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:
| B                                                             |       C |       D |   E |   F |       G |      H |   I |   J |      K |       L |       M |
|:--------------------------------------------------------------|--------:|--------:|----:|----:|--------:|-------:|----:|----:|-------:|--------:|--------:|
| AICRP on Cotton, CICR, Nagpur                                 |    0    | 1381.66 |   0 |   0 | 1381.66 |   0    |   0 |   0 |   0    | 1381.66 |    0    |
| AINPJAF, CRIJAF, Barrackpore                                  |    0    |  157.13 |   0 |   0 |  157.13 |  80.95 |   0 |   0 |  80.95 |  238.08 |    0    |
| NRRI, Cuttack                                                 | 4700    | 3291.29 |   0 |   0 | 3291.29 |   0    |   0 |   0 |   0    | 3291.29 | 4700    |
| Incentivizing Research in Agriculture, NRRI, Cuttack          |    0    |    0    |   0 |   0 |    0    |   0    |   0 |   0 |   0    |    0    |    0    |
| CTRI, Rajamundry                                              | 2322    | 2368.22 |   0 |   0 | 2368.22 |   0    |   0 |   0 |   0    | 2368.22 | 2322    |
| NETWORK on Tobacco, CTRI, Rajamundry                          |    0    |  202.8  |   0 |   0 |  202.8  |   0    |   0 |   0 |   0    |  202.8  |    0    |
| Pesticide Residues, IARI, New Delhi                           |    0    |  430.58 |   0 |   0 |  430.58 |   0    |   0 |   0 |   0    |  430.58 |    0    |
| AICRP Nematode, IARI, New Delhi                               |    0    |  109.52 |   0 |   0 |  109.52 |  40.48 |   0 |   0 |  40.48 |  150    |    0    |
| CRP On Hybrid Technology, IARI, New Delhi                     |    0    |    0    |   0 |   0 |    0    |   0    |   0 |   0 |   0    |    0    |    0    |
| CRP On Molecular  Breeding,  IARI, New Delhi                  |    0    |    0    |   0 |   0 |    0    |   0    |   0 |   0 |   0    |    0    |    0    |
| AICRP on Honey Bee & Pollinators, NBAIR, Bengaluru            |    0    |  300.1  |   0 |   0 |  300.1  |  66    |   0 |   0 |  66    |  366.1  |    0    |
| IARI Types Deemed University,  Assam                          |    0    |    0    |   0 |   0 |    0    |   0    |   0 |   0 |   0    |    0    |    0    |
| IARI Types Deemed University,  Jharkhand                      |    0    |  100.38 |   0 |   0 |  100.38 |   0    |   0 |   0 |   0    |  100.38 |    0    |
| AICRP on Forage Crops and Utilization, IGFRI, Jhansi          |    0    |  770.22 |   0 |   0 |  770.22 |  92.58 |   0 |   0 |  92.58 |  862.8  |    0    |
| IIPR, Kanpur                                                  |  172    | 2632.28 |   0 |   0 | 2632.28 |   0    |   0 |   0 |   0    | 2632.28 |  172    |
| AICRP on Chickpea, IIPR , Kanpur                              |    0    |  820.73 |   0 |   0 |  820.73 |  62.96 |   0 |   0 |  62.96 |  883.69 |    0    |
| AICRP on Mullarp, IIPR , Kanpur                               |    0    | 1008.28 |   0 |   0 | 1008.28 | 123.02 |   0 |   0 | 123.02 | 1131.3  |    0    |
| AICRP on Pigeonpea, IIPR, Kanpur                              |    0    |  711.43 |   0 |   0 |  711.43 | 130    |   0 |   0 | 130    |  841.43 |    0    |
| AICRP on Arid Legumes, IIPR Kanpur                            |    0    |  322.13 |   0 |   0 |  322.13 |   0    |   0 |   0 |   0    |  322.13 |    0    |
| AICRP on Sugercane, IISR, Lucknow                             |    0    |  653.64 |   0 |   0 |  653.64 |  60    |   0 |   0 |  60    |  713.64 |    0    |
| NBAIM, Maunath Bhanjan                                        |   21.8  |  451.25 |   0 |   0 |  451.25 |   0    |   0 |   0 |   0    |  451.25 |   21.8  |
| AMAAS, NBAIM, Mau                                             |    0    |    0    |   0 |   0 |    0    |   0    |   0 |   0 |   0    |    0    |    0    |
| AICRP POTENTIAL CROP, NBPGR, New Delhi                        |    0    |  240.72 |   0 |   0 |  240.72 |   0    |   0 |   0 |   0    |  240.72 |    0    |
| CRP-AGRO BIODIVERSITY, NBPGR, New Delhi                       |    0    |    0    |   0 |   0 |    0    |   0    |   0 |   0 |   0    |    0    |    0    |
| AINP On Soil Arthropod Pests, NRCIPM, New Delhi               |    0    |  184.5  |   0 |   0 |  184.5  |  52.13 |   0 |   0 |  52.13 |  236.63 |    0    |
| AINP on  Agricultural Acarology, NRCIPM, New Delhi            |    0    |  155.92 |   0 |   0 |  155.92 |  18    |   0 |   0 |  18    |  173.92 |    0    |
| AICRP on Groudnut, DGR, Junagadh                              |    0    |  810.83 |   0 |   0 |  810.83 |   0    |   0 |   0 |   0    |  810.83 |    0    |
| NETWORK PROJECT ON TRANSGENIC IN CROPS,  NRCPB,  New Delhi    |    0    |    0    |   0 |   0 |    0    |   0    |   0 |   0 |   0    |    0    |    0    |
| AICRP on R&M, DR & MR, Bharatpur                              |    0    |  796.66 |   0 |   0 |  796.66 |  84.35 |   0 |   0 |  84.35 |  881.01 |    0    |
| AICRP on Sorghum, IIMR, Hyderabd                              |    0    |  705.08 |   0 |   0 |  705.08 |   0    |   0 |   0 |   0    |  705.08 |    0    |
| AICRP on Pearl Millets, IIMR, Hyderabad                       |    0    |  792.5  |   0 |   0 |  792.5  |   0    |   0 |   0 |   0    |  792.5  |    0    |
| AICRP on Small Millets, IIMR, Hyderabad                       |    0    |  470.05 |   0 |   0 |  470.05 |   0    |   0 |   0 |   0    |  470.05 |    0    |
| IISR, Indore                                                  |   40    | 1145.81 |   0 |   0 | 1145.81 |   0    |   0 |   0 |   0    | 1145.81 |   40    |
| AICRP on Soyabean, Indore                                     |    0    |  723.56 |   0 |   0 |  723.56 |  83.75 |   0 |   0 |  83.75 |  807.31 |    0    |
| AICRP on Biological Control, NBAIR, Benglaluru                |    0    |  192.87 |   0 |   0 |  192.87 |  32.51 |   0 |   0 |  32.51 |  225.38 |    0    |
| AICRP On Maize, IIMR, Ludhiana                                |    0    | 1643.29 |   0 |   0 | 1643.29 |   0    |   0 |   0 |   0    | 1643.29 |    0    |
| AICRP on Oilseed, Hyderabad                                   |    0    | 1000    |   0 |   0 | 1000    |   0    |   0 |   0 |   0    | 1000    |    0    |
| AICRP on Linseed, IIOR, Hyderabad                             |    0    |  361.38 |   0 |   0 |  361.38 |  57.11 |   0 |   0 |  57.11 |  418.49 |    0    |
| AICRP on Sesame & Niger, IIOR, Hyderabad                      |    0    |  354.11 |   0 |   0 |  354.11 |   0    |   0 |   0 |   0    |  354.11 |    0    |
| AICRP on Rice, IIRR, Hyderabad                                |    0    | 2802.33 |   0 |   0 | 2802.33 | 300    |   0 |   0 | 300    | 3102.33 |    0    |
| CRP on  Rice Biofortification, IIRR, Hyderabad                |    0    |    0    |   0 |   0 |    0    |   0    |   0 |   0 |   0    |    0    |    0    |
| AICRP on Wheat & Barley, IIWBR, Karnal                        |    0    | 1580.85 |   0 |   0 | 1580.85 |  57.48 |   0 |   0 |  57.48 | 1638.33 |    0    |
| IISS, Maunath Bhanjan                                         |    1.25 |  329.04 |   0 |   0 |  329.04 |   0    |   0 |   0 |   0    |  329.04 |    1.25 |
| AICRP NSP (CROPS), DSR, Maunath Bhanjan                       |    0    | 1882.16 |   0 |   0 | 1882.16 | 132.25 |   0 |   0 | 132.25 | 2014.41 |    0    |
| Seed Production in Agricultural Corps and Fisheries, DSR, Mau |    0    |    0    |   0 |   0 |    0    |   0    |   0 |   0 |   0    |    0    |    0    |
| NIBSM, Raipur                                                 |    0    |  369.04 |   0 |   0 |  369.04 |   0    |   0 |   0 |   0    |  369.04 |    0    |
| IIAB, Ranchi                                                  |    0    |  324.84 |   0 |   0 |  324.84 |   0    |   0 |   0 |   0    |  324.84 |    0    |
| CAZRI, JODHPUR (AINP on Vertibrate Pest Management)           |    0    |  283.74 |   0 |   0 |  283.74 |  50    |   0 |   0 |  50    |  333.74 |    0    |



label: G=D+E+F
K=H+I+J
labeled_formulas: F=C*E
E=C*H
I=C*E
J=C*E
E=C*K
F=C*H
I=C*F
J=C*F
F=C*K
M=C+F
M=C+I
M=C+J
F=D*E
G=D+E
I=D*E
J=D*E
G=D+F
I=D*F
J=D*F
I=D-G
J=D-G
L=D+H
L=D+K
F=E*G
F=E*H
F=E*K
F=E*L
F=E*M
I=E*G
J=E*G
K=E+H
E=H*M
I=E*L
I=E*M
J=E*L
J=E*M
E=K*M
I=F*G
J=F*G
K=F+H
F=H*M
I=F*L
I=F*M
J=F*L
J=F*M
F=K*M
G=D+E+F
K=H+I+J
F=(C+D)*E
G=(C*E)+D
E=(C*D)*H
I=(C+D)*E
J=(C+D)*E
E=(C*D)*K
E=(D-L)*C
G=(C*F)+D
F=(C*D)*H
I=(C+D)*F
J=(C+D)*F
F=(C*D)*K
F=(D-L)*C
F=(C-M)*D
G=(C*H)+D
G=(C*I)+D
G=(C*J)+D
G=(C*K)+D
I=(D-L)*C
I=(C-M)*D
J=(D-L)*C
J=(C-M)*D
F=(C*E)*G
F=(C+E)*H
F=(C+E)*K
F=(C*E)*L
F=(C-M)*E
E=(C*G)*H
I=(C*E)*G
J=(C*E)*G
E=(C*G)*K
E=(G-L)*C
K=(C*E)+H
E=(C*H)*L
E=(C*H)*M
I=(C*E)*L
I=(C-M)*E
J=(C*E)*L
J=(C-M)*E
E=(C*K)*L
E=(C*K)*M
F=(C*G)*H
I=(C*F)*G
J=(C*F)*G
F=(C*G)*K
F=(G-L)*C
F=(C-M)*G
K=(C*F)+H
F=(C*H)*L
F=(C*H)*M
output: {"Arithmetic-Relationship": ["G=D+E+F", "K=H+I+J"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_549055___xlsx_5c95eaea11ab14be5cc1e3123ff3659cd812a073.xlsx___line_327