import math

# fdlibm's split of ln 2: k * LN2_HI is exact for every k this range needs.
LN2 = 0.6931471805599453
LN2_HI = 6.93147180369123816490e-01
LN2_LO = 1.90821492927058770002e-10


def exp(x: float) -> float:
    """e^x using only +, -, * and /, in the same order as the TypeScript and
    Rust versions, so all three return the same double. See the README."""
    if isinstance(x, bool) or not isinstance(x, (int, float)) or not math.isfinite(x) or x < -708 or x > 709:
        raise ValueError("exp needs x between -708 and 709, received %r" % (x,))
    x = float(x)
    k = math.floor(x / LN2 + 0.5)
    r = x - k * LN2_HI - k * LN2_LO
    p = 1 / 20922789888000
    p = 1 / 1307674368000 + r * p
    p = 1 / 87178291200 + r * p
    p = 1 / 6227020800 + r * p
    p = 1 / 479001600 + r * p
    p = 1 / 39916800 + r * p
    p = 1 / 3628800 + r * p
    p = 1 / 362880 + r * p
    p = 1 / 40320 + r * p
    p = 1 / 5040 + r * p
    p = 1 / 720 + r * p
    p = 1 / 120 + r * p
    p = 1 / 24 + r * p
    p = 1 / 6 + r * p
    p = 1 / 2 + r * p
    p = 1 + r * p
    result = 1 + r * p
    for _ in range(k):
        result *= 2
    for _ in range(-k):
        result /= 2
    return result