Datasets:
answer stringlengths 4 6 | benchmark_version stringclasses 1
value | change dict | distractor_formula_ids listlengths 2 2 | effective_parameters unknown | family stringclasses 4
values | formula dict | id stringlengths 21 26 | is_gold bool 1
class | knowledge_distractor stringlengths 1.95k 3.54k | knowledge_domain stringlengths 530 1.23k | knowledge_formula stringlengths 381 1.03k | knowledge_formula_expr stringlengths 216 407 | knowledge_name stringlengths 269 491 | knowledge_wrong stringlengths 638 1.34k | level int64 1 4 | math_type stringclasses 50
values | mode stringclasses 4
values | parameters unknown | problem stringlengths 105 438 | prompts dict | solution stringlengths 321 682 | split stringclasses 1
value | subject stringclasses 17
values | template_id int64 0 2 | wrong_formula_id stringlengths 6 6 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
6.247 | cropmath-v1 | null | [
"CMF014",
"CMF011"
] | {
"Biom_plant_yesterday": 704.9,
"Coef_Rm": 0.0039000000000000003,
"DVI": 0.48,
"Tmn": 24.8
} | carbon_nitrogen_cycle | {
"expression": "0.0432*24*(Biom_plant_yesterday/0.45)*Coef_Rm*2^((Tmn-25)/10) / (if DVI>1: DVI^2; else: 1)",
"id": "CMF008",
"latex": "R_m=0.0432\\cdot24(Biom/0.45)C_m2^{(T-25)/10}",
"name": "植株维持呼吸",
"name_en": "carbon-nitrogen cycling plant maintenance respiration",
"precision": 3,
"unit": "g C/m2/day"... | CMF008_direct_t0_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: carbon-nitrogen cycling crop water stress factor (作物水分胁迫因子)
Formula (LaTeX): F_W=f(\theta,\theta_{wp},\theta_{min},\theta_{max})
Formula: F_Water = if Soil_Water<=Wilt_point: 0; if Soil_Wa... | Formula name: carbon-nitrogen cycling plant maintenance respiration (植株维持呼吸)
Formula (LaTeX): R_m=0.0432\cdot24(Biom/0.45)C_m2^{(T-25)/10}
Formula: Rm = 0.0432*24*(Biom_plant_yesterday/0.45)*Coef_Rm*2^((Tmn-25)/10) / (if DVI>1: DVI^2; else: 1)
Operator notes: * means multiplication, / means division, ** or ^ means powe... | Formula name: carbon-nitrogen cycling plant maintenance respiration (植株维持呼吸)
Formula (LaTeX): R_m=0.0432\cdot24(Biom/0.45)C_m2^{(T-25)/10}
Formula: Rm = 0.0432*24*(Biom_plant_yesterday/0.45)*Coef_Rm*2^((Tmn-25)/10) / (if DVI>1: DVI^2; else: 1)
Operator notes: * means multiplication, / means division, ** or ^ means powe... | Formula: Rm = 0.0432*24*(Biom_plant_yesterday/0.45)*Coef_Rm*2^((Tmn-25)/10) / (if DVI>1: DVI^2; else: 1)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: g C/m2/day | Relevant formula name: carbon-nitrogen cycling plant maintenance respiration (植株维持呼吸).
Formula: Rm = 0.0432*24*(Biom_plant_yesterday/0.45)*Coef_Rm*2^((Tmn-25)/10) / (if DVI>1: DVI^2; else: 1)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, ... | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: carbon-nitrogen cycling crop water stress factor (作物水分胁迫因子)
Formula (LaTeX): F_W=f(\theta,\theta_{wp},\theta_{min},\theta_{max})
Formula: F_Water = if Soil_Water<=Wilt_point: 0; if Soil_Water<Crop_W... | 2 | Q10 with DVI correction | direct | {
"Biom_plant_yesterday": 704.9,
"Coef_Rm": 0.0039000000000000003,
"DVI": 0.48,
"Tmn": 24.8
} | A carbon-nitrogen cycling respiration calculation estimates carbon-nitrogen cycling plant maintenance respiration. The measured inputs are Biom_plant_yesterday=704.9 g C/m2, Coef_Rm=0.0039 g C/g C/s, Tmn=24.8 C, DVI=0.48 dimensionless. What is the carbon-nitrogen cycling plant maintenance respiration? Give the final nu... | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as carbon-nitrogen cycling plant maintenance respiration.
Use the verified formula:
\[R_m=0.0432\cdot24(Biom/0.45)C_m2^{(T-25)/10}\]
In calculation-friendly notation, this is:
Rm = 0.0432*24*(Biom_plant_yesterday/0.45)*Coef_Rm*2^((Tmn-25)/10) / (if DVI>1: DVI^2; else: 1).
Substitute the rel... | dev | carbon-nitrogen cycling respiration | 0 | CMF014 |
72.07 | cropmath-v1 | {
"new_value": 30,
"old_value": 29.3,
"parameter": "To"
} | [
"CMF033",
"CMF037"
] | {
"ABIOMASS": 13378,
"PDT": 7,
"Q10": 2.18,
"T": 24.3,
"To": 30
} | growth_yield | {
"expression": "(0.0091 - 0.0001 * PDT) * ABIOMASS * Q10**((T-To)/10)",
"id": "CMF048",
"latex": "RM=(0.0091-0.0001\\cdot PDT)\\cdot ABIOMASS\\cdot Q_{10}^{(T-T_o)/10}",
"name": "维持呼吸",
"name_en": "Maintenance respiration",
"precision": 2,
"unit": "kg/ha/day"
} | CMF048_sensitivity_t2_0001 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Potential leaf area index (潜在叶面积指数)
Formula (LaTeX): LAI_P=LAI_0e^{RP\cdot GDD}
Formula: LAIP = LAI0 * exp(RP * GDD)
Operator notes: * means multiplication, / means division, ** or ^ means... | Formula name: Maintenance respiration (维持呼吸)
Formula (LaTeX): RM=(0.0091-0.0001\cdot PDT)\cdot ABIOMASS\cdot Q_{10}^{(T-T_o)/10}
Formula: RM = (0.0091 - 0.0001 * PDT) * ABIOMASS * Q10**((T-To)/10)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logari... | Formula name: Maintenance respiration (维持呼吸)
Formula (LaTeX): RM=(0.0091-0.0001\cdot PDT)\cdot ABIOMASS\cdot Q_{10}^{(T-T_o)/10}
Formula: RM = (0.0091 - 0.0001 * PDT) * ABIOMASS * Q10**((T-To)/10)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logari... | Formula: RM = (0.0091 - 0.0001 * PDT) * ABIOMASS * Q10**((T-To)/10)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: kg/ha/day | Relevant formula name: Maintenance respiration (维持呼吸).
Formula: RM = (0.0091 - 0.0001 * PDT) * ABIOMASS * Q10**((T-To)/10)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: kg/ha/day | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Daily dry matter increment (日干物质增量)
Formula (LaTeX): GCR=\frac{DTGA-RM-RG}{1-b}
Formula: GCR = (DTGA - RM - RG) / (1 - b)
Operator notes: * means multiplication, / means division, ** or ^ means powe... | 3 | Product with Q10 temperature response | sensitivity | {
"ABIOMASS": 13378,
"PDT": 7,
"Q10": 2.18,
"T": 24.3,
"To": 29.3
} | In respiration, we analyze how Maintenance respiration responds to parameter changes. Baseline: PDT=7.0 physiological days, ABIOMASS=13378.0 kg/ha, Q10=2.18 dimensionless, T=24.3 C, To=29.3 C. After changing To from 29.3 to 30.0, compute the new Maintenance respiration. Give the numeric value in kg/ha/day. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Maintenance respiration.
Use the verified formula:
\[RM=(0.0091-0.0001\cdot PDT)\cdot ABIOMASS\cdot Q_{10}^{(T-T_o)/10}\]
In calculation-friendly notation, this is:
RM = (0.0091 - 0.0001 * PDT) * ABIOMASS * Q10**((T-To)/10).
Substitute the relevant values:
PDT=7.0 physiological days, ABI... | dev | Respiration | 2 | CMF033 |
28.34 | cropmath-v1 | {
"new_value": 31.5,
"old_value": 28.6,
"parameter": "Tair"
} | [
"CMF025",
"CMF023"
] | {
"Tair": 31.5
} | methane_emission | {
"expression": "4.4 + 0.76 * Tair",
"id": "CMF024",
"latex": "T_{soil}=4.4+0.76T_{air}",
"name": "土壤温度估算",
"name_en": "Soil temperature from air temperature",
"precision": 2,
"unit": "C"
} | CMF024_sensitivity_t1_0001 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Soil temperature from air temperature (土壤温度估算)
Formula (LaTeX): T_{soil}=4.4+0.76T_{air}
Formula: Tsoil = 4.4 + 0.76 * Tair
Operator notes: * means multiplication, / means division, ** or ... | Formula name: Soil temperature from air temperature (土壤温度估算)
Formula (LaTeX): T_{soil}=4.4+0.76T_{air}
Formula: Tsoil = 4.4 + 0.76 * Tair
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output un... | Formula name: Soil temperature from air temperature (土壤温度估算)
Formula (LaTeX): T_{soil}=4.4+0.76T_{air}
Formula: Tsoil = 4.4 + 0.76 * Tair
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output un... | Formula: Tsoil = 4.4 + 0.76 * Tair
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: C | Relevant formula name: Soil temperature from air temperature (土壤温度估算).
Formula: Tsoil = 4.4 + 0.76 * Tair
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: C | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Water-content decomposition factor (水分分解因子)
Formula (LaTeX): WI=0.49e^{3.88W_c-5.4W_c^2}
Formula: WI = 0.49 * exp(3.88 * WaterC - 5.4 * WaterC^2)
Operator notes: * means multiplication, / means divi... | 2 | Linear | sensitivity | {
"Tair": 28.6
} | Given current measurements Tair=28.6 C in methane, what would the Soil temperature from air temperature be if Tair were adjusted to 31.5? Provide the numeric value in C. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Soil temperature from air temperature.
Use the verified formula:
\[T_{soil}=4.4+0.76T_{air}\]
In calculation-friendly notation, this is:
Tsoil = 4.4 + 0.76 * Tair.
Substitute the relevant values:
Tair=31.5 C.
The computed value is 28.34 C.
Therefore, the final numeric answer is \boxed{28... | dev | Methane | 1 | CMF025 |
0.708 | cropmath-v1 | null | [
"CMF024",
"CMF023"
] | {
"WaterC": 0.606
} | methane_emission | {
"expression": "0.49 * exp(3.88 * WaterC - 5.4 * WaterC^2)",
"id": "CMF025",
"latex": "WI=0.49e^{3.88W_c-5.4W_c^2}",
"name": "水分分解因子",
"name_en": "Water-content decomposition factor",
"precision": 3,
"unit": "fraction"
} | CMF025_direct_t2_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Methane temperature index (甲烷温度指数)
Formula (LaTeX): TI=Q_{10}^{(t_{sl}-30)/10}
Formula: TI = Q10^((min(t_soil,30)-30)/10)
Operator notes: * means multiplication, / means division, ** or ^ ... | Formula name: Water-content decomposition factor (水分分解因子)
Formula (LaTeX): WI=0.49e^{3.88W_c-5.4W_c^2}
Formula: WI = 0.49 * exp(3.88 * WaterC - 5.4 * WaterC^2)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/l... | Formula name: Water-content decomposition factor (水分分解因子)
Formula (LaTeX): WI=0.49e^{3.88W_c-5.4W_c^2}
Formula: WI = 0.49 * exp(3.88 * WaterC - 5.4 * WaterC^2)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/l... | Formula: WI = 0.49 * exp(3.88 * WaterC - 5.4 * WaterC^2)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | Relevant formula name: Water-content decomposition factor (水分分解因子).
Formula: WI = 0.49 * exp(3.88 * WaterC - 5.4 * WaterC^2)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Soil temperature from air temperature (土壤温度估算)
Formula (LaTeX): T_{soil}=4.4+0.76T_{air}
Formula: Tsoil = 4.4 + 0.76 * Tair
Operator notes: * means multiplication, / means division, ** or ^ means po... | 1 | Exponential quadratic | direct | {
"WaterC": 0.606
} | In a methane, the Water-content decomposition factor is computed as part of methane modeling. With WaterC=0.606 fraction, determine the numeric value in fraction. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Water-content decomposition factor.
Use the verified formula:
\[WI=0.49e^{3.88W_c-5.4W_c^2}\]
In calculation-friendly notation, this is:
WI = 0.49 * exp(3.88 * WaterC - 5.4 * WaterC^2).
Substitute the relevant values:
WaterC=0.606 fraction.
The computed value is 0.708 fraction.
Therefore... | dev | Methane | 2 | CMF024 |
50.61 | cropmath-v1 | null | [
"CMF002",
"CMF010"
] | {
"GrainYield": 8113,
"NUptake": 160.3
} | carbon_nitrogen_cycle | {
"expression": "GrainYield / NUptake",
"id": "CMF003",
"latex": "NUE=\\frac{GrainYield}{NUptake}",
"name": "氮利用效率",
"name_en": "Nitrogen use efficiency",
"precision": 2,
"unit": "kg grain/kg N"
} | CMF003_direct_t1_0001 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: carbon-nitrogen cycling gross primary production (总初级生产力)
Formula (LaTeX): GPP=P_{opt}F_TF_WF_{CO2}DL\cdot0.0432
Formula: GPP = Photo_Rate_opt * F_T * F_Water * F_CO2 * Day_Length_hour * 0... | Formula name: Nitrogen use efficiency (氮利用效率)
Formula (LaTeX): NUE=\frac{GrainYield}{NUptake}
Formula: NUE = GrainYield / NUptake
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: kg g... | Formula name: Nitrogen use efficiency (氮利用效率)
Formula (LaTeX): NUE=\frac{GrainYield}{NUptake}
Formula: NUE = GrainYield / NUptake
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: kg g... | Formula: NUE = GrainYield / NUptake
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: kg grain/kg N | Relevant formula name: Nitrogen use efficiency (氮利用效率).
Formula: NUE = GrainYield / NUptake
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: kg grain/kg N | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: carbon-nitrogen cycling gross primary production (总初级生产力)
Formula (LaTeX): GPP=P_{opt}F_TF_WF_{CO2}DL\cdot0.0432
Formula: GPP = Photo_Rate_opt * F_T * F_Water * F_CO2 * Day_Length_hour * 0.0432
Oper... | 1 | Ratio | direct | {
"GrainYield": 8113,
"NUptake": 160.3
} | Given GrainYield=8113.0 kg/ha, NUptake=160.3 kg N/ha, calculate the Nitrogen use efficiency for a nitrogen. The result should be in kg grain/kg N. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Nitrogen use efficiency.
Use the verified formula:
\[NUE=\frac{GrainYield}{NUptake}\]
In calculation-friendly notation, this is:
NUE = GrainYield / NUptake.
Substitute the relevant values:
GrainYield=8113.0 kg/ha, NUptake=160.3 kg N/ha.
The computed value is 50.61 kg grain/kg N.
Therefor... | dev | Nitrogen | 1 | CMF002 |
1.04 | cropmath-v1 | {
"new_value": 0.59,
"old_value": 0.65,
"parameter": "beta"
} | [
"CMF030",
"CMF034"
] | {
"Cx": 363,
"beta": 0.59
} | growth_yield | {
"expression": "1 + beta * ln(Cx / 340)",
"id": "CMF029",
"latex": "F_{CO2}=1+\\beta\\ln(C_x/340)",
"name": "二氧化碳影响因子",
"name_en": "CO2 response factor",
"precision": 2,
"unit": "multiplier"
} | CMF029_sensitivity_t2_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Physiological age factor (生理年龄因子)
Formula (LaTeX): F_{PA}=1\;(PDT<28),\quad e^{-a(PDT-28)}\;(PDT\ge 28)
Formula: FPA = if PDT<28: 1; else: exp(-a*(PDT-28))
Operator notes: * means multipli... | Formula name: CO2 response factor (二氧化碳影响因子)
Formula (LaTeX): F_{CO2}=1+\beta\ln(C_x/340)
Formula: FCO2 = 1 + beta * ln(Cx / 340)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: frac... | Formula name: CO2 response factor (二氧化碳影响因子)
Formula (LaTeX): F_{CO2}=1+\beta\ln(C_x/340)
Formula: FCO2 = 1 + beta * ln(Cx / 340)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: frac... | Formula: FCO2 = 1 + beta * ln(Cx / 340)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | Relevant formula name: CO2 response factor (二氧化碳影响因子).
Formula: FCO2 = 1 + beta * ln(Cx / 340)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Physiological age factor (生理年龄因子)
Formula (LaTeX): F_{PA}=1\;(PDT<28),\quad e^{-a(PDT-28)}\;(PDT\ge 28)
Formula: FPA = if PDT<28: 1; else: exp(-a*(PDT-28))
Operator notes: * means multiplication, / ... | 2 | Logarithmic | sensitivity | {
"Cx": 363,
"beta": 0.65
} | In photosynthesis, we analyze how CO2 response factor responds to parameter changes. Baseline: Cx=363.0 ppm, beta=0.65 dimensionless. After changing beta from 0.65 to 0.59, compute the new CO2 response factor. Give the numeric value in fraction. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as CO2 response factor.
Use the verified formula:
\[F_{CO2}=1+\beta\ln(C_x/340)\]
In calculation-friendly notation, this is:
FCO2 = 1 + beta * ln(Cx / 340).
Substitute the relevant values:
Cx=363.0 ppm, beta=0.59 dimensionless.
The computed value is 1.04 fraction.
Therefore, the final numer... | dev | Photosynthesis | 2 | CMF030 |
183.14 | cropmath-v1 | {
"new_value": 223.6,
"old_value": 248.4,
"parameter": "SLAc"
} | [
"CMF051",
"CMF044"
] | {
"GDD": 611.2,
"SLAc": 223.6
} | growth_yield | {
"expression": "if GDD<=1200: (-0.0002*GDD^2-0.5604*GDD+581.04)*(SLAc/200); else: 200*(SLAc/200)",
"id": "CMF053",
"latex": "SLA=(-0.0002GDD^2-0.5604GDD+581.04)(SLA_c/200)",
"name": "比叶面积",
"name_en": "Specific leaf area",
"precision": 2,
"unit": "cm2/g"
} | CMF053_sensitivity_t2_0001 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Specific leaf area (比叶面积)
Formula (LaTeX): SLA=(-0.0002GDD^2-0.5604GDD+581.04)(SLA_c/200)
Formula: SLA = if GDD<=1200: (-0.0002*GDD^2-0.5604*GDD+581.04)*(SLAc/200); else: 200*(SLAc/200)
Op... | Formula name: Specific leaf area (比叶面积)
Formula (LaTeX): SLA=(-0.0002GDD^2-0.5604GDD+581.04)(SLA_c/200)
Formula: SLA = if GDD<=1200: (-0.0002*GDD^2-0.5604*GDD+581.04)*(SLAc/200); else: 200*(SLAc/200)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural log... | Formula name: Specific leaf area (比叶面积)
Formula (LaTeX): SLA=(-0.0002GDD^2-0.5604GDD+581.04)(SLA_c/200)
Formula: SLA = if GDD<=1200: (-0.0002*GDD^2-0.5604*GDD+581.04)*(SLAc/200); else: 200*(SLAc/200)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural log... | Formula: SLA = if GDD<=1200: (-0.0002*GDD^2-0.5604*GDD+581.04)*(SLAc/200); else: 200*(SLAc/200)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: cm2/g | Relevant formula name: Specific leaf area (比叶面积).
Formula: SLA = if GDD<=1200: (-0.0002*GDD^2-0.5604*GDD+581.04)*(SLAc/200); else: 200*(SLAc/200)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
O... | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Relative thermal effectiveness (相对热效应)
Formula (LaTeX): RTE=\left[\frac{T-T_b}{T_o-T_b}\left(\frac{T_m-T}{T_m-T_o}\right)^{(T_m-T_o)/(T_o-T_b)}\right]^{TS}
Formula: RTE = (((T - Tb)/(To - Tb)) * (((... | 3 | Piecewise polynomial | sensitivity | {
"GDD": 611.2,
"SLAc": 248.4
} | In leaf area growth, we analyze how Specific leaf area responds to parameter changes. Baseline: GDD=611.2 C day, SLAc=248.4 cm2/g. After changing SLAc from 248.4 to 223.6, compute the new Specific leaf area. Give the numeric value in cm2/g. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Specific leaf area.
Use the verified formula:
\[SLA=(-0.0002GDD^2-0.5604GDD+581.04)(SLA_c/200)\]
In calculation-friendly notation, this is:
SLA = if GDD<=1200: (-0.0002*GDD^2-0.5604*GDD+581.04)*(SLAc/200); else: 200*(SLAc/200).
Substitute the relevant values:
GDD=611.2 C day, SLAc=223.6 ... | dev | Leaf area growth | 2 | CMF051 |
0.35 | cropmath-v1 | null | [
"CMF036",
"CMF053"
] | {
"PDT": 47.6,
"a": 0.053
} | growth_yield | {
"expression": "if PDT<28: 1; else: exp(-a*(PDT-28))",
"id": "CMF030",
"latex": "F_{PA}=1\\;(PDT<28),\\quad e^{-a(PDT-28)}\\;(PDT\\ge 28)",
"name": "生理年龄因子",
"name_en": "Physiological age factor",
"precision": 2,
"unit": "fraction"
} | CMF030_direct_t0_0001 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Canopy extinction coefficient (冠层消光系数)
Formula (LaTeX): K=0.0087PDT+0.2222
Formula: K = 0.0087 * PDT + 0.2222
Operator notes: * means multiplication, / means division, ** or ^ means power,... | Formula name: Physiological age factor (生理年龄因子)
Formula (LaTeX): F_{PA}=1\;(PDT<28),\quad e^{-a(PDT-28)}\;(PDT\ge 28)
Formula: FPA = if PDT<28: 1; else: exp(-a*(PDT-28))
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the... | Formula name: Physiological age factor (生理年龄因子)
Formula (LaTeX): F_{PA}=1\;(PDT<28),\quad e^{-a(PDT-28)}\;(PDT\ge 28)
Formula: FPA = if PDT<28: 1; else: exp(-a*(PDT-28))
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the... | Formula: FPA = if PDT<28: 1; else: exp(-a*(PDT-28))
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | Relevant formula name: Physiological age factor (生理年龄因子).
Formula: FPA = if PDT<28: 1; else: exp(-a*(PDT-28))
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Canopy extinction coefficient (冠层消光系数)
Formula (LaTeX): K=0.0087PDT+0.2222
Formula: K = 0.0087 * PDT + 0.2222
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) me... | 2 | Piecewise exponential decay | direct | {
"PDT": 47.6,
"a": 0.053
} | A photosynthesis calculation estimates Physiological age factor. The measured inputs are PDT=47.6 physiological days, a=0.053 dimensionless. What is the physiological age factor? Give the final numeric value in fraction. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Physiological age factor.
Use the verified formula:
\[F_{PA}=1\;(PDT<28),\quad e^{-a(PDT-28)}\;(PDT\ge 28)\]
In calculation-friendly notation, this is:
FPA = if PDT<28: 1; else: exp(-a*(PDT-28)).
Substitute the relevant values:
PDT=47.6 physiological days, a=0.053 dimensionless.
The comp... | dev | Photosynthesis | 0 | CMF036 |
56.2 | cropmath-v1 | null | [
"CMF048",
"CMF042"
] | {
"SDEPTH": 1.6
} | growth_yield | {
"expression": "45 + 7 * SDEPTH",
"id": "CMF028",
"latex": "EMGDD=45+7SDEPTH",
"name": "出苗热量需求",
"name_en": "Emergence thermal requirement",
"precision": 1,
"unit": "C day"
} | CMF028_direct_t2_0001 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Maintenance respiration (维持呼吸)
Formula (LaTeX): RM=(0.0091-0.0001\cdot PDT)\cdot ABIOMASS\cdot Q_{10}^{(T-T_o)/10}
Formula: RM = (0.0091 - 0.0001 * PDT) * ABIOMASS * Q10**((T-To)/10)
Opera... | Formula name: Emergence thermal requirement (出苗热量需求)
Formula (LaTeX): EMGDD=45+7SDEPTH
Formula: EMGDD = 45 + 7 * SDEPTH
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: C day
Paramete... | Formula name: Emergence thermal requirement (出苗热量需求)
Formula (LaTeX): EMGDD=45+7SDEPTH
Formula: EMGDD = 45 + 7 * SDEPTH
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: C day
Paramete... | Formula: EMGDD = 45 + 7 * SDEPTH
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: C day | Relevant formula name: Emergence thermal requirement (出苗热量需求).
Formula: EMGDD = 45 + 7 * SDEPTH
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: C day | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Maintenance respiration (维持呼吸)
Formula (LaTeX): RM=(0.0091-0.0001\cdot PDT)\cdot ABIOMASS\cdot Q_{10}^{(T-T_o)/10}
Formula: RM = (0.0091 - 0.0001 * PDT) * ABIOMASS * Q10**((T-To)/10)
Operator notes:... | 1 | Linear | direct | {
"SDEPTH": 1.6
} | In a phenology, the Emergence thermal requirement is computed as part of phenology modeling. With SDEPTH=1.6 cm, determine the numeric value in C day. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Emergence thermal requirement.
Use the verified formula:
\[EMGDD=45+7SDEPTH\]
In calculation-friendly notation, this is:
EMGDD = 45 + 7 * SDEPTH.
Substitute the relevant values:
SDEPTH=1.6 cm.
The computed value is 56.2 C day.
Therefore, the final numeric answer is \boxed{56.2}.
#### 56.... | dev | Phenology | 2 | CMF048 |
0.09 | cropmath-v1 | {
"new_value": 44.7,
"old_value": 38.9,
"parameter": "PDT"
} | [
"CMF032",
"CMF038"
] | {
"PDT": 44.7
} | growth_yield | {
"expression": "1 - (-0.0000842*PDT^2 + 0.01*PDT + 0.63)",
"id": "CMF043",
"latex": "PIRO=1-PISH",
"name": "地下部分配指数",
"name_en": "Root partitioning index",
"precision": 2,
"unit": "fraction"
} | CMF043_sensitivity_t0_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Temperature response factor (温度响应因子)
Formula (LaTeX): F_T=\sin(\frac{T-T_b}{T_{ol}-T_b}\frac{\pi}{2}); 1; \cos(\frac{T-T_{ou}}{T_{max}-T_{ou}}\frac{\pi}{2})
Formula: F_T = if Tb<=T<Tol: si... | Formula name: Root partitioning index (地下部分配指数)
Formula (LaTeX): PIRO=1-PISH
Formula: PIRO = 1 - (-0.0000842*PDT^2 + 0.01*PDT + 0.63)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: ... | Formula name: Root partitioning index (地下部分配指数)
Formula (LaTeX): PIRO=1-PISH
Formula: PIRO = 1 - (-0.0000842*PDT^2 + 0.01*PDT + 0.63)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: ... | Formula: PIRO = 1 - (-0.0000842*PDT^2 + 0.01*PDT + 0.63)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | Relevant formula name: Root partitioning index (地下部分配指数).
Formula: PIRO = 1 - (-0.0000842*PDT^2 + 0.01*PDT + 0.63)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Temperature response factor (温度响应因子)
Formula (LaTeX): F_T=\sin(\frac{T-T_b}{T_{ol}-T_b}\frac{\pi}{2}); 1; \cos(\frac{T-T_{ou}}{T_{max}-T_{ou}}\frac{\pi}{2})
Formula: F_T = if Tb<=T<Tol: sin(pi/2*(T-... | 2 | Residual from shoot partitioning | sensitivity | {
"PDT": 38.9
} | A dry matter partitioning calculation involves sensitivity analysis. The current measurements are PDT=38.9 physiological days. A field technician asks what the root partitioning index would become if PDT changed to 44.7. Report the new final numeric value in fraction. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Root partitioning index.
Use the verified formula:
\[PIRO=1-PISH\]
In calculation-friendly notation, this is:
PIRO = 1 - (-0.0000842*PDT^2 + 0.01*PDT + 0.63).
Substitute the relevant values:
PDT=44.7 physiological days.
The computed value is 0.09 fraction.
Therefore, the final numeric an... | dev | Dry matter partitioning | 0 | CMF032 |
0.241 | cropmath-v1 | null | [
"CMF045",
"CMF035"
] | {
"PDT": 2.2
} | growth_yield | {
"expression": "0.0087 * PDT + 0.2222",
"id": "CMF036",
"latex": "K=0.0087PDT+0.2222",
"name": "冠层消光系数",
"name_en": "Canopy extinction coefficient",
"precision": 3,
"unit": "dimensionless"
} | CMF036_direct_t2_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Canopy extinction coefficient (冠层消光系数)
Formula (LaTeX): K=0.0087PDT+0.2222
Formula: K = 0.0087 * PDT + 0.2222
Operator notes: * means multiplication, / means division, ** or ^ means power,... | Formula name: Canopy extinction coefficient (冠层消光系数)
Formula (LaTeX): K=0.0087PDT+0.2222
Formula: K = 0.0087 * PDT + 0.2222
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: dimensionl... | Formula name: Canopy extinction coefficient (冠层消光系数)
Formula (LaTeX): K=0.0087PDT+0.2222
Formula: K = 0.0087 * PDT + 0.2222
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: dimensionl... | Formula: K = 0.0087 * PDT + 0.2222
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: dimensionless | Relevant formula name: Canopy extinction coefficient (冠层消光系数).
Formula: K = 0.0087 * PDT + 0.2222
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: dimensionless | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Stem partitioning index (茎鞘分配指数)
Formula (LaTeX): PIS=1-PIGL-PIP
Formula: PIS = 1 - (if PDT<26: 0.54-0.0046*PDT; else: 1.4532*exp(-0.0492*PDT)) - (Y_grain/B_above/0.87)/(1+exp(-0.2804*(PDT-39)))
Ope... | 1 | Linear | direct | {
"PDT": 2.2
} | In a photosynthesis, the Canopy extinction coefficient is computed as part of photosynthesis modeling. With PDT=2.2 physiological days, determine the numeric value in dimensionless. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Canopy extinction coefficient.
Use the verified formula:
\[K=0.0087PDT+0.2222\]
In calculation-friendly notation, this is:
K = 0.0087 * PDT + 0.2222.
Substitute the relevant values:
PDT=2.2 physiological days.
The computed value is 0.241 dimensionless.
Therefore, the final numeric answer... | dev | Photosynthesis | 2 | CMF045 |
0.763 | cropmath-v1 | null | [
"CMF015",
"CMF017"
] | {
"Com": 3.488,
"Cr": 4.31,
"FEh": 0.428,
"TI": 0.722
} | methane_emission | {
"expression": "max(0, 0.27 * FEh * (TI * Cr + Com))",
"id": "CMF022",
"latex": "P=\\max(0,0.27F_{Eh}(TI\\cdot C_r+Com))",
"name": "甲烷产生量",
"name_en": "Methane production",
"precision": 3,
"unit": "g CH4/m2/day"
} | CMF022_direct_t0_0001 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Methane production (甲烷产生量)
Formula (LaTeX): P=\max(0,0.27F_{Eh}(TI\cdot C_r+Com))
Formula: P = max(0, 0.27 * FEh * (TI * Cr + Com))
Operator notes: * means multiplication, / means division... | Formula name: Methane production (甲烷产生量)
Formula (LaTeX): P=\max(0,0.27F_{Eh}(TI\cdot C_r+Com))
Formula: P = max(0, 0.27 * FEh * (TI * Cr + Com))
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
O... | Formula name: Methane production (甲烷产生量)
Formula (LaTeX): P=\max(0,0.27F_{Eh}(TI\cdot C_r+Com))
Formula: P = max(0, 0.27 * FEh * (TI * Cr + Com))
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
O... | Formula: P = max(0, 0.27 * FEh * (TI * Cr + Com))
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: g CH4/m2/day | Relevant formula name: Methane production (甲烷产生量).
Formula: P = max(0, 0.27 * FEh * (TI * Cr + Com))
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: g CH4/m2/day | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Root-exudate carbon substrate (根系分泌碳底物)
Formula (LaTeX): C_r=0.0018VI\cdot SI\cdot W^{1.25}
Formula: Cr = 0.0018 * VI * SI * W ** 1.25
Operator notes: * means multiplication, / means division, ** or... | 1 | Maximum with chained drivers | direct | {
"Com": 3.488,
"Cr": 4.31,
"FEh": 0.428,
"TI": 0.722
} | A methane calculation estimates Methane production. The measured inputs are FEh=0.428 fraction, TI=0.722 fraction, Cr=4.31 g C/m2/day, Com=3.488 g C/m2/day. What is the methane production? Give the final numeric value in g CH4/m2/day. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Methane production.
Use the verified formula:
\[P=\max(0,0.27F_{Eh}(TI\cdot C_r+Com))\]
In calculation-friendly notation, this is:
P = max(0, 0.27 * FEh * (TI * Cr + Com)).
Substitute the relevant values:
FEh=0.428 fraction, TI=0.722 fraction, Cr=4.31 g C/m2/day, Com=3.488 g C/m2/day.
Th... | dev | Methane | 0 | CMF015 |
End of preview. Expand in Data Studio
CropMath
English | 简体中文
CropMath contains agricultural mechanistic formula questions with numeric
reference answers and controlled knowledge conditions. The cropmath-v1
snapshot is publicly available at
myy555/CropMath; the
accompanying prompt builders, scorer and validators are in the code repository
YuanyuanMa03/CropMath.
Contents and split relationships
| Configuration | dev | test | gold | hidden_public |
|---|---|---|---|---|
| default | 252 | 751 | 95 | — |
| eval_prompts | 1,512 | 4,506 | 570 | — |
| hidden_public | — | — | — | 160 |
The 95 gold questions are copied from test for auditing; do not add them to the test count or treat them as an independent split. There are 1,003 unique development/test questions. The six-condition expansion repeats the same questions with different knowledge blocks; it does not create independent questions. The formula catalog contains 62 public identifiers, CMF001–CMF062.
The public process categories are growth_yield, carbon_nitrogen_cycle,
methane_emission, and environmental_response. Reasoning modes are direct,
sensitivity, branch, and chain_2.
Loading from the Hub
from datasets import load_dataset
questions = load_dataset("myy555/CropMath", "default")
prompts = load_dataset("myy555/CropMath", "eval_prompts")
auxiliary = load_dataset("myy555/CropMath", "hidden_public")
assert len(questions["test"]) == 751
assert len(prompts["test"]) == 4506
assert len(auxiliary["hidden_public"]) == 160
Pin the released dataset revision in experiment records. Do not put access tokens in code or prediction files.
To work offline or to run the bundled validators, download this repository and
use it as a local path. The standalone dataset directory also contains
pyproject.toml, uv.lock, validation scripts and dataset tests. From its root:
uv sync --locked
uv run --locked pytest -q tests
uv run --locked python scripts/validate_cropmath_release.py --release-dir . --no-scan-repo-root
uv run --locked python scripts/validate_formula_catalog.py --path metadata/formula_catalog.csv
For the copy inside the GitHub repository, use that repository's root README commands instead. Validation success means the specified local checks passed; it does not establish scientific validity or online Viewer behavior.
The paper's full statistics tables (per-cell accuracy with cluster bootstrap 95% CIs, paired cluster tests with exact McNemar and FDR fields, thinking-mode control, parser hit rates, prompt-token statistics, K_wrong subset accuracies, tolerance robustness and behavior-distribution tables) are provided as CSV files under paper_stats/.
Fields and use
default rows include id, problem, formula, parameters, reasoning mode,
knowledge blocks, per-condition prompts, answer and solution.
eval_prompts rows include a condition-specific id, the original sample_id,
condition, prompt, answer_float, precision and grouping metadata.
Only send the selected prompt to a model. Do not include the answer, solution,
other conditions' knowledge blocks or scoring metadata in the model input.
The six conditions are C (formula and inputs), K_name (name), K_formula (parameter semantics), K_domain (domain context), K_distractor (distractors), and K_wrong (an incorrect formula). The target remains the reference answer to the original task even when K_wrong supplies an incorrect formula.
Numeric scoring uses:
abs(prediction - answer) <= max(0.5 * 10**(-precision), abs(answer) * 0.01)
Unparseable predictions count as incorrect. Preserve sample pairing across
conditions and account for formula-level clustering in statistical inference.
See eval.yaml for the serialized protocol and HIDDEN_POLICY.md for auxiliary-set access.
Provenance and limitations
The snapshot contains standardized expressions, reference labels, a public formula catalog and audit metadata. It does not distribute private calculator implementations, generation code or a complete per-formula bibliographic mapping. Consequently, this package supports reusing questions and checking numeric predictions against stored labels, but does not independently reproduce the entire formula acquisition and reference-answer generation process.
The audit CSV and protocols are supplied records, not a new independent human audit performed by the package validator. Automated parser tests check the serialized solutions; they do not certify the human-audit provenance. Inputs are synthetic, and this benchmark does not establish reliability on field observations, complete crop simulations or real agricultural decisions.
The 160 auxiliary questions are public while their answers are withheld. No
hosted scoring service is supplied. ID disjointness and withheld labels are not
proof of absence of training contamination. See HIDDEN_POLICY.md.
Licensing and attribution
Dataset contents are provided under CC BY 4.0; see LICENSE. Validation code
included in this dataset repository uses the MIT terms in CODE_LICENSE.
The GitHub repository carries a separate MIT license for its code.
Attribution metadata is provided in CITATION.cff, including the code
repository link. No paper DOI is claimed. Existing notices are preserved. See
reproducibility scope for what these artifacts support.
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