Math Expressions

Math expressions let you compute values inline on either side of a comparison, or inside computed values, without needing to pre-compute fields in your data.

Syntax

Math expressions support full nested arithmetic:

<expression> <comparison> <expression>

An expression can contain:

• properties
• literal numbers
• computed value references like @total
• +, -, *, /, %, ^
• math functions: floor, ceil, round, abs, sqrt, min, max, clamp
• aggregate expressions: sum of, average of, min of, max of
• natural-language aliases
• parentheses

Operator	Accepted forms
addition	+, plus, added to
subtraction	-, minus, subtracted by
multiplication	*, times, multiplied by
division	/, divided by
modulo	%, modulo, remainder of
power	^, power of, to the power of

Precedence

The engine applies normal arithmetic precedence:

1. parentheses and math functions
2. exponentiation
3. multiplication, division, and modulo
4. addition and subtraction

This means multiplication happens before addition:

__subtotal__ of **Order** + __tax__ of **Order** * 2 is greater than 100

Use parentheses when you want a different grouping:

(__subtotal__ of **Order** + __tax__ of **Order**) * 2 is greater than 100

Addition

__subtotal__ of **Order** + __tax__ of **Order** is greater than 100

Aliases also work:

__subtotal__ of **Order** plus __tax__ of **Order** is greater than 100

Interactive Example

Reset

Policy Rule

A **Order** requires signature
if __subtotal__ of **Order** + __tax__ of **Order** is greater than 100.

A **Order** requires signature if __subtotal__ of **Order** + __tax__ of **Order** is greater than 100.

Test Data (JSON)

{
  "Order": { "subtotal": 90, "tax": 15 }
}

{ "Order": { "subtotal": 90, "tax": 15 } }

Run

Mix a property with a literal:

Interactive Example

Reset

Policy Rule

A **Product** is premium
if __base_price__ of **Product** + 20 is greater than 50.

A **Product** is premium if __base_price__ of **Product** + 20 is greater than 50.

Test Data (JSON)

{
  "Product": { "base_price": 35 }
}

{ "Product": { "base_price": 35 } }

Run

Subtraction

__balance__ of **Account** - __pending__ of **Account** is at least 0

Interactive Example

Reset

Policy Rule

A **Account** has sufficient funds
if __balance__ of **Account** - __reserved__ of **Account** is at least 100.

A **Account** has sufficient funds if __balance__ of **Account** - __reserved__ of **Account** is at least 100.

Test Data (JSON)

{
  "Account": { "balance": 500, "reserved": 350 }
}

{ "Account": { "balance": 500, "reserved": 350 } }

Run

Multiplication

__quantity__ of **Order** * __unit_price__ of **Order** is greater than 1000

Interactive Example

Reset

Policy Rule

A **Order** qualifies for wholesale pricing
if __quantity__ of **Order** * __unit_price__ of **Order** is at least 500.

A **Order** qualifies for wholesale pricing if __quantity__ of **Order** * __unit_price__ of **Order** is at least 500.

Test Data (JSON)

{
  "Order": { "quantity": 10, "unit_price": 60 }
}

{ "Order": { "quantity": 10, "unit_price": 60 } }

Run

Division

__revenue__ of **Store** / __expenses__ of **Store** is greater than 1.5

Interactive Example

Reset

Policy Rule

A **Store** is profitable
if __revenue__ of **Store** / __expenses__ of **Store** is greater than 1.

A **Store** is profitable if __revenue__ of **Store** / __expenses__ of **Store** is greater than 1.

Test Data (JSON)

{
  "Store": { "revenue": 12000, "expenses": 8000 }
}

{ "Store": { "revenue": 12000, "expenses": 8000 } }

Run

Modulo

Modulo returns the remainder after division. It shares precedence with * and /.

__count__ of **Order** % 2 is equal to 0

Aliases also work:

__count__ of **Order** modulo 2 is equal to 0

__count__ of **Order** remainder of 2 is equal to 0

Interactive Example

Reset

Policy Rule

A **Order** is even
if __count__ of **Order** % 2 is equal to 0.

A **Order** is even if __count__ of **Order** % 2 is equal to 0.

Test Data (JSON)

{
  "Order": { "count": 10 }
}

{ "Order": { "count": 10 } }

Run

Power

Exponentiation raises the left side to the power of the right side.

__score__ of **Applicant** power of 2 is greater than 49

Aliases also work:

__score__ of **Applicant** ^ 2 is greater than 49

__score__ of **Applicant** to the power of 2 is greater than 49

Interactive Example

Reset

Policy Rule

A **Applicant** is approved
if __score__ of **Applicant** power of 2 is greater than 49.

A **Applicant** is approved if __score__ of **Applicant** power of 2 is greater than 49.

Test Data (JSON)

{
  "Applicant": { "score": 8 }
}

{ "Applicant": { "score": 8 } }

Run

Math Functions

Math functions return transformed numbers. Unary functions accept one expression; min, max, and clamp accept multiple arguments.

Function	Description
floor of (...)	round down to the nearest integer
ceil of (...)	round up to the nearest integer
round of (...)	round to the nearest integer
round X to N places	round to a fixed number of decimal places
abs of (...)	absolute value
sqrt(...)	square root
min(...)	smallest argument
max(...)	largest argument
clamp(value, min, max)	bound a value within a range

floor of

floor of (__price__ of **Order** * 1.1) is equal to 11

Interactive Example

Reset

Policy Rule

A **Order** is rounded down
if floor of (__price__ of **Order** * 1.1) is equal to 11.

A **Order** is rounded down if floor of (__price__ of **Order** * 1.1) is equal to 11.

Test Data (JSON)

{
  "Order": { "price": 10.5 }
}

{ "Order": { "price": 10.5 } }

Run

ceil of

ceil of (__price__ of **Order** * 1.1) is equal to 12

Interactive Example

Reset

Policy Rule

A **Order** is rounded up
if ceil of (__price__ of **Order** * 1.1) is equal to 12.

A **Order** is rounded up if ceil of (__price__ of **Order** * 1.1) is equal to 12.

Test Data (JSON)

{
  "Order": { "price": 10.5 }
}

{ "Order": { "price": 10.5 } }

Run

round of

round of (__score__ of **User** / 3) is equal to 4

Interactive Example

Reset

Policy Rule

A **User** is scored
if round of (__score__ of **User** / 3) is equal to 4.

A **User** is scored if round of (__score__ of **User** / 3) is equal to 4.

Test Data (JSON)

{
  "User": { "score": 11 }
}

{ "User": { "score": 11 } }

Run

You can also use the natural form round X to N places:

round __score__ of **User** to 2 places is equal to 3.14

abs of

abs of (__balance__ of **Account** - __limit__ of **Account**) is less than 50

Interactive Example

Reset

Policy Rule

A **Account** is close to the limit
if abs of (__balance__ of **Account** - __limit__ of **Account**) is less than 50.

A **Account** is close to the limit if abs of (__balance__ of **Account** - __limit__ of **Account**) is less than 50.

Test Data (JSON)

{
  "Account": { "balance": 1030, "limit": 1000 }
}

{ "Account": { "balance": 1030, "limit": 1000 } }

Run

sqrt

sqrt(81) is equal to 9

min / max / clamp

min(9, 4, 7) is equal to 4

max(2, 9, 4) is equal to 9

clamp(20, 0, 10) is equal to 10

Aggregate Expressions In Math

sum of, average of, min of, and max of can be used as arithmetic expressions, not just directly in comparisons:

total := sum of __prices__ of **Order**.
average_price := average of __prices__ of **Order**.

A **Order** qualifies
if @total is greater than 50
and @average_price is greater than 10.

These aggregate expressions also accept numeric strings in arrays, such as ["15", "25", "20"].

Math functions compose with the rest of the grammar:

Interactive Example

Reset

Policy Rule

A **Obj** qualifies
if floor of (__x__ of **Obj** % 2 * 25 / 100 * __allowance__ of **Obj**) is greater than 0.

A **Obj** qualifies if floor of (__x__ of **Obj** % 2 * 25 / 100 * __allowance__ of **Obj**) is greater than 0.

Test Data (JSON)

{
  "Obj": { "x": 5, "allowance": 100 }
}

{ "Obj": { "x": 5, "allowance": 100 } }

Run

Nested Expressions

You can nest expressions and put arithmetic on both sides of the comparison:

(__used__ of **Quota** + __buffer__ of **Quota**) * 2 is less than __limit__ of **Quota** * 3 - 1

Interactive Example

Reset

Policy Rule

A **Quota** is safe
if (__used__ of **Quota** + __buffer__ of **Quota**) * 2 is less than __limit__ of **Quota** * 3 - 1.

A **Quota** is safe if (__used__ of **Quota** + __buffer__ of **Quota**) * 2 is less than __limit__ of **Quota** * 3 - 1.

Test Data (JSON)

{
  "Quota": { "used": 10, "buffer": 4, "limit": 7 }
}

{ "Quota": { "used": 10, "buffer": 4, "limit": 7 } }

Run

Combining with Other Conditions

Math expressions can be combined with and and or like any other condition:

Interactive Example

Reset

Policy Rule

A **Applicant** is approved
if __income__ of **Applicant** - __debt__ of **Applicant** is at least 30000
and __age__ of **Applicant** is at least 18.

A **Applicant** is approved if __income__ of **Applicant** - __debt__ of **Applicant** is at least 30000 and __age__ of **Applicant** is at least 18.

Test Data (JSON)

{
  "Applicant": { "income": 70000, "debt": 25000, "age": 30 }
}

{ "Applicant": { "income": 70000, "debt": 25000, "age": 30 } }

Run

Errors And Traces

Every arithmetic step must resolve to numbers.

• Numeric strings such as "12.5" are accepted in arithmetic.
• Non-numeric operands return a type error that includes the failing expression.
• Division by zero returns an evaluation error that includes the full expression.
• Execution traces expose the evaluated left-hand expression path and the final right-hand value, so the UI can explain what was compared.

Example errors:

Arithmetic expression $.Applicant.status resolved to a non-numeric string "active", but numeric operands are required
Division by zero in arithmetic expression ($.Student.total / ($.Student.count - $.Student.count))

Summary

Capability	Supported
literal numbers	yes
property references	yes
math on the left side	yes
math on the right side	yes
nested expressions	yes
parentheses	yes
precedence (^ before *///% before +/-)	yes
computed value references (@name)	yes
aggregate expressions (sum of, average of, min of, max of)	yes
math functions (floor, ceil, round, abs, sqrt, min, max, clamp)	yes

Operator	Accepted forms	Example
addition	+, plus, added to	__subtotal__ of **Order** plus __tax__ of **Order** is greater than 50
subtraction	-, minus, subtracted by	__balance__ of **Account** minus __reserved__ of **Account** is at least 0
multiplication	*, times, multiplied by	__qty__ of **Order** times __price__ of **Order** is greater than 100
division	/, divided by	__revenue__ of **Store** divided by __costs__ of **Store** is greater than 1
modulo	%, modulo, remainder of	__count__ of **Order** % 2 is equal to 0
power	^, power of, to the power of	__score__ of **Applicant** power of 2 is greater than 49

Function	Example
floor of	floor of (__price__ of **Order** * 1.1) is equal to 11
ceil of	ceil of (__price__ of **Order** * 1.1) is equal to 12
round of	round of (__score__ of **User** / 3) is equal to 4
round ... to ... places	round __score__ of **User** to 2 places is equal to 3.14
abs of	abs of (__balance__ of **Account** - __limit__ of **Account**) is less than 50
sqrt	sqrt(81) is equal to 9
min	min(9, 4, 7) is equal to 4
max	max(2, 9, 4) is equal to 9
clamp	clamp(20, 0, 10) is equal to 10