def arctan2_diff(x1, x2):
return (x1[1] * x2[0] - x1[0] * x2[1]) / (np.square(x1[0]) +
np.square(x2[0]))
register_diff(np.divide, divide_diff) register_diff(np.true_divide, divide_diff) register_diff(np.power, pow_diff) register_diff(np.positive, lambda x: +x[1]) register_diff(np.negative, lambda x: -x[1]) register_diff(np.conj, lambda x: np.conj(x[1])) register_diff(np.conj, lambda x: np.conj(x[1])) register_diff(np.exp, lambda x: x[1] * np.exp(x[0])) register_diff(np.exp2, lambda x: x[1] * np.log(2) * np.exp(x[0])) register_diff(np.log, lambda x: x[1] / x[0]) register_diff(np.log2, lambda x: x[1] / (np.log(2) * x[0])) register_diff(np.log10, lambda x: x[1] / (np.log(10) * x[0])) register_diff(np.sqrt, lambda x: x[1] / (2 * np.sqrt(x[0]))) register_diff(np.square, lambda x: 2 * x[1] * x[0]) register_diff(np.cbrt, lambda x: x[1] / (3 * (x[0]**(2 / 3)))) register_diff(np.reciprocal, lambda x: -x[1] / np.square(x[0])) register_diff(np.broadcast_to, lambda x, shape: np.broadcast_to(x[1], shape)) register_diff(np.sin, lambda x: x[1] * np.cos(x[0])) register_diff(np.cos, lambda x: -x[1] * np.sin(x[0])) register_diff(np.tan, lambda x: x[1] / np.square(np.cos(x[0]))) register_diff(np.arcsin, lambda x: x[1] / np.sqrt(1 - np.square(x[0]))) register_diff(np.arccos, lambda x: -x[1] / np.sqrt(1 - np.square(x[0]))) register_diff(np.arctan, lambda x: x[1] / (1 + np.square(x[0]))) register_diff(np.arctan2, arctan2_diff) register_diff(np.sinh, lambda x: x[1] * np.cosh(x[0])) register_diff(np.cosh, lambda x: x[1] * np.sinh(x[0])) register_diff(np.tanh, lambda x: x[1] / np.square(np.cosh(x[0]))) register_diff(np.arcsinh, lambda x: x[1] / np.sqrt(1 + np.square(x[0]))) register_diff(np.arccosh, lambda x: x[1] / np.sqrt(1 - np.square(x[0])))