
from math import isclose, sqrt



def 					lowerCAmelCase__							(	SCREAMING_SNAKE_CASE_:							float	,       SCREAMING_SNAKE_CASE_:							float	,       SCREAMING_SNAKE_CASE_:							float      )			->      tuple[float, float, float]:




				'''simple docstring'''





				A__        =			point_y / 4 / point_x
				A__        =			2 * normal_gradient / (1 + normal_gradient * normal_gradient)
				A__        =			(1 - normal_gradient * normal_gradient) / (
				    1 + normal_gradient * normal_gradient
				)
				A__        =			(sa - ca * incoming_gradient) / (ca + sa * incoming_gradient)

				# to find the next point, solve the simultaeneous equations:
				# y^2 + 4x^2 = 100
				# y - b = m * (x - a)
				# ==> A x^2 + B x + C = 0
				A__        =			outgoing_gradient**2 + 4
				A__        =			2 * outgoing_gradient * (point_y - outgoing_gradient * point_x)
				A__        =			(point_y - outgoing_gradient * point_x) ** 2 - 1_0_0

				A__        =			(
				    -linear_term - sqrt(linear_term**2 - 4 * quadratic_term * constant_term      )
				) / (2 * quadratic_term)
				A__        =			(
				    -linear_term + sqrt(linear_term**2 - 4 * quadratic_term * constant_term      )
				) / (2 * quadratic_term)

				# two solutions, one of which is our input point
				A__        =			x_minus if isclose(SCREAMING_SNAKE_CASE_	,       SCREAMING_SNAKE_CASE_      ) else x_plus
				A__        =			point_y + outgoing_gradient * (next_x - point_x)

				return next_x, next_y, outgoing_gradient



def 					lowerCAmelCase__							(	SCREAMING_SNAKE_CASE_:							float = 1.4	,       SCREAMING_SNAKE_CASE_:							float = -9.6      )			->      int:




				'''simple docstring'''





				A__        =			0
				A__        =			first_x_coord
				A__        =			first_y_coord
				A__        =			(10.1 - point_y) / (0.0 - point_x)

				while not (-0.01 <= point_x <= 0.01 and point_y > 0):
								A__    ,				A__    ,				A__        =			next_point(SCREAMING_SNAKE_CASE_	,       SCREAMING_SNAKE_CASE_	,       SCREAMING_SNAKE_CASE_      )
								num_reflections += 1

				return num_reflections


if __name__ == "__main__":
	print(f"""{solution() = }""")




from ..utils import is_flax_available, is_torch_available


if is_torch_available():
	from .autoencoder_kl import AutoencoderKL
	from .controlnet import ControlNetModel
	from .dual_transformer_ad import DualTransformeraDModel
	from .modeling_utils import ModelMixin
	from .prior_transformer import PriorTransformer
	from .ta_film_transformer import TaFilmDecoder
	from .transformer_ad import TransformeraDModel
	from .unet_ad import UNetaDModel
	from .unet_ad import UNetaDModel
	from .unet_ad_condition import UNetaDConditionModel
	from .unet_ad_condition import UNetaDConditionModel
	from .vq_model import VQModel

if is_flax_available():
	from .controlnet_flax import FlaxControlNetModel
	from .unet_ad_condition_flax import FlaxUNetaDConditionModel
	from .vae_flax import FlaxAutoencoderKL

