npm package: @stdlib/math-base-special-expm1rel
Description: Relative error exponential.
Author: The Stdlib Authors
Latest version: 0.2.4

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# expm1rel

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->

> Compute the relative error exponential.

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<section class="intro">

The relative error exponential is defined as

<!-- <equation class="equation" label="eq:relative_error_exponential" align="center" raw="f(x) = \frac{e^x - 1}{x}" alt="Equation for the relative error exponential."> -->

<div class="equation" align="center" data-raw-text="f(x) = \frac{e^x - 1}{x}" data-equation="eq:relative_error_exponential">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@237a80443a932a41f0195d0b9fc7699aa8c8e417/lib/node_modules/@stdlib/math/base/special/expm1rel/docs/img/equation_relative_error_exponential.svg" alt="Equation for the relative error exponential.">
    <br>
</div>

<!-- </equation> -->

</section>

<!-- /.intro -->

<!-- Package usage documentation. -->

<section class="installation">

## Installation

```bash
npm install @stdlib/math-base-special-expm1rel
```

</section>

<section class="usage">

## Usage

```javascript
var expm1rel = require( '@stdlib/math-base-special-expm1rel' );
```

#### expm1rel( x )

Computes the relative error exponential.

```javascript
var v = expm1rel( 0.0 );
// returns 1.0

v = expm1rel( 1.0 );
// returns ~1.718

v = expm1rel( -1.0 );
// returns ~0.632

v = expm1rel( NaN );
// returns NaN
```

</section>

<!-- /.usage -->

<!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="notes">

## Notes

-   When `x` is near zero, `exp(x)-1` can suffer catastrophic cancellation (i.e., a significant loss in precision). `expm1rel` avoids such a loss in precision.

</section>

<!-- /.notes -->

<!-- Package usage examples. -->

<section class="examples">

## Examples

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

```javascript
var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var expm1rel = require( '@stdlib/math-base-special-expm1rel' );

var opts = {
    'dtype': 'float64'
};
var x = uniform( 100, -50.0, 50.0, opts );

logEachMap( '(e^%0.3f - 1)/%0.3f = %0.3f', x, x, expm1rel );
```

</section>

<!-- /.examples -->

<!-- C interface documentation. -->

* * *

<section class="c">

## C APIs

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<section class="intro">

</section>

<!-- /.intro -->

<!-- C usage documentation. -->

<section class="usage">

### Usage

```c
#include "stdlib/math/base/special/expm1rel.h"
```

#### stdlib_base_expm1rel( x )

Computes the relative error exponential.

```c
double out = stdlib_base_expm1rel( 0.0 );
// returns 1.0

out = stdlib_base_expm1rel( 1.0 );
// returns ~1.718
```

The function accepts the following arguments:

-   **x**: `[in] double` input value.

```c
double stdlib_base_expm1rel( const double x );
```

</section>

<!-- /.usage -->

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<section class="notes">

</section>

<!-- /.notes -->

<!-- C API usage examples. -->

<section class="examples">

### Examples

```c
#include "stdlib/math/base/special/expm1rel.h"
#include <stdlib.h>
#include <stdio.h>

int main( void ) {
    double x;
    double v;
    int i;

    for ( i = 0; i < 100; i++ ) {
        x = ( ( (double)rand() / (double)RAND_MAX ) * 100.0 ) - 50.0;
        v = stdlib_base_expm1rel( x );
        printf( "(e^%lf - 1)/%lf = %lf\n", x, x, v );
    }
}
```

</section>

<!-- /.examples -->

</section>

<!-- /.c -->

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</section>

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* * *

## See Also

-   <span class="package-name">[`@stdlib/math-base/special/exp`][@stdlib/math/base/special/exp]</span><span class="delimiter">: </span><span class="description">natural exponential function.</span>
-   <span class="package-name">[`@stdlib/math-base/special/expm1`][@stdlib/math/base/special/expm1]</span><span class="delimiter">: </span><span class="description">compute exp(x) - 1.</span>

</section>

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<section class="main-repo" >

* * *

## Notice

This package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].

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---

## License

See [LICENSE][stdlib-license].


## Copyright

Copyright &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

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