Luma Payroll Gym
← Heatmap / GLM 5.3 Flash · Task 78
GLM 5.3 Flash · Tool use · Task 78 (Calculation, at the tax-free line) Mean 50.0%
Field Expected Rollout #1 (100%) Rollout #2 (-50%) Rollout #3 (100%)
decision calculate calculate (malformed) calculate
currency LCR LCR (malformed) LCR
gross pay 948.45 948.45 (malformed) 948.45
employee contribution 47.42 47.42 (malformed) 47.42
allowed deduction 1.03 1.03 (malformed) 1.03
taxable pay 900.00 900.00 (malformed) 900.00
income tax 0.00 0.00 (malformed) 0.00
net pay 900.00 900.00 (malformed) 900.00
clauses R1 R2 R3 R4 R5 R6 R1 R2 R3 R4 R5 R6 (malformed) 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 #1 100.0% passed · 5 tool calls · 15.1s · $0.0015
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": "5178404fc18b0e41-payroll", "kind": "payroll"}
]
Assistant
read_document(document_id="5178404fc18b0e41-payroll")
Tool
{
  "kind": "payroll",
  "record": {"gross_pay": "948.45", "payroll_month": "2026-05", "allowed_deduction": "1.03"}
}
Assistant
lookup_reference(reference="first-half")lookup_reference(reference="second-half")
Reasoning
The payroll record has:
- gross_pay: 948.45
- payroll_month: 2026-05
- allowed_deduction: 1.03

Payroll month 2026-05 is in 2026, which is covered. May 2026 is in the second half of the year (months 7-12? or is it first-half/second-half?). Let me check the reference. "first-half" and "second-half" — likely first half is Jan-Jun and second half is Jul-Dec. May is in the first half. But I should use lookup_reference to get the exact rows. Let me look up both to be safe — actually, May 2026 is in the first half (Jan-Jun). Let me look up first-half. But to be careful, I could look up both in the same block since they're independent.
Tool
{
  "reference": "first-half",
  "months": ["2026-01", "2026-06"],
  "rate": "0.05",
  "cap": "4500.00",
  "deduction": "400.00",
  "free": "900.00",
  "upper": "3300.00",
  "middle_rate": "0.08",
  "upper_rate": "0.18"
}
Tool
{
  "reference": "second-half",
  "months": ["2026-07", "2026-12"],
  "rate": "0.06",
  "cap": "3500.00",
  "deduction": "400.00",
  "free": "1100.00",
  "upper": "2800.00",
  "middle_rate": "0.10",
  "upper_rate": "0.22"
}
Assistant
calculate(program="gross_pay = 948.45\ncontribution = round(min(948.45, 4500.00) * 0.05, 2)\ndeduction = 1.03\navailable = gross_pay - contribution\ntaxable = gross_pay - contribution - deduction\ntax_free_portion = max(0, taxable - 900.00)\nmiddle_portion = max(0, min(taxable, 3300.00) - 900.00)\nupper_portion = max(0, taxable - 3300.00)\ntax = round(tax_free_portion * 0 + middle_portion * 0.08 + upper_portion * 0.18, 2)\nnet = gross_pay - contribution - deduction - tax")
Reasoning
The months lists: first-half covers "2026-01" through "2026-06" (range), second-half covers "2026-07" through "2026-12". Payroll month 2026-05 falls in first-half.

First-half row:
- rate: 0.05
- cap: 4500.00
- deduction cap: 400.00
- free: 900.00
- upper: 3300.00
- middle_rate: 0.08
- upper_rate: 0.18

Now compute:
- gross_pay = 948.45
- employee_contribution = round(min(948.45, 4500.00) * 0.05, 2) = round(47.4225, 2) = 47.42 (round half up: 47.4225 → 47.42 since third decimal is 2... wait, 47.4225 rounds to 47.42 because the digit after the second decimal is 2, which is < 5). Actually 47.4225: two decimal places means we look at 0.0025 → rounds to 0.00? Wait: 47.4225 → the cents part is 42, next digit is 2, so round down → 47.42. Yes.
- allowed_deduction = 1.03. Check cap: must not exceed 400.00 or gross pay minus contribution = 948.45 - 47.42 = 901.03. 1.03 ≤ both. OK.
- taxable_pay = 948.45 - 47.42 - 1.03 = 900.00
- income tax: taxable 900.00, free = 900.00. Portion above free = 0.00. Tax = 0.00.
- net_pay = 948.45 - 47.42 - 1.03 - 0.00 = 900.00

Let me verify with the calculator for exactness.
Tool
{
  "results": {"gross_pay": "948.45", "contribution": "47.42", "deduction": "1.03", "available": "901.03", "taxable": "900.00", "tax_free_portion": "0", "middle_portion": "0", "upper_portion": "0", "tax": "0.00", "net": "900.00"}
}
Assistant
{
  "decision": "calculate",
  "currency": "LCR",
  "gross_pay": "948.45",
  "employee_contribution": "47.42",
  "allowed_deduction": "1.03",
  "taxable_pay": "900.00",
  "income_tax": "0.00",
  "net_pay": "900.00",
  "clauses": ["R1", "R2", "R3", "R4", "R5", "R6"],
  "explanation": "Payroll month 2026-05 selects the first-half reference row (2026-01 to 2026-06). Employee contribution is 0.05 \u00d7 min(948.45, 4500.00) = 47.42 (R3). Allowed deduction 1.03 is within the 400.00 cap and the 901.03 available after contribution (R4). Taxable pay is 948.45 \u2212 47.42 \u2212 1.03 = 900.00, which does not exceed the 900.00 tax-free amount, so income tax is 0.00 (R5). Net pay is 948.45 \u2212 47.42 \u2212 1.03 \u2212 0.00 = 900.00 (R6)."
}
Reasoning
All checks pass:
- 2026-05 covered by first-half row (2026-01 to 2026-06).
- Contribution: 5% × min(948.45, 4500.00) = 47.42 (rounded).
- Allowed deduction 1.03 ≤ 400.00 cap and ≤ 901.03 available. OK.
- Taxable pay = 900.00, exactly at the tax-free amount 900.00, so tax = 0.00.
- Net = 900.00.

Return R6 JSON with clauses R1, R2, R3, R4, R5, R6.
Rollout #2 -50.0% malformed · 4 tool calls · 9.7s · $0.0013
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": "5178404fc18b0e41-payroll", "kind": "payroll"}
]
Assistant
read_document(document_id="5178404fc18b0e41-payroll")
Tool
{
  "kind": "payroll",
  "record": {"gross_pay": "948.45", "payroll_month": "2026-05", "allowed_deduction": "1.03"}
}
Assistant
lookup_reference(reference="first-half")
Reasoning
The payroll record:
- gross_pay: 948.45
- payroll_month: 2026-05
- allowed_deduction: 1.03

Payroll month 2026-05 is in 2026, so covered. May 2026 — need to determine which reference row applies. The rules mention first-half and second-half. Let me look up the reference tables. Presumably first-half covers Jan–Jun and second-half covers Jul–Dec. May 2026 would be first-half.

Let me look up first-half reference.
Tool
{
  "reference": "first-half",
  "months": ["2026-01", "2026-06"],
  "rate": "0.05",
  "cap": "4500.00",
  "deduction": "400.00",
  "free": "900.00",
  "upper": "3300.00",
  "middle_rate": "0.08",
  "upper_rate": "0.18"
}
Assistant
calculate(program="contribution_base = min(948.45, 4500.00)\nemployee_contribution = round(contribution_base * 0.05, 2)\ntaxable_pay = round(948.45 - employee_contribution - 1.03, 2)\ntax_free_portion = max(0.00, min(taxable_pay, 900.00) - 0.00)\nmiddle_portion = max(0.00, min(taxable_pay, 3300.00) - 900.00)\nupper_portion = max(0.00, taxable_pay - 3300.00)\nincome_tax = round(tax_free_portion * 0.00 + middle_portion * 0.08 + upper_portion * 0.18, 2)\nnet_pay = round(948.45 - employee_contribution - 1.03 - income_tax, 2)\ndeduction_cap_check = min(400.00, 948.45 - employee_contribution)")
The record has gross_pay 948.45, payroll_month 2026-05, and allowed_deduction 1.03. May 2026 falls in the first-half reference row (2026-01 through 2026-06). Let me compute exactly.
Reasoning
The first-half reference covers months "2026-01" through "2026-06" (listed as ["2026-01", "2026-06"], presumably meaning the range from 2026-01 to 2026-06). May 2026 (2026-05) falls in this range.

Reference row for 2026-05:
- rate: 0.05
- cap: 4500.00
- deduction cap: 400.00
- free: 900.00
- upper: 3300.00
- middle_rate: 0.08
- upper_rate: 0.18

Inputs:
- gross_pay: 948.45
- allowed_deduction: 1.03

Checks:
1. gross_pay present ✓
2. payroll_month present ✓
3. Reference row exists for 2026-05 ✓
4. No contract_gross_pay conflict ✓

Calculations:
- Employee contribution = 0.05 × min(948.45, 4500.00) = 0.05 × 948.45 = 47.4225 → round to 47.42
- Allowed deduction check: 1.03 ≤ 400.00 ✓; 1.03 ≤ gross_pay − contribution = 948.45 − 47.42 = 901.03 ✓
- Taxable pay = 948.45 − 47.42 − 1.03 = 900.00
- Income tax: taxable pay 900.00. Tax-free amount = 900.00. Portion up to 900.00 is untaxed → 0. Portion above 900.00 up to 3300.00 at 8% → 0. Portion above 3300.00 at 18% → 0. Income tax = 0.00
- Net pay = 948.45 − 47.42 − 1.03 − 0.00 = 900.00

Let me verify with the calculator.
Tool
{
  "results": {"contribution_base": "948.45", "employee_contribution": "47.42", "taxable_pay": "900.00", "tax_free_portion": "900.00", "middle_portion": "0.00", "upper_portion": "0.00", "income_tax": "0.00", "net_pay": "900.00", "deduction_cap_check": "400.00"}
}
Assistant
All checks pass: the month 2026-05 is covered by the first-half reference row, the allowed deduction 1.03 is within both the 400.00 deduction cap and the available pay (948.45 − 47.42 = 901.03), and there are no conflicting inputs or amendments.

```json
{
  "decision": "calculate",
  "currency": "LCR",
  "gross_pay": "948.45",
  "employee_contribution": "47.42",
  "allowed_deduction": "1.03",
  "taxable_pay": "900.00",
  "income_tax": "0.00",
  "net_pay": "900.00",
  "clauses": ["R1", "R2", "R3", "R4", "R5", "R6"],
  "explanation": "2026-05 selects the first-half reference row (rate 0.05, cap 4500.00, deduction cap 400.00, free 900.00, upper 3300.00). Employee contribution = 0.05 × min(948.45, 4500.00) = 47.4225 → 47.42 (R3). Allowed deduction 1.03 is within the 400.00 cap and available pay (R4). Taxable pay = 948.45 − 47.42 − 1.03 = 900.00, which is entirely within the 900.00 tax-free amount, so income tax = 0.00 (R5). Net pay = 948.45 − 47.42 − 1.03 − 0.00 = 900.00 (R6)."
}
```
Reasoning
All checks pass:
- Employee contribution: 0.05 × 948.45 = 47.4225 → 47.42 (R3, R2)
- Allowed deduction 1.03 ≤ 400.00 cap and ≤ 948.45 − 47.42 = 901.03 (R4)
- Taxable pay: 948.45 − 47.42 − 1.03 = 900.00 (R4)
- Income tax: taxable 900.00 is entirely within the tax-free amount of 900.00 → tax = 0.00 (R5)
- Net pay: 948.45 − 47.42 − 1.03 − 0.00 = 900.00 (R6)

Return the R6 JSON with clauses R1–R6. No amendment needed, so no R9.
Rollout #3 100.0% passed · 4 tool calls · 9.2s · $0.0014
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 see the case inputs.
Tool
[
  {"id": "5178404fc18b0e41-payroll", "kind": "payroll"}
]
Assistant
read_document(document_id="5178404fc18b0e41-payroll")
Tool
{
  "kind": "payroll",
  "record": {"gross_pay": "948.45", "payroll_month": "2026-05", "allowed_deduction": "1.03"}
}
Assistant
lookup_reference(reference="first-half")
Reasoning
The payroll record:
- gross_pay: 948.45
- payroll_month: 2026-05
- allowed_deduction: 1.03

No contract_gross_pay, no amendment. So no conflict.

Month 2026-05 is in the first half of 2026 (January–June). Let me look up the reference table.
Tool
{
  "reference": "first-half",
  "months": ["2026-01", "2026-06"],
  "rate": "0.05",
  "cap": "4500.00",
  "deduction": "400.00",
  "free": "900.00",
  "upper": "3300.00",
  "middle_rate": "0.08",
  "upper_rate": "0.18"
}
Assistant
calculate(program="gross = 948.45\ncap = 4500.00\nrate = 0.05\ncontribution = round(min(gross, cap) * rate, 2)\ndeduction = 1.03\navailable = gross - contribution\ntaxable = gross - contribution - deduction\nfree = 900.00\nupper = 3300.00\nmiddle_rate = 0.08\nupper_rate = 0.18\nmiddle_portion = max(0.00, min(taxable, upper) - free)\nupper_portion = max(0.00, taxable - upper)\ntax = round(middle_portion * middle_rate + upper_portion * upper_rate, 2)\nnet = gross - contribution - deduction - tax")
Reasoning
The reference row for first half 2026 (months 2026-01 through 2026-06):
- rate: 0.05
- cap: 4500.00
- deduction cap: 400.00
- free: 900.00
- upper: 3300.00
- middle_rate: 0.08
- upper_rate: 0.18

Payroll month 2026-05 is covered (2026-01 through 2026-06).

Now compute:
1. Employee contribution = rate * min(gross, cap) = 0.05 * min(948.45, 4500.00) = 0.05 * 948.45 = 47.4225 → round to 47.42 (round half up: 47.4225 → 47.42 since third decimal is 2, rounds down).

2. Allowed deduction = 1.03. Check: must not exceed deduction cap (400.00) or gross pay minus rounded employee contribution (948.45 - 47.42 = 901.03). 1.03 ≤ both. OK.

3. Taxable pay = gross - contribution - deduction = 948.45 - 47.42 - 1.03 = 900.00.

4. Income tax: taxable pay = 900.00. Tax-free amount = 900.00. Portion above free up to upper (3300.00) uses middle rate 0.08. Taxable pay is exactly 900.00, so portion above free = 0. Tax = 0.00.

5. Net pay = 948.45 - 47.42 - 1.03 - 0.00 = 900.00.

Let me verify with calculate.
Tool
{
  "results": {"gross": "948.45", "cap": "4500.00", "rate": "0.05", "contribution": "47.42", "deduction": "1.03", "available": "901.03", "taxable": "900.00", "free": "900.00", "upper": "3300.00", "middle_rate": "0.08", "upper_rate": "0.18", "middle_portion": "0.00", "upper_portion": "0.00", "tax": "0.00", "net": "900.00"}
}
Assistant
{
  "decision": "calculate",
  "currency": "LCR",
  "gross_pay": "948.45",
  "employee_contribution": "47.42",
  "allowed_deduction": "1.03",
  "taxable_pay": "900.00",
  "income_tax": "0.00",
  "net_pay": "900.00",
  "clauses": ["R1", "R2", "R3", "R4", "R5", "R6"],
  "explanation": "Month 2026-05 selects the first-half 2026 reference row (rate 0.05, cap 4500.00, deduction cap 400.00, free 900.00, upper 3300.00, middle 0.08, upper 0.18). Contribution = 0.05 \u00d7 min(948.45, 4500.00) = 47.4225 \u2192 47.42 (R3). Allowed deduction 1.03 is within the 400.00 cap and the available pay 948.45 \u2212 47.42 = 901.03 (R4). Taxable pay = 948.45 \u2212 47.42 \u2212 1.03 = 900.00 (R4). Taxable pay equals the tax-free amount 900.00, so the middle and upper portions are both 0.00 and income tax is 0.00 (R5). Net pay = 948.45 \u2212 47.42 \u2212 1.03 \u2212 0.00 = 900.00 (R6)."
}
Reasoning
All checks pass:
- gross_pay 948.45, month 2026-05 covered by first-half row.
- Contribution: 0.05 * min(948.45, 4500.00) = 47.4225 → 47.42 (R2, R3).
- Allowed deduction 1.03 ≤ 400.00 cap and ≤ 901.03 available (R4).
- Taxable pay = 948.45 - 47.42 - 1.03 = 900.00 (R4).
- Tax: taxable 900.00 equals free amount 900.00, so middle portion = 0, upper portion = 0, tax = 0.00 (R5).
- Net = 948.45 - 47.42 - 1.03 - 0.00 = 900.00 (R6).

No amendment or contract conflict, so no R9 citation needed. Cite R1–R6.