Luma Payroll Gym
← Heatmap / GLM 5.3 Flash · Task 19
GLM 5.3 Flash · Tool use · Task 19 (Calculation, upper bracket) Mean 50.0%
Field Expected Rollout #1 (-50%) Rollout #2 (100%) Rollout #3 (100%)
decision calculate (malformed) calculate calculate
currency LCR (malformed) LCR LCR
gross pay 4326.01 (malformed) 4326.01 4326.01
employee contribution 302.82 (malformed) 302.82 302.82
allowed deduction 386.64 (malformed) 386.64 386.64
taxable pay 3636.55 (malformed) 3636.55 3636.55
income tax 198.58 (malformed) 198.58 198.58
net pay 3437.97 (malformed) 3437.97 3437.97
clauses R1 R2 R3 R4 R5 R6 (malformed) R1 R2 R3 R4 R5 R6 R1 R2 R3 R4 R5 R6
Prompt
Process this monthly payroll record under the supplied rulebook. Return the R6 or R7 JSON answer.
Retrieve the case inputs with list_documents and read_document. Reference rows are available only through lookup_reference. Use calculate for exact decimal arithmetic.
Rollouts
Rollout #1 -50.0% malformed · 4 tool calls · 13.3s · $0.0021
ComponentScoreClauses
decision 0.0% R1 R2 R3 R4 R5 R6
exact 0.0% R1 R2 R3 R4 R5 R6
field accuracy 0.0% R1 R2 R3 R4 R5 R6
citations 0.0% R1 R2 R3 R4 R5 R6
Assistant
list_documents()
Reasoning
Let me start by listing the documents to get the case inputs.
Tool
[
  {"id": "f8d9f5fe0eb33c57-payroll", "kind": "payroll"}
]
Assistant
read_document(document_id="f8d9f5fe0eb33c57-payroll")
Tool
{
  "kind": "payroll",
  "record": {"gross_pay": "4326.01", "payroll_month": "2026-03", "allowed_deduction": "386.64"}
}
Assistant
lookup_reference(reference="first-half")
The record has gross_pay 4326.01, payroll_month 2026-03, and allowed_deduction 386.64. March 2026 falls in the first half of 2026, so I'll look up the first-half reference row.
Reasoning
The payroll record:
- gross_pay: 4326.01
- payroll_month: 2026-03
- allowed_deduction: 386.64

2026-03 is in the second half of 2026 (months 07-12? or first half is 01-06?). Let me check the reference tables. "first-half" likely covers 2026-01 through 2026-06, "second-half" covers 2026-07 through 2026-12. March 2026 is in the first half.

Let me look up the first-half reference.
Tool
{
  "reference": "first-half",
  "months": ["2026-01", "2026-06"],
  "rate": "0.07",
  "cap": "4500.00",
  "deduction": "400.00",
  "free": "1200.00",
  "upper": "3600.00",
  "middle_rate": "0.08",
  "upper_rate": "0.18"
}
Assistant
calculate(program="contribution = round(4326.01 * 0.07, 2)\ndeduction_ok_cap = min(386.64, 400.00)\ndeduction_ok_pay = min(386.64, 4326.01 - contribution)\nallowed_deduction = min(deduction_ok_cap, deduction_ok_pay)\ntaxable_pay = 4326.01 - contribution - allowed_deduction\nmiddle_portion = min(taxable_pay, 3600.00) - 1200.00\nupper_portion = max(0, taxable_pay - 3600.00)\nincome_tax = round(max(0, middle_portion) * 0.08 + upper_portion * 0.18, 2)\nnet_pay = 4326.01 - contribution - allowed_deduction - income_tax")
The first-half row applies (months 2026-01 through 2026-06): rate 0.07, cap 4500.00, deduction cap 400.00, free 1200.00, upper 3600.00, middle_rate 0.08, upper_rate 0.18. Now I'll compute the exact figures.
Reasoning
First-half row (2026-01 through 2026-06):
- rate: 0.07
- cap: 4500.00
- deduction cap: 400.00
- free: 1200.00
- upper: 3600.00
- middle_rate: 0.08
- upper_rate: 0.18

Check R4: allowed_deduction must not exceed min(deduction cap 400.00, gross_pay - rounded contribution).

Employee contribution = 0.07 * min(4500.00, 4326.01) = 0.07 * 4326.01 = 302.8207 → round to 302.82.

Allowed deduction check: 386.64 ≤ 400.00 ✓. Gross pay minus contribution: 4326.01 - 302.82 = 4023.19. 386.64 ≤ 4023.19 ✓. So allowed_deduction = 386.64.

Taxable pay = 4326.01 - 302.82 - 386.64 = 3636.55.

Income tax:
- Free: 1200.00 → untaxed.
- Portion above 1200 up to 3600: 3600 - 1200 = 2400 at 0.08 = 192.00.
- Portion above 3600: 3636.55 - 3600 = 36.55 at 0.18 = 6.579 → 6.579. Total = 192.00 + 6.579 = 198.579 → round half up to 198.58.

Wait, R2 says "Do not round intermediate bracket products separately before summing income tax." So sum 192.00 + 6.579 = 198.579, round half up → 198.58.

Net pay = 4326.01 - 302.82 - 386.64 - 198.58 = ?

4326.01 - 302.82 = 4023.19. 4023.19 - 386.64 = 3636.55. 3636.55 - 198.58 = 3437.97.

Let me verify with the calculator.
Tool
{
  "results": {"contribution": "302.82", "deduction_ok_cap": "386.64", "deduction_ok_pay": "386.64", "allowed_deduction": "386.64", "taxable_pay": "3636.55", "middle_portion": "2400.00", "upper_portion": "36.55", "income_tax": "198.58", "net_pay": "3437.97"}
}
Assistant
All inputs are valid and the calculation is complete. The month 2026-03 is covered by the first-half reference row; the deduction 386.64 is within both the 400.00 cap and available pay (4326.01 − 302.82 = 4023.19); tax brackets sum to 198.579, rounded half-up to 198.58.

{"decision": "calculate", "currency": "LCR", "gross_pay": "4326.01", "employee_contribution": "302.82", "allowed_deduction": "386.64", "taxable_pay": "3636.55", "income_tax": "198.58", "net_pay": "3437.97", "clauses": ["R1", "R2", "R3", "R4", "R5", "R6"], "explanation": "2026-03 selects the first-half row (rate 0.07, cap 4500.00, deduction cap 400.00, free 1200.00, upper 3600.00, middle 0.08, upper 0.18). Contribution = 0.07 × min(4500.00, 4326.01) = 302.82. Allowed deduction 386.64 is within the 400.00 cap and available pay 4023.19. Taxable pay = 4326.01 − 302.82 − 386.64 = 3636.55. Tax = 2400.00 × 0.08 + 36.55 × 0.18 = 198.579 → 198.58. Net pay = 4326.01 − 302.82 − 386.64 − 198.58 = 3437.97."}
Reasoning
All checks pass:
- R1: month 2026-03 covered by first-half row.
- R2: money valid, two decimals, round-half-up.
- R3: contribution = 0.07 × min(4500.00, 4326.01) = 302.82.
- R4: allowed_deduction 386.64 ≤ 400.00 cap and ≤ 4326.01 - 302.82 = 4023.19. Taxable = 3636.55.
- R5: 1200 free; 2400 × 0.08 = 192.00; 36.55 × 0.18 = 6.579; total 198.579 → 198.58.
- R6: net pay = 4326.01 - 302.82 - 386.64 - 198.58 = 3437.97.

Return JSON with decision, currency, fields, clauses R1-R6. No amendment needed, no conflict.
Rollout #2 100.0% passed · 5 tool calls · 12.6s · $0.0017
ComponentScoreClauses
decision 100.0% R1 R2 R3 R4 R5 R6
exact 100.0% R1 R2 R3 R4 R5 R6
field accuracy 100.0% R1 R2 R3 R4 R5 R6
citations 100.0% R1 R2 R3 R4 R5 R6
Assistant
list_documents()
Reasoning
Let me start by listing the documents to get the case inputs.
Tool
[
  {"id": "f8d9f5fe0eb33c57-payroll", "kind": "payroll"}
]
Assistant
read_document(document_id="f8d9f5fe0eb33c57-payroll")
Tool
{
  "kind": "payroll",
  "record": {"gross_pay": "4326.01", "payroll_month": "2026-03", "allowed_deduction": "386.64"}
}
Assistant
lookup_reference(reference="first-half")lookup_reference(reference="second-half")
Reasoning
The payroll record:
- gross_pay: 4326.01
- payroll_month: 2026-03
- allowed_deduction: 386.64

2026-03 is in 2026, so covered. March 2026 is in the second half (months 7-12 are second half? or 1-6 first half, 7-12 second half). Let me check the reference tables. March is month 3, so likely first half. Let me look up both to be safe — actually, I should determine which half March belongs to. Typically first-half = Jan-Jun, second-half = Jul-Dec. Let me look up the first-half reference (and maybe second-half to confirm boundaries). The lookup tool says "Read first-half or second-half payroll reference rates and effective months." I'll look up first-half since March is likely in the first half, but let me check both to be sure of the boundaries. Actually the tool returns effective months, so looking up first-half should tell me which months it covers. Let me call both in parallel to be safe.
Tool
{
  "reference": "first-half",
  "months": ["2026-01", "2026-06"],
  "rate": "0.07",
  "cap": "4500.00",
  "deduction": "400.00",
  "free": "1200.00",
  "upper": "3600.00",
  "middle_rate": "0.08",
  "upper_rate": "0.18"
}
Tool
{
  "reference": "second-half",
  "months": ["2026-07", "2026-12"],
  "rate": "0.05",
  "cap": "4500.00",
  "deduction": "400.00",
  "free": "1200.00",
  "upper": "3600.00",
  "middle_rate": "0.08",
  "upper_rate": "0.22"
}
Assistant
calculate(program="gross_pay = 4326.01\ncontribution_base = min(4326.01, 4500.00)\nemployee_contribution = round(contribution_base * 0.07, 2)\ndeduction_cap_check = max(386.64, 400.00)\navailable_check = gross_pay - employee_contribution\nallowed_deduction = 386.64\ntaxable_pay = gross_pay - employee_contribution - allowed_deduction\nmiddle_portion = 3600.00 - 1200.00\nmiddle_tax = middle_portion * 0.08\nupper_portion = taxable_pay - 3600.00\nupper_tax = upper_portion * 0.18\nincome_tax = round(middle_tax + upper_tax, 2)\nnet_pay = gross_pay - employee_contribution - allowed_deduction - income_tax")
The applicable row for 2026-03 is the first-half row (months 2026-01 through 2026-06). Now I'll compute the exact figures.
Reasoning
Payroll month 2026-03. First-half covers months 2026-01 through 2026-06 (the "months" field shows ["2026-01", "2026-06"] — presumably a range from 2026-01 to 2026-06). March 2026 falls in the first half. So the applicable row:

- rate: 0.07
- cap: 4500.00
- deduction cap: 400.00
- free: 1200.00
- upper: 3600.00
- middle_rate: 0.08
- upper_rate: 0.18

Now compute:
- Employee contribution = 0.07 * min(4326.01, 4500.00) = 0.07 * 4326.01 = 302.8207 → round half up to 302.82
- Allowed deduction = 386.64. Check: must not exceed deduction cap 400.00, nor gross pay minus rounded contribution = 4326.01 - 302.82 = 4023.19. 386.64 ≤ both. OK.
- Taxable pay = 4326.01 - 302.82 - 386.64 = 3636.55
- Income tax: free = 1200, upper = 3600.
  - Portion up to 1200: untaxed.
  - Portion 1200 to 3600: 3600 - 1200 = 2400 at 0.08 = 192.00
  - Portion above 3600: 3636.55 - 3600 = 36.55 at 0.18 = 6.579
  - Total = 192.00 + 6.579 = 198.579 → round half up → 198.58
- Net pay = 4326.01 - 302.82 - 386.64 - 198.58 = 3437.97

Let me verify with the calculator.
Tool
{
  "results": {"gross_pay": "4326.01", "contribution_base": "4326.01", "employee_contribution": "302.82", "deduction_cap_check": "400.00", "available_check": "4023.19", "allowed_deduction": "386.64", "taxable_pay": "3636.55", "middle_portion": "2400.00", "middle_tax": "192.0000", "upper_portion": "36.55", "upper_tax": "6.5790", "income_tax": "198.58", "net_pay": "3437.97"}
}
Assistant
{
  "decision": "calculate",
  "currency": "LCR",
  "gross_pay": "4326.01",
  "employee_contribution": "302.82",
  "allowed_deduction": "386.64",
  "taxable_pay": "3636.55",
  "income_tax": "198.58",
  "net_pay": "3437.97",
  "clauses": ["R1", "R2", "R3", "R4", "R5", "R6"],
  "explanation": "Payroll month 2026-03 selects the first-half reference row (rate 0.07, cap 4500.00, deduction cap 400.00, free 1200.00, upper 3600.00, middle 0.08, upper rate 0.18). Employee contribution = 0.07 \u00d7 min(4326.01, 4500.00) = 302.82 (R3). Allowed deduction 386.64 is within the 400.00 cap and within gross pay minus contribution (4023.19), so it stands (R4). Taxable pay = 4326.01 \u2212 302.82 \u2212 386.64 = 3636.55. Income tax is marginal: (3600.00 \u2212 1200.00) \u00d7 0.08 = 192.00 plus (3636.55 \u2212 3600.00) \u00d7 0.18 = 6.579, totaling 198.58 after R2 rounding (R5). Net pay = 4326.01 \u2212 302.82 \u2212 386.64 \u2212 198.58 = 3437.97 (R6)."
}
Reasoning
All checks pass:
- Employee contribution: 0.07 × min(4326.01, 4500.00) = 302.8207 → 302.82 (R3)
- Allowed deduction 386.64 ≤ deduction cap 400.00 and ≤ gross − contribution = 4023.19 (R4)
- Taxable pay = 4326.01 − 302.82 − 386.64 = 3636.55 (R4)
- Income tax: (3600−1200)×0.08 = 192.00; (3636.55−3600)×0.18 = 6.579; total 198.579 → 198.58 (R5)
- Net pay = 4326.01 − 302.82 − 386.64 − 198.58 = 3437.97 (R6)

Return the JSON with clauses R1, R2, R3, R4, R5, R6.
Rollout #3 100.0% passed · 4 tool calls · 11.3s · $0.0019
ComponentScoreClauses
decision 100.0% R1 R2 R3 R4 R5 R6
exact 100.0% R1 R2 R3 R4 R5 R6
field accuracy 100.0% R1 R2 R3 R4 R5 R6
citations 100.0% R1 R2 R3 R4 R5 R6
Assistant
list_documents()
Reasoning
Let me start by listing the documents to get the case inputs.
Tool
[
  {"id": "f8d9f5fe0eb33c57-payroll", "kind": "payroll"}
]
Assistant
read_document(document_id="f8d9f5fe0eb33c57-payroll")
Tool
{
  "kind": "payroll",
  "record": {"gross_pay": "4326.01", "payroll_month": "2026-03", "allowed_deduction": "386.64"}
}
Assistant
lookup_reference(reference="first-half")
Reasoning
The payroll record:
- gross_pay: 4326.01
- payroll_month: 2026-03
- allowed_deduction: 386.64

2026-03 is covered by the reference rows. I need to look up the reference for the month. 2026-03 is March, which is in the first half of the year (first-half covers January–June presumably). Let me look up the first-half reference.
Tool
{
  "reference": "first-half",
  "months": ["2026-01", "2026-06"],
  "rate": "0.07",
  "cap": "4500.00",
  "deduction": "400.00",
  "free": "1200.00",
  "upper": "3600.00",
  "middle_rate": "0.08",
  "upper_rate": "0.18"
}
Assistant
calculate(program="contribution = round(min(4500.00, 4326.01) * 0.07, 2)\navail_check = 4326.01 - contribution\ntaxable = 4326.01 - contribution - 386.64\nmiddle_portion = min(3600.00, taxable) - 1200.00\nupper_portion = max(0.00, taxable - 3600.00)\ntax = round(middle_portion * 0.08 + upper_portion * 0.18, 2)\nnet = 4326.01 - contribution - 386.64 - tax")
The record is complete: gross_pay 4326.01, payroll_month 2026-03 (covered by the first-half reference row), allowed_deduction 386.64. Now I'll compute exactly.
Reasoning
The first-half reference covers 2026-01 through 2026-06 (months listed as ["2026-01", "2026-06"], presumably a range). 2026-03 falls within this range.

Reference row:
- rate: 0.07
- cap: 4500.00
- deduction: 400.00
- free: 1200.00
- upper: 3600.00
- middle_rate: 0.08
- upper_rate: 0.18

Now calculate:
- Employee contribution = 0.07 * min(4326.01, 4500.00) = 0.07 * 4326.01 = 302.8207 → round to 302.82
- Allowed deduction: 386.64. Check: must not exceed deduction cap 400.00 (yes, 386.64 ≤ 400.00) and gross pay minus rounded contribution: 4326.01 - 302.82 = 4023.19. 386.64 ≤ 4023.19. OK.
- Taxable pay = 4326.01 - 302.82 - 386.64 = 3636.55
- Income tax: 
  - Free: 1200.00 → untaxed
  - Middle bracket: 3600.00 - 1200.00 = 2400.00 at 0.08 = 192.00
  - Upper bracket: 3636.55 - 3600.00 = 36.55 at 0.18 = 6.579 → but "Do not round intermediate bracket products separately before summing income tax." So total = 192.00 + 6.579 = 198.579 → round to 198.58
- Net pay = 4326.01 - 302.82 - 386.64 - 198.58 = 3437.97

Let me verify with the calculator.
Tool
{
  "results": {"contribution": "302.82", "avail_check": "4023.19", "taxable": "3636.55", "middle_portion": "2400.00", "upper_portion": "36.55", "tax": "198.58", "net": "3437.97"}
}
Assistant
{
  "decision": "calculate",
  "currency": "LCR",
  "gross_pay": "4326.01",
  "employee_contribution": "302.82",
  "allowed_deduction": "386.64",
  "taxable_pay": "3636.55",
  "income_tax": "198.58",
  "net_pay": "3437.97",
  "clauses": ["R1", "R2", "R3", "R4", "R5", "R6"],
  "explanation": "2026-03 selects the first-half reference row (rate 0.07, cap 4500.00, deduction cap 400.00, free 1200.00, upper 3600.00, middle 0.08, upper 0.18). Contribution = 0.07 \u00d7 min(4326.01, 4500.00) = 302.82. Allowed deduction 386.64 is within the 400.00 cap and within available pay (4326.01 \u2212 302.82 = 4023.19). Taxable pay = 4326.01 \u2212 302.82 \u2212 386.64 = 3636.55. Tax = 2400.00 \u00d7 0.08 + 36.55 \u00d7 0.18 = 198.579 \u2192 198.58 (rounded once on the summed total). Net pay = 4326.01 \u2212 302.82 \u2212 386.64 \u2212 198.58 = 3437.97."
}
Reasoning
All checks pass:
- Contribution: 0.07 × min(4326.01, 4500.00) = 302.82 (R3)
- Allowed deduction 386.64 ≤ 400.00 cap and ≤ 4023.19 available (R4)
- Taxable pay: 4326.01 - 302.82 - 386.64 = 3636.55 (R4)
- Tax: 2400.00 × 0.08 + 36.55 × 0.18 = 192.00 + 6.579 = 198.579 → 198.58 (R5)
- Net: 4326.01 - 302.82 - 386.64 - 198.58 = 3437.97 (R6)

Return the JSON object with the required fields. No markdown fences, no prose.