human
I wrote the below code

    n = (len(x) - 1)
    m = ([1] * (n + 1))
    w = ([1] * (n + 1))
    delta_x = [(x2 - x1) for (x1, x2) in zip(x, x[1:])]
    if (type == 'catmull_rom'):
        type = 'cardinal'
        c = 0
    if (type == 'finite_difference'):
        for i in range(1, n):
            m[i] = w[i] = ((0.5 * (((y[(i + 1)] - y[i]) / (x[(i + 1)] - x[i])) + ((y[i] - y[(i - 1)]) / (x[i] - x[(i - 1)])))) if ((x[(i + 1)] - x[i]) and (x[i] - x[(i - 1)])) else 0)
    elif (type == 'kochanek_bartels'):
        c = (c or 0)
        b = (b or 0)
        t = (t or 0)
        for i in range(1, n):
            m[i] = (0.5 * (((((1 - t) * (1 + b)) * (1 + c)) * (y[i] - y[(i - 1)])) + ((((1 - t) * (1 - b)) * (1 - c)) * (y[(i + 1)] - y[i]))))
            w[i] = (0.5 * (((((1 - t) * (1 + b)) * (1 - c)) * (y[i] - y[(i - 1)])) + ((((1 - t) * (1 - b)) * (1 + c)) * (y[(i + 1)] - y[i]))))
    if (type == 'cardinal'):
        c = (c or 0)
        for i in range(1, n):
            m[i] = w[i] = ((((1 - c) * (y[(i + 1)] - y[(i - 1)])) / (x[(i + 1)] - x[(i - 1)])) if (x[(i + 1)] - x[(i - 1)]) else 0)
    def p(i, x_):
        t = ((x_ - x[i]) / delta_x[i])
        t2 = (t * t)
        t3 = (t2 * t)
        h00 = (((2 * t3) - (3 * t2)) + 1)
        h10 = ((t3 - (2 * t2)) + t)
        h01 = (((-2) * t3) + (3 * t2))
        h11 = (t3 - t2)
        return ((((h00 * y[i]) + ((h10 * m[i]) * delta_x[i])) + (h01 * y[(i + 1)])) + ((h11 * w[(i + 1)]) * delta_x[i]))
    for i in range((n + 1)):
        (yield (x[i], y[i]))
        if ((i == n) or (delta_x[i] == 0)):
            continue
        for s in range(1, precision):
            X = (x[i] + ((s * delta_x[i]) / precision))
            (yield (X, p(i, X)))

What's a good function header?
assistant
#Here's a good function header.

def hermite_interpolate(x, y, precision=250, type='cardinal', c=None, b=None, t=None):