
'''simple docstring'''







from math import isclose, sqrt







def 				SCREAMING_SNAKE_CASE__	(   __A			,				__A			,				__A	)       ->	tuple[float, float, float]:
	_snake_case   						=		point_y / 4 / point_x
	_snake_case   						=		2 * normal_gradient / (1 + normal_gradient * normal_gradient)
	_snake_case   						=		(1 - normal_gradient * normal_gradient) / (
	    1 + normal_gradient * normal_gradient
	)
	_snake_case   						=		(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
	_snake_case   						=		outgoing_gradient**2 + 4
	_snake_case   						=		2 * outgoing_gradient * (point_y - outgoing_gradient * point_x)
	_snake_case   						=		(point_y - outgoing_gradient * point_x) ** 2 - 100

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

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

	return next_x, next_y, outgoing_gradient







def 				SCREAMING_SNAKE_CASE__	(   __A = 1.4			,				__A = -9.6	)       ->	int:
	_snake_case   						=		0
	_snake_case   						=		first_x_coord
	_snake_case   						=		first_y_coord
	_snake_case   						=		(1_0.1 - point_y) / (0.0 - point_x)

	while not (-0.0_1 <= point_x <= 0.0_1 and point_y > 0):
		_snake_case						, _snake_case						, _snake_case   						=		next_point(__A			,				__A			,				__A	)
		num_reflections += 1

	return num_reflections


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



'''simple docstring'''







import argparse

import intel_extension_for_pytorch as ipex
import torch

from diffusers import DPMSolverMultistepScheduler, StableDiffusionPipeline


lowercase    :							Optional[Any]      =					argparse.ArgumentParser("Stable Diffusion script with intel optimization", add_help=False)
parser.add_argument("--dpm", action="store_true", help="Enable DPMSolver or not")
parser.add_argument("--steps", default=None, type=int, help="Num inference steps")
lowercase    :							Tuple      =					parser.parse_args()


lowercase    :							Optional[int]      =					"cpu"
lowercase    :							Optional[Any]      =					"a lovely <dicoo> in red dress and hat, in the snowly and brightly night, with many brighly buildings"

lowercase    :							Optional[int]      =					"path-to-your-trained-model"
lowercase    :							List[str]      =					StableDiffusionPipeline.from_pretrained(model_id)
if args.dpm:
					lowercase    :							str      =					DPMSolverMultistepScheduler.from_config(pipe.scheduler.config)
lowercase    :							Dict      =					pipe.to(device)

# to channels last
lowercase    :							Optional[Any]      =					pipe.unet.to(memory_format=torch.channels_last)
lowercase    :							int      =					pipe.vae.to(memory_format=torch.channels_last)
lowercase    :							Optional[Any]      =					pipe.text_encoder.to(memory_format=torch.channels_last)
if pipe.requires_safety_checker:
					lowercase    :							Optional[int]      =					pipe.safety_checker.to(memory_format=torch.channels_last)

# optimize with ipex
lowercase    :							Any      =					torch.randn(2, 4, 64, 64)
lowercase    :							Optional[int]      =					torch.rand(1) * 999
lowercase    :							Optional[Any]      =					torch.randn(2, 77, 768)
lowercase    :							Optional[Any]      =					(sample, timestep, encoder_hidden_status)
try:
					lowercase    :							List[Any]      =					ipex.optimize(pipe.unet.eval(), dtype=torch.bfloataa, inplace=True, sample_input=input_example)
except Exception:
					lowercase    :							List[str]      =					ipex.optimize(pipe.unet.eval(), dtype=torch.bfloataa, inplace=True)
lowercase    :							Tuple      =					ipex.optimize(pipe.vae.eval(), dtype=torch.bfloataa, inplace=True)
lowercase    :							Optional[Any]      =					ipex.optimize(pipe.text_encoder.eval(), dtype=torch.bfloataa, inplace=True)
if pipe.requires_safety_checker:
					lowercase    :							Tuple      =					ipex.optimize(pipe.safety_checker.eval(), dtype=torch.bfloataa, inplace=True)

# compute
lowercase    :							List[str]      =					666
lowercase    :							Tuple      =					torch.Generator(device).manual_seed(seed)
lowercase    :							Union[str, Any]      =					{"generator": generator}
if args.steps is not None:
					lowercase    :							Dict      =					args.steps

with torch.cpu.amp.autocast(enabled=True, dtype=torch.bfloataa):
					lowercase    :							List[str]      =					pipe(prompt, **generate_kwargs).images[0]

# save image
image.save("generated.png")

