# scipy.special.exprel#

scipy.special.exprel(x, out=None) = <ufunc 'exprel'>#

Relative error exponential, `(exp(x) - 1)/x`.

When x is near zero, `exp(x)` is near 1, so the numerical calculation of `exp(x) - 1` can suffer from catastrophic loss of precision. `exprel(x)` is implemented to avoid the loss of precision that occurs when x is near zero.

Parameters:
xndarray

Input array. x must contain real numbers.

outndarray, optional

Optional output array for the function values

Returns:
scalar or ndarray

`(exp(x) - 1)/x`, computed element-wise.

Notes

New in version 0.17.0.

Examples

```>>> import numpy as np
>>> from scipy.special import exprel
```
```>>> exprel(0.01)
1.0050167084168056
>>> exprel([-0.25, -0.1, 0, 0.1, 0.25])
array([ 0.88479687,  0.95162582,  1.        ,  1.05170918,  1.13610167])
```

Compare `exprel(5e-9)` to the naive calculation. The exact value is `1.00000000250000000416...`.

```>>> exprel(5e-9)
1.0000000025
```
```>>> (np.exp(5e-9) - 1)/5e-9
0.99999999392252903
```