# scipy.special.expm1

scipy.special.expm1(x, out=None) = <ufunc 'expm1'>

  Compute `exp(x) - 1`.

  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. `expm1(x)` is implemented to avoid the loss of precision that occurs when x is near zero.

  Parameters:
    x array_like

      x must contain real numbers.

    out ndarray, optional

      Optional output array for the function values

  Returns:
    scalar or ndarray

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

  Examples

      >>> import numpy as np
      >>> from scipy.special import expm1

      >>> expm1(1.0)
      1.7182818284590451
      >>> expm1([-0.2, -0.1, 0, 0.1, 0.2])
      array([-0.18126925, -0.09516258,  0.        ,  0.10517092,  0.22140276])

  The exact value of `exp(7.5e-13) - 1` is:

      7.5000000000028125000000007031250000001318...*10**-13.

  Here is what `expm1(7.5e-13)` gives:

      >>> expm1(7.5e-13)
      7.5000000000028135e-13

  Compare that to `exp(7.5e-13) - 1`, where the subtraction results in a “catastrophic” loss of precision:

      >>> np.exp(7.5e-13) - 1
      7.5006667543675576e-13