bay (GRB)                       |   5 |   0 |   5 |    7 |    2 |
|  70 | Columbus/West Point/Starkville (GTR)  |   5 |   0 |   5 |    7 |    2 |
|  71 | Helena (HLN)                          |   5 |   0 |   5 |    7 |    2 |
|  72 | Jackson Hole, WY (JAC)                |   5 |   0 |   5 |    7 |    2 |
|  73 | Jackson Evers Int'l, MS (JAN)         |   5 |   0 |   5 |    7 |    2 |
|  74 | Lincoln, NE (LNK)                     |   5 |   0 |   5 |    7 |    2 |
|  75 | Saginaw (MBS)                         |   5 |   0 |   5 |    7 |    2 |
|  76 | Harrisburg Int'l (MDT)                |   5 |   0 |   5 |    7 |    2 |
|  77 | Montgomery (MGM)                      |   5 |   0 |   5 |    7 |    2 |
|  78 | Melbourne, FL (MLB)                   |   5 |   0 |   5 |    7 |    2 |
|  79 | Moline (MLI)                          |   5 |   0 |   5 |    7 |    2 |
|  80 | Mobile Regional (MOB)                 |   5 |   0 |   5 |    7 |    2 |
|  81 | Madison, WI (MSN)                     |   5 |   0 |   5 |    7 |    2 |
|  82 | Myrtle Beach (MYR)                    |   5 |   0 |   5 |    7 |    2 |
|  83 | Peoria (PIA)                          |   5 |   0 |   5 |    7 |    2 |
|  84 | Palm Springs (PSP)                    |   5 |   0 |   5 |    7 |    2 |
|  85 | Portland Int'l Jetport (PWM)          |   5 |   0 |   5 |    7 |    2 |
|  86 | Roanoke (ROA)                         |   5 |   0 |   5 |    7 |    2 |
|  87 | Rochester, MN (RST)                   |   5 |   0 |   5 |    7 |    2 |
|  88 | South Bend (SBN)                      |   5 |   0 |   5 |    7 |    2 |
|  89 | St. George (SGU)                      |   5 |   0 |   5 |    7 |    2 |
|  90 | Traverse City (TVC)                   |   5 |   0 |   5 |    7 |    2 |
|  91 | Fayetteville/Springdale (XNA)         |   5 |   0 |   5 |    7 |    2 |
|  92 | Lansing (LAN)                         |   5 |   0 |   5 |    8 |    3 |
|  93 | Anchorage Ted Stevens (ANC)           |   3 |   0 |   3 |   11 |    8 |
|  94 | Alpena (APN)                          |   3 |   0 |   3 |   12 |    9 |
|  95 | Brainerd (BRD)                        |   3 |   0 |   3 |   12 |    9 |
|  96 | Escanaba (ESC)                        |   3 |   0 |   3 |   12 |    9 |
|  97 | Hibbing (HIB)                         |   3 |   0 |   3 |   12 |    9 |
|  98 | International Falls (INL)             |   3 |   0 |   3 |   12 |    9 |
|  99 | Butte (BTM)                           |   3 |   0 |   3 |   13 |   10 |
| 100 | Sault Sainte Marie, MI (CIU)          |   3 |   0 |   3 |   13 |   10 |
| 101 | Iron Mountain/Kingsford (IMT)         |   3 |   0 |   3 |   13 |   10 |
| 102 | Northwest Florida Beaches (ECP)       |   5 |   0 |   5 |   13 |    8 |
| 103 | Billings (BIL)                        |   5 |   0 |   5 |   13 |    8 |
| 104 | Elmira/Corning (ELM)                  |   5 |   0 |   5 |   13 |    8 |
| 105 | Gulfport (GPT)                        |   5 |   0 |   5 |   13 |    8 |
| 106 | Greensboro (GSO)                      |   5 |   0 |   5 |   13 |    8 |
| 107 | Greenville/Spartanburg Int'l (GSP)    |   5 |   0 |   5 |   13 |    8 |
| 108 | West Palm Beach Int'l (PBI)           |   5 |   0 |   5 |   13 |    8 |
| 109 | Greater Rochester (ROC)               |   5 |   0 |   5 |   13 |    8 |
| 110 | Springfield, MO (SGF)                 |   5 |   0 |   5 |   13 |    8 |
| 111 | Syracuse (SYR)                        |   5 |   0 |   5 |   13 |    8 |
| 112 | Aberdeen, SD (ABR)                    |   3 |   0 |   3 |   14 |   11 |
| 113 | Bemidji (BJI)                         |   3 |   0 |   3 |   14 |   11 |
| 114 | Colorado Springs (COS)                |   3 |   0 |   3 |   14 |   11 |
| 115 | Fresno Yosemite (FAT)                 |   3 |   0 |   3 |   14 |   11 |
| 116 | Rhinelander (RHI)                     |   3 |   0 |   3 |   14 |   11 |
| 117 | Albuquerque (ABQ)                     |   5 |   0 |   5 |   14 |    9 |
| 118 | Albany, NY (ALB)                      |   5 |   0 |   5 |   14 |    9 |
| 119 | Appleton (ATW)                        |   5 |   0 |   5 |   14 |    9 |
| 120 | Birmingham, AL (BHM)                  |   5 |   0 |   5 |   14 |    9 |
| 121 | Bismarck (BIS)                        |   5 |   0 |   5 |   14 |    9 |
| 122 | Columbia, SC (CAE)                    |   5 |   0 |   5 |   14 |    9 |
| 123 | Chattanooga (CHA)                     |   5 |   0 |   5 |   14 |    9 |
| 124 | Charleston, SC (CHS)                  |   5 |   0 |   5 |   14 |    9 |
| 125 | Dayton James M. Cox (DAY)             |   5 |   0 |   5 |   14 |    9 |
| 126 | Des Moines (DSM)                      |   5 |   0 |   5 |   14 |    9 |
| 127 | Eugene (EUG)                          |   5 |   0 |   5 |   14 |    9 |
| 128 | Fargo (FAR)                           |   5 |   0 |   5 |   14 |    9 |
| 129 | Fayetteville Grannis, NC (FAY)        |   5 |   0 |   5 |   14 |    9 |
| 130 | Sioux Falls (FSD)                     |   5 |   0 |   5 |   14 |    9 |
| 131 | Gainesville, FL (GNV)                 |   5 |   0 |   5 |   14 |    9 |
| 132 | Grand Rapids, MI (GRR)                |   5 |   0 |   5 |   14 |    9 |
| 133 | Honolulu (HNL)                        |   5 |   0 |   5 |   14 |    9 |
| 134 | Huntsville (HSV)                      |   5 |   0 |   5 |   14 |    9 |
| 135 | Idaho Falls (IDA)                     |   5 |   0 |   5 |   14 |    9 |
| 136 | Wilmington, NC (ILM)                  |   5 |   0 |   5 |   14 |    9 |
| 137 | Jacksonville Int'l, FL (JAX)          |   5 |   0 |   5 |   14 |    9 |
| 138 | Little Rock (LIT)                     |   5 |   0 |   5 |   14 |    9 |
| 139 | Medford (MFR)                         |   5 |   0 |   5 |   14 |    9 |
| 140 | Minot Int'l (MOT)                     |   5 |   0 |   5 |   14 |    9 |
| 141 | Missoula (MSO)                        |   5 |   0 |   5 |   14 |    9 |
| 142 | New Orleans Int'l (MSY)               |   5 |   0 |   5 |   14 |    9 |
| 143 | Jacksonville, NC (OAJ)                |   5 |   0 |   5 |   14 |    9 |
| 144 | Rapid City Regional (RAP)             |   5 |   0 |   5 |   14 |    9 |
| 145 | Redmond (RDM)                         |   5 |   0 |   5 |   14 |    9 |
| 146 | Richmond Int'l, VA (RIC)              |   5 |   0 |   5 |   14 |    9 |
| 147 | Reno/Tahoe (RNO)                      |   5 |   0 |   5 |   14 |    9 |
| 148 | Savannah Int'l (SAV)                  |   5 |   0 |   5 |   14 |    9 |
| 149 | Shreveport Regional (SHV)             |   5 |   0 |   5 |   14 |    9 |
| 150 | Sarasota/Bradenton (SRQ)              |   5 |   0 |   5 |   14 |    9 |
| 151 | Tallahassee (TLH)                     |   5 |   0 |   5 |   14 |    9 |
| 152 | Bristol, TN (TRI)                     |   5 |   0 |   5 |   14 |    9 |
| 153 | Tulsa Int'l (TUL)                     |   5 |   0 |   5 |   14 |    9 |
| 154 | Destin-Fort Walton Beach (VPS)        |   5 |   0 |   5 |   14 |    9 |
| 155 | Pellston (PLN)                        |   3 |   0 |   3 |   17 |   14 |
| 156 | Evansville (EVV)                      |   5 |   0 |   5 |   20 |   15 |
| 157 | Lexington, KY (LEX)                   |   5 |   0 |   5 |   20 |   15 |
| 158 | Milwaukee General Mitchell (MKE)      |   5 |   0 |   5 |   20 |   15 |
| 159 | Pensacola Gulf Coast Regional (PNS)   |   5 |   0 |   5 |   20 |   15 |
| 160 | Buffalo (BUF)                         |   5 |   0 |   5 |   21 |   16 |
| 161 | Memphis Int'l (MEM)                   |   5 |   0 |   5 |   21 |   16 |
| 162 | Miami Int'l (MIA)                     |   5 |   0 |   5 |   21 |   16 |
| 163 | Oklahoma City Will Rogers World (OKC) |   5 |   0 |   5 |   21 |   16 |
| 164 | Louisville Int'l (SDF)                |   5 |   0 |   5 |   21 |   16 |
| 165 | Tucson Int'l (TUS)                    |   5 |   0 |   5 |   21 |   16 |
| 166 | Knoxville McGhee Tyson (TYS)          |   5 |   0 |   5 |   21 |   16 |
| 167 | Charlotte Int'l (CLT)                 |   5 |   0 |   5 |   27 |   22 |
| 168 | Spokane Int'l (GEG)                   |   5 |   0 |   5 |   27 |   22 |
| 169 | Omaha Eppley (OMA)                    |   5 |   0 |   5 |   27 |   22 |
| 170 | Norfolk Int'l, VA (ORF)               |   5 |   0 |   5 |   27 |   22 |
| 171 | Pasco (PSC)                           |   5 |   0 |   5 |   27 |   22 |
| 172 | St. Louis Lambert Int'l (STL)         |   5 |   0 |   5 |   27 |   22 |
| 173 | Nashville Int'l (BNA)                 |   5 |   0 |   5 |   28 |   23 |
| 174 | Philadelphia Int'l (PHL)              |   5 |   0 |   5 |   28 |   23 |
| 175 | Fort Myers Southwest Florida (RSW)    |   5 |   0 |   5 |   28 |   23 |
| 176 | Tampa Int'l (TPA)                     |   5 |   0 |   5 |   28 |   23 |
| 177 | Pittsburgh Int'l (PIT)                |   5 |   0 |   5 |   33 |   28 |
| 178 | Austin Bergstrom Int'l (AUS)          |   5 |   0 |   5 |   34 |   29 |
| 179 | Cleveland Hopkins (CLE)               |   5 |   0 |   5 |   34 |   29 |
| 180 | Indianapolis Int'l (IND)              |   5 |   0 |   5 |   34 |   29 |
| 181 | Hartford Bradley (BDL)                |   5 |   0 |   5 |   35 |   30 |
| 182 | Columbus John Glenn, OH (CMH)         |   5 |   0 |   5 |   35 |   30 |
| 183 | Washington National (DCA)             |   5 |   0 |   5 |   35 |   30 |
| 184 | Houston Intc'l (IAH)                  |   5 |   0 |   5 |   35 |   30 |
| 185 | Orlando Int'l (MCO)                   |   5 |   0 |   5 |   35 |   30 |
| 186 | Boise (BOI)                           |   5 |   0 |   5 |   41 |   36 |
| 187 | Dallas/Fort Worth (DAL, DFW)          |   5 |   0 |   5 |   42 |   37 |
| 188 | Kansas City Int'l (MCI)               |   5 |   0 |   5 |   42 |   37 |
| 189 | Raleigh/Durham (RDU)                  |   5 |   0 |   5 |   42 |   37 |
| 190 | San Diego Int'l (SAN)                 |   5 |   0 |   5 |   42 |   37 |
| 191 | San Antonio Int'l (SAT)               |   5 |   0 |   5 |   48 |   43 |
| 192 | Cincinnati Int'l (CVG)                |   5 |   0 |   5 |   49 |   44 |
| 193 | Sacramento Int'l (SMF)                |   5 |   0 |   5 |   49 |   44 |
| 194 | Denver Int'l (DEN)                    |   5 |   0 |   5 |   56 |   51 |
| 195 | Boston (BOS)                          |   5 |   0 |   5 |   61 |   56 |
| 196 | Portland Int'l (PDX)                  |   5 |   0 |   5 |   61 |   56 |
| 197 | Phoenix Sky Harbor (PHX)              |   5 |   0 |   5 |   63 |   58 |
| 198 | Chicago (MDW, ORD)                    |   5 |   0 |   5 |   64 |   59 |
| 199 | Las Vegas McCarran (LAS)              |   5 |   0 |   5 |   70 |   65 |
| 200 | San Francisco, CA (SFO)               |   5 |   0 |   5 |   77 |   72 |
| 201 | New York JFK (JFK)                    |   5 |   0 |   5 |   83 |   78 |
| 202 | Los Angeles (LAX) / Burbank (BUR)     |   5 |   0 |   5 |  242 |  237 |
| 203 | Seattle Tacoma Int'l (SEA)            |   5 |   0 |   5 |  329 |  324 |
| 204 | Minneapolis/St. Paul (MSP)            |   5 |   0 |   5 |  638 |  633 |
| 205 | Salt Lake City (SLC)                  |   5 |   0 |   5 |  682 |  677 |
| 206 | Detroit Metropolitan (DTW)            |   5 |   0 |   5 |  793 |  788 |
| 207 | Atlanta Hartsfield Jackson (ATL)      |   5 |   0 |   5 | 1430 | 1425 |



label: G=E+F
labeled_formulas: G=E+F
H=E+I
G=(C*F)+E
F=(E-G)*H
F=(E-G)*I
I=(F-G)+H
output: {"Arithmetic-Relationship": ["G=E+F"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_4702___xlsx_ff44d438e97f5b6428e63b6c5cb32756e923b066.xlsx___line_662