


from math import isclose, sqrt


def     lowercase	(    a     , a     , a ):



		'''simple docstring'''




		SCREAMING_SNAKE_CASE_				:int				     =						point_y / 4 / point_x
		SCREAMING_SNAKE_CASE_				:Optional[int]				     =						2 * normal_gradient / (1 + normal_gradient * normal_gradient)
		SCREAMING_SNAKE_CASE_				:Any				     =						(1 - normal_gradient * normal_gradient) / (
		    1 + normal_gradient * normal_gradient
		)
		SCREAMING_SNAKE_CASE_				:List[Any]				     =						(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
		SCREAMING_SNAKE_CASE_				:Any				     =						outgoing_gradient**2 + 4
		SCREAMING_SNAKE_CASE_				:int				     =						2 * outgoing_gradient * (point_y - outgoing_gradient * point_x)
		SCREAMING_SNAKE_CASE_				:Dict				     =						(point_y - outgoing_gradient * point_x) ** 2 - 100

		SCREAMING_SNAKE_CASE_				:List[str]				     =						(
		    -linear_term - sqrt(linear_term**2 - 4 * quadratic_term * constant_term )
		) / (2 * quadratic_term)
		SCREAMING_SNAKE_CASE_				:List[Any]				     =						(
		    -linear_term + sqrt(linear_term**2 - 4 * quadratic_term * constant_term )
		) / (2 * quadratic_term)

		# two solutions, one of which is our input point
		SCREAMING_SNAKE_CASE_				:Optional[Any]				     =						x_minus if isclose(a     , a ) else x_plus
		SCREAMING_SNAKE_CASE_				:Optional[int]				     =						point_y + outgoing_gradient * (next_x - point_x)

		return next_x, next_y, outgoing_gradient


def     lowercase	(    a = 1.4     , a = -9.6 ):



		'''simple docstring'''




		SCREAMING_SNAKE_CASE_				:int				     =						0
		SCREAMING_SNAKE_CASE_				:float				     =						first_x_coord
		SCREAMING_SNAKE_CASE_				:float				     =						first_y_coord
		SCREAMING_SNAKE_CASE_				:float				     =						(10.1 - point_y) / (0.0 - point_x)

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

		return num_reflections


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










import os

from bleurt import score  # From: git+https://github.com/google-research/bleurt.git

import datasets


SCREAMING_SNAKE_CASE__     					=			datasets.logging.get_logger(__name__)


SCREAMING_SNAKE_CASE__     					=			"\\n@inproceedings{bleurt,\n  title={BLEURT: Learning Robust Metrics for Text Generation},\n  author={Thibault Sellam and Dipanjan Das and Ankur P. Parikh},\n  booktitle={ACL},\n  year={2020},\n  url={https://arxiv.org/abs/2004.04696}\n}\n"

SCREAMING_SNAKE_CASE__     					=			"\\nBLEURT a learnt evaluation metric for Natural Language Generation. It is built using multiple phases of transfer learning starting from a pretrained BERT model (Devlin et al. 2018)\nand then employing another pre-training phrase using synthetic data. Finally it is trained on WMT human annotations. You may run BLEURT out-of-the-box or fine-tune\nit for your specific application (the latter is expected to perform better).\n\nSee the project's README at https://github.com/google-research/bleurt#readme for more information.\n"

SCREAMING_SNAKE_CASE__     					=			"\nBLEURT score.\n\nArgs:\n    `predictions` (list of str): prediction/candidate sentences\n    `references` (list of str): reference sentences\n    `checkpoint` BLEURT checkpoint. Will default to BLEURT-tiny if None.\n\nReturns:\n    'scores': List of scores.\nExamples:\n\n    >>> predictions = [\"hello there\", \"general kenobi\"]\n    >>> references = [\"hello there\", \"general kenobi\"]\n    >>> bleurt = datasets.load_metric(\"bleurt\")\n    >>> results = bleurt.compute(predictions=predictions, references=references)\n    >>> print([round(v, 2) for v in results[\"scores\"]])\n    [1.03, 1.04]\n"

SCREAMING_SNAKE_CASE__     					=			{
    "bleurt-tiny-128": "https://storage.googleapis.com/bleurt-oss/bleurt-tiny-128.zip",
    "bleurt-tiny-512": "https://storage.googleapis.com/bleurt-oss/bleurt-tiny-512.zip",
    "bleurt-base-128": "https://storage.googleapis.com/bleurt-oss/bleurt-base-128.zip",
    "bleurt-base-512": "https://storage.googleapis.com/bleurt-oss/bleurt-base-512.zip",
    "bleurt-large-128": "https://storage.googleapis.com/bleurt-oss/bleurt-large-128.zip",
    "bleurt-large-512": "https://storage.googleapis.com/bleurt-oss/bleurt-large-512.zip",
    "BLEURT-20-D3": "https://storage.googleapis.com/bleurt-oss-21/BLEURT-20-D3.zip",
    "BLEURT-20-D6": "https://storage.googleapis.com/bleurt-oss-21/BLEURT-20-D6.zip",
    "BLEURT-20-D12": "https://storage.googleapis.com/bleurt-oss-21/BLEURT-20-D12.zip",
    "BLEURT-20": "https://storage.googleapis.com/bleurt-oss-21/BLEURT-20.zip",
}



@datasets.utils.file_utils.add_start_docstrings(_DESCRIPTION		,		_KWARGS_DESCRIPTION							)
class 						_UpperCAmelCase      (     datasets.Metric							):






		def _snake_case		(						self				:     List[str]):
				return datasets.MetricInfo(
				    description=_DESCRIPTION   ,  citation=_CITATION   ,  homepage="https://github.com/google-research/bleurt"   ,  inputs_description=_KWARGS_DESCRIPTION   ,  features=datasets.Features(
				        {
				            "predictions": datasets.Value("string"   ,  id="sequence"),
				            "references": datasets.Value("string"   ,  id="sequence"),
				        })   ,  codebase_urls=["https://github.com/google-research/bleurt"]   ,  reference_urls=["https://github.com/google-research/bleurt", "https://arxiv.org/abs/2004.04696"]   ,  )






		def _snake_case		(						self				:     Any   ,  UpperCAmelCase				:     Any):
				# check that config name specifies a valid BLEURT model
				if self.config_name == "default":
						logger.warning(
						    "Using default BLEURT-Base checkpoint for sequence maximum length 128. "
						    "You can use a bigger model for better results with e.g.: datasets.load_metric('bleurt', 'bleurt-large-512').")
						SCREAMING_SNAKE_CASE_				:str				     =						"bleurt-base-128"

				if self.config_name.lower() in CHECKPOINT_URLS:
						SCREAMING_SNAKE_CASE_				:Dict				     =						self.config_name.lower()

				elif self.config_name.upper() in CHECKPOINT_URLS:
						SCREAMING_SNAKE_CASE_				:Dict				     =						self.config_name.upper()

				else:
						raise KeyError(
						    F"{self.config_name} model not found. You should supply the name of a model checkpoint for bleurt in {CHECKPOINT_URLS.keys()}")

				# download the model checkpoint specified by self.config_name and set up the scorer
				SCREAMING_SNAKE_CASE_				:Optional[Any]				     =						dl_manager.download_and_extract(CHECKPOINT_URLS[checkpoint_name])
				SCREAMING_SNAKE_CASE_				:Dict				     =						score.BleurtScorer(os.path.join(UpperCAmelCase   ,  UpperCAmelCase))







		def _snake_case		(						self				:     Union[str, Any]   ,  UpperCAmelCase				:     List[str]   ,  UpperCAmelCase				:     Union[str, Any]):
				SCREAMING_SNAKE_CASE_				:Optional[int]				     =						self.scorer.score(references=UpperCAmelCase   ,  candidates=UpperCAmelCase)
				return {"scores": scores}






