venv/lib/python3.10/site-packages/scipy/special/_precompute/wrightomega.py

import numpy as np

try:
    import mpmath
except ImportError:
    pass


def mpmath_wrightomega(x):
    return mpmath.lambertw(mpmath.exp(x), mpmath.mpf('-0.5'))


def wrightomega_series_error(x):
    series = x
    desired = mpmath_wrightomega(x)
    return abs(series - desired) / desired


def wrightomega_exp_error(x):
    exponential_approx = mpmath.exp(x)
    desired = mpmath_wrightomega(x)
    return abs(exponential_approx - desired) / desired


def main():
    desired_error = 2 * np.finfo(float).eps
    print('Series Error')
    for x in [1e5, 1e10, 1e15, 1e20]:
        with mpmath.workdps(100):
            error = wrightomega_series_error(x)
        print(x, error, error < desired_error)

    print('Exp error')
    for x in [-10, -25, -50, -100, -200, -400, -700, -740]:
        with mpmath.workdps(100):
            error = wrightomega_exp_error(x)
        print(x, error, error < desired_error)


if __name__ == '__main__':
    main()