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# erf

> [Error function][error-function].

<section class="intro">

The [error function][error-function] is defined as

<!-- <equation class="equation" label="eq:error_function" align="center" raw="\operatorname{erf}(x) = \frac{2}{\sqrt\pi}\int_0^x e^{-t^2}\,\mathrm dt" alt="Error function."> -->

<div class="equation" align="center" data-raw-text="\operatorname{erf}(x) = \frac{2}{\sqrt\pi}\int_0^x e^{-t^2}\,\mathrm dt" data-equation="eq:error_function">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/erf/docs/img/equation_error_function.svg" alt="Error function.">
    <br>
</div>

<!-- </equation> -->

</section>

<!-- /.intro -->

<section class="usage">

## Usage

```javascript
var erf = require( '@stdlib/math/base/special/erf' );
```

#### erf( x )

Evaluates the [error function][error-function].

```javascript
var y = erf( 2.0 );
// returns ~0.9953

y = erf( -1.0 );
// returns ~-0.8427
```

If provided `NaN`, the function returns `NaN`.

```javascript
var y = erf( NaN );
// returns NaN
```

The [error function][error-function] is an [odd function][odd-function]; i.e., `erf(-x) = -erf(x)`. Thus, in accordance with the [IEEE 754][ieee754] standard, if provided `-0`, the function returns `-0`.

```javascript
var y = erf( -0.0 );
// returns -0.0
```

</section>

<!-- /.usage -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

```javascript
var linspace = require( '@stdlib/array/linspace' );
var erf = require( '@stdlib/math/base/special/erf' );

var x = linspace( -10.0, 10.0, 100 );
var y;
var i;

for ( i = 0; i < x.length; i++ ) {
    y = erf( x[ i ] );
    console.log( 'x: %d, erf(x): %d', x[ i ], y );
}
```

</section>

<!-- /.examples -->

<section class="links">

[error-function]: https://en.wikipedia.org/wiki/Error_function

[odd-function]: https://en.wikipedia.org/wiki/Even_and_odd_functions

[ieee754]: https://en.wikipedia.org/wiki/IEEE_754-1985

</section>

<!-- /.links -->