# Function simplify #

Simplify an expression tree.

A list of rules are applied to an expression, repeating over the list until no further changes are made. It’s possible to pass a custom set of rules to the function as second argument. A rule can be specified as an object, string, or function:

``````const rules = [
{ l: 'n1*n3 + n2*n3', r: '(n1+n2)*n3' },
'n1*n3 + n2*n3 -> (n1+n2)*n3',
function (node) {
// ... return a new node or return the node unchanged
return node
}
]
``````

String and object rules consist of a left and right pattern. The left is used to match against the expression and the right determines what matches are replaced with. The main difference between a pattern and a normal expression is that variables starting with the following characters are interpreted as wildcards:

• ‘n’ - matches any Node
• ‘c’ - matches any ConstantNode
• ‘v’ - matches any Node that is not a ConstantNode

The default list of rules is exposed on the function as `simplify.rules` and can be used as a basis to built a set of custom rules.

For more details on the theory, see:

An optional `options` argument can be passed as last argument of `simplify`. There is currently one option available: `exactFractions`, a boolean which is `true` by default.

## Syntax #

``````simplify(expr)
simplify(expr, rules)
simplify(expr, rules)
simplify(expr, rules, scope)
simplify(expr, rules, scope, options)
simplify(expr, scope)
simplify(expr, scope, options)
``````

### Parameters #

Parameter Type Description
`expr` Node | string The expression to be simplified
`rules` Array<{l:string, r: string} | string | function> Optional list with custom rules

### Returns #

Type Description
Node Returns the simplified form of `expr`

## Examples #

``````math.simplify('2 * 1 * x ^ (2 - 1)')      // Node "2 * x"
math.simplify('2 * 3 * x', {x: 4})        // Node "24"
const f = math.parse('2 * 1 * x ^ (2 - 1)')
math.simplify(f)                          // Node "2 * x"
math.simplify('0.4 * x', {}, {exactFractions: true})  // Node "x * 2 / 5"
math.simplify('0.4 * x', {}, {exactFractions: false}) // Node "0.4 * x"
``````