Order Expressions in Formulas

As you build a formula, keep in mind that all functions have an order of precedence shown in the following table, where level one is the highest order of precedence. Expressions with a high order of precedence are evaluated before those at lower levels. When an expression has operators of equal precedence, it is evaluated from left to right. You can use parentheses to override other precedence rules when necessary because any expression within parentheses is always evaluated first. Terms have no order of precedence because they cannot be evaluated further. Order of Precedence of Operators in Formulas shows the first six levels of the order of precedence.

Order of Precedence of Operators in Formulas
Level 1	Parentheses
Level 2	Functions in the function browser lists, And, Or, Not
Level 3	*, ÷, Modulo
Level 4	+, -
Level 5	Comparisons: <, ≤, =, ≠, ≥, >, ≤ x <, < x ≤, < x <
Level 6	Logical Operators &, \|, !

Note: When a function has an expression as its argument, the argument has a higher order of precedence than it would if enclosed in parentheses outside the function.

Build a Formula in Order of Precedence

It is best to build a formula starting with any expression that serves as an argument. This is because functions have a high order of precedence and are always grouped with their corresponding arguments. It is also a good idea to create expressions working from highest to lowest order of precedence when possible. If you need parentheses, be sure to type the open parenthesis before entering the expression to be enclosed.

For example, given a data table with the columns A, B, and C, use the following steps to compose the expression A(B + C). Note that this expression is not the same as A x B + C, which evaluates as (A x B) + C.

To enter the expression

1.	Select Table Columns from the formula element browser list.

2.	Click column A in the Table Columns list.

3.	Click the multiplication button in the Formula Editor keypad.

4.	Type an open parenthesis:

5.	Click column B in the Table Columns list.

6.	Click the addition button in the Formula Editor keypad.

7.	Click column C in the Table Columns list.

Because the order of precedence determines which arguments are affected by each functions, it also affects the grouping of expressions. Select functions in the formula to verify how the order-of-precedence rules have been applied.

Structure Formulas for Efficient Evaluation

Usually, it is not necessary to structure formulas with efficient evaluation in mind. Most formulas evaluate almost instantaneously regardless of their structure. This is because statistical functions and constant expressions are evaluated only once when a column’s values are calculated.

However, when you are creating conditional expressions, keep in mind that Match evaluates faster and uses less memory than an equivalent Condition function, If. (Note that Match ignores trailing spaces and If does not.)

For example, using Big Class.jmp, you can predict a child’s height from his age as shown in The Match Conditional Evaluates Faster Than the If Function. There is a base height of 58.125 inches to which a quantity is added depending on the value of the age variable.

The Match Conditional Evaluates Faster Than the If Function

The Match conditional evaluates faster than the If function because the age variable is evaluated only once for each row in the data table. The If condition must evaluate the age variable at each If clause for each row until a clause evaluates as true.