# 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:

```
var 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:

- Strategies for simplifying math expressions (Stackoverflow)
- Symbolic computation - Simplification (Wikipedia)

## Syntax #

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

### 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}
var f = math.parse('2 * 1 * x ^ (2 - 1)');
math.simplify(f); // Node {2 * x}
```