# 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:

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

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.`fractionsLimit`

: when`exactFractions`

is true, a fraction will be returned only when both numerator and denominator are smaller than`fractionsLimit`

. Default value is 10000.

## 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"
```