Operator precedence
The order in which various parts of an expression are evaluated affects the result. The operator precedence unambiguously determines the order in which sub-expressions are evaluated.
Multiplication and division are performed before addition and subtraction.
For example, 3 * 4 +2 is the same as 2 + 3 * 4 and gives the answer 14.
Exponents and roots are performed before multiplication and addition.
For example, 3 + 5 ^ 2 is the same as 3 + 5 and gives the answer 28.
-3 ^ 2 is the same as -3 and gives the answer -9.
Use brackets (parentheses) to avoid confusion.
For example, 2 + 3 * 4 is the same as 2 + (3 * 4) and gives the answer 14.
Parentheses change the order of precedence as terms inside in parentheses are performed first.
For example, (2 + 3) * 4 gives the answer 20.
or, (3 + 5) ^2 is the same as (3 + 5) and gives the answer 64.
You must surround the arguments of a function with parentheses.
For example, y = sqrt(2), y = tan(x), y = sin(x + z).
Relational operators are performed after addition and subtraction.
For example, a+b >= c+d is the same as (a+b) >= (c+d).
Logical operators are performed after relational operators, though parentheses are often added for clarity.
For example:
5 == 2+3 OR 10 <= 3*3
is the same as:
(5 == (2+3)) OR (10 <= (3*3))
but is normally written as
(5 == 2+3) OR (10 <= 3*3).
Precedence
| Order | Operation | Description |
|---|---|---|
| 1 | () | function call, operations grouped in parentheses |
| 2 | [] | operations grouped in square brackets |
| 3 | + - ! | unary prefix (unary operations have only one operand, such as, !x, -y) |
| 4 | cm mm um ft in th | unit conversion |
| 5 | ^ | exponents and roots |
| 6 | * / % | multiplication, division, modulo |
| 7 | + - | addition and subtraction |
| 8 | < <= > >= (LT, LE, GT, GE) | relational comparisons: less than, less than or equal, greater than, greater than or equal |
| 9 | == != (EQ, NE) | relational comparisons: equals, not equals |
| 10 | AND | logical operator AND |
| 11 | NOT | logical operator NOT |
| 12 | XOR | logical operator XOR |
| 13 | OR | logical operator OR |
| 14 | , | separation of elements in a list |
Examples of precedence:
| Expression | Equivalent |
|---|---|
| a * - 2 | a * (- 2) |
| !x == 0 | (!x) == 0 |
| $a = -b + c * d – e | $a = ((-b) + (c * d)) – e |
| $a = b + c % d – e | $a = (b + (c % d)) – e |
| $x = y == z | $x = (y == z) |
| $x = -t + q * r / c | $x = ((-t) + ((q * r) / c)) |
| $x = a % b * c + d | $x = (((a % b) * c) + d) |
| $a = b <= c | d != e |
| $a = !b | c & d |
| $a = b mm * c in + d | $a = (((b mm) * (c in)) + d) |