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SR Benchmark

SRToolkit.dataset.sr_benchmark

SR_benchmark 

SR_benchmark(benchmark_name: str, base_dir: str, datasets: List[Union[SR_dataset, Tuple[str, SR_dataset]]] = None, augmentation_map: dict = None, metadata: dict = None)

Initializes an instance of the SR_benchmark class.

Parameters:

Name Type Description Default
benchmark_name str

The name of this benchmark.

 required
base_dir str

The directory where the datasets will be stored.

 required
datasets List[Union[SR_dataset, Tuple[str, SR_dataset]]]

A list of SR_dataset instances or tuples containing the name of the dataset and an instance of SR_dataset. When name of the dataset is not provided, the dataset will be named 'benchmark_name'_'index of dataset in the list + 1'

 None
augmentation_map dict

A dictionary mapping augmenter names to their respective classes.

 None
metadata dict

An optional dictionary containing metadata about this benchmark. This could include information such as the name of the benchmark, a citation for the benchmark, number of datasets, etc.

 None

Raises:

Type Description
Exception

If elements in the "datasets" argument are not instances of SR_dataset or tuples containing the name of the dataset and an instance of SR_dataset.
Source code in SRToolkit/dataset/sr_benchmark.py 
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def __init__(self, benchmark_name: str, base_dir: str,
             datasets: List[Union[SR_dataset, Tuple[str, SR_dataset]]] = None,
             augmentation_map: dict = None, metadata: dict = None):
    """
    Initializes an instance of the SR_benchmark class.

    Args:
        benchmark_name: The name of this benchmark.
        base_dir: The directory where the datasets will be stored.
        datasets: A list of SR_dataset instances or tuples containing the name of the dataset and an instance of
            SR_dataset. When name of the dataset is not provided, the dataset will be named
            'benchmark_name'_'index of dataset in the list + 1'
        augmentation_map: A dictionary mapping augmenter names to their respective classes.
        metadata: An optional dictionary containing metadata about this benchmark. This could include information
            such as the name of the benchmark, a citation for the benchmark, number of datasets, etc.

    Raises:
        Exception: If elements in the "datasets" argument are not instances of SR_dataset or tuples containing
            the name of the dataset and an instance of SR_dataset.
    """
    self.benchmark_name = benchmark_name
    self.base_dir = base_dir
    if augmentation_map is None:
        self.augmentation_map = RESULT_AUGMENTERS
    self.datasets = {}
    self.metadata = {} if metadata is None else metadata
    if datasets is not None:
        for i, dataset in enumerate(datasets):
            if isinstance(dataset, SR_dataset):
                self.add_dataset_instance(benchmark_name + "_" + str(i+1), dataset)
            elif isinstance(dataset, tuple) and isinstance(dataset[0], str) and isinstance(dataset[1], SR_dataset):
                self.add_dataset_instance(dataset[0], dataset[1])
            else:
                raise ValueError("[SR_benchmark] Dataset inside the datasets argument must be either a tuple "
                                 "(name, SR_dataset) or a SR_dataset instance.")

add_dataset_instance 

add_dataset_instance(dataset_name: str, dataset: SR_dataset)

Adds an instance of the SR_dataset class to the benchmark.

Parameters:

Name Type Description Default
dataset_name str

The name of the dataset.

 required
dataset SR_dataset

An instance of the SR_dataset class.

 required
Source code in SRToolkit/dataset/sr_benchmark.py 
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def add_dataset_instance(self, dataset_name: str, dataset: SR_dataset):
    """
    Adds an instance of the SR_dataset class to the benchmark.

    Args:
         dataset_name: The name of the dataset.
         dataset: An instance of the SR_dataset class.
    """
    self.datasets[dataset_name]["sr_dataset"] = dataset
    self.datasets[dataset_name]["num_variables"] = dataset.X.shape[1]

add_dataset 

add_dataset(dataset: Union[str, array, Tuple[array, array]], symbol_library: SymbolLibrary, dataset_name: Optional[str] = None, ranking_function: str = 'rmse', max_evaluations: int = -1, ground_truth: Optional[Union[List[str], Node, ndarray]] = None, original_equation: Optional[str] = None, success_threshold: Optional[float] = None, result_augmenters: Optional[List[ResultAugmenter]] = None, seed: Optional[int] = None, dataset_metadata: Optional[dict] = None, **kwargs)

Adds a dataset to the benchmark.

Parameters:

Name Type Description Default
dataset Union[str, array, Tuple[array, array]]

Data used in the dataset. Can be: - A string representing the path to a NumPy archive (.npz) containing the dataset. It should either the absolute path to the data, path relative to the base_dir 'base_dir'/'dataset', or empty, in that case the dataset will be loaded from 'base_dir'/'dataset_name'.npz. The .npz file must contain the features (saved in 'X') and if 'rmse' is used as the ranking function, the target (saved in 'y'). - A 2d numpy array containing the features (X). If 'rmse' is used as the ranking function, ground truth should also be provided to calculate the target (y). Once added, the data will be saved at 'base_dir'/'dataset_name'.npz. - A tuple containing the features (X) and the target (y). If 'bed' is used as the ranking function, the target will be ignored. Once added, the data will be saved at 'base_dir'/'dataset_name'.npz.

 required
symbol_library SymbolLibrary

The symbol library to use.

 required
dataset_name Optional[str]

The name of the dataset. If None, a name will be generated automatically as 'benchmark_name'_'index+1'.

 None
ranking_function str

The ranking function used during evaluation. Can be: 'rmse', 'bed'.

 'rmse'
max_evaluations int

The maximum number of expressions to evaluate. Less than 0 means no limit.

 -1
ground_truth Optional[Union[List[str], Node, ndarray]]

The ground truth expression. Can either a list of symbols, a SRToolkit.utils.Node, or a numpy array representing behavior of an expressions. When 'bed' is used as the ranking function, ground truth must be provided.

 None
original_equation Optional[str]

The original equation from which the ground truth expression was generated.

 None
success_threshold Optional[float]

The threshold below which the experiment is considered successful. If None, the threshold will be calculated automatically. See SRToolkit.evaluation.SR_evaluator for more details.

 None
result_augmenters Optional[List[ResultAugmenter]]

The list of result augmenters to use.

 None
seed Optional[int]

The seed to use for random number generation. If None, number generation will be random.

 None
dataset_metadata Optional[dict]

An optional dictionary containing metadata about this dataset. This could include information such as the name of the dataset, a citation for the dataset, number of variables, etc.

 None

Other Parameters:

Name Type Description
method str

The method to be used for minimization. Currently, only "L-BFGS-B" is supported/tested. Default is "L-BFGS-B".
tol float

The tolerance for termination. Default is 1e-6.
gtol float

The tolerance for the gradient norm. Default is 1e-3.
max_iter int

The maximum number of iterations. Default is 100.
constant_bounds Tuple[float, float]

A tuple of two elements, specifying the lower and upper bounds for the constant values. Default is (-5, 5).
initialization str

The method to use for initializing the constant values. Currently, only "random" and "mean" are supported. "random" creates a vector with random values sampled within the bounds. "mean" creates a vector where all values are calculated as (lower_bound + upper_bound)/2. Default is "random".
max_constants int

The maximum number of constants allowed in the expression. Default is 8.
max_expr_length int

The maximum length of the expression. Default is -1 (no limit).
num_points_sampled int

The number of points to sample when estimating the behavior of an expression. Default is 64. If num_points_sampled==-1, then the number of points sampled is equal to the number of points in the dataset.
bed_X Optional[ndarray]

Points used for BED evaluation. If None and domain_bounds are given, points are sampled from the domain. If None and domain_bounds are not givem, points are randomly selected from X. Default is None.
num_consts_sampled int

Number of constants sampled for BED evaluation. Default is 32.
domain_bounds Optional[List[Tuple[float, float]]]

Bounds for the domain to be used if bed_X is None to sample random points. Default is None.
Source code in SRToolkit/dataset/sr_benchmark.py 
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def add_dataset(
    self,
    dataset: Union[str, np.array, Tuple[np.array, np.array]],
    symbol_library: SymbolLibrary,
    dataset_name: Optional[str] = None,
    ranking_function: str = "rmse",
    max_evaluations: int = -1,
    ground_truth: Optional[Union[List[str], Node, np.ndarray]] = None,
    original_equation: Optional[str] = None,
    success_threshold: Optional[float] = None,
    result_augmenters: Optional[List[ResultAugmenter]] = None,
    seed: Optional[int] = None,
    dataset_metadata: Optional[dict] = None,
    **kwargs
):
    """
    Adds a dataset to the benchmark.

    Args:
        dataset: Data used in the dataset. Can be:
            - A string representing the path to a NumPy archive (.npz) containing the dataset. It should either
            the absolute path to the data, path relative to the base_dir 'base_dir'/'dataset', or empty, in that
            case the dataset will be loaded from 'base_dir'/'dataset_name'.npz. The .npz file must contain the
            features (saved in 'X') and if 'rmse' is used as the ranking function, the target (saved in 'y').
            - A 2d numpy array containing the features (X). If 'rmse' is used as the ranking function, ground truth
            should also be provided to calculate the target (y). Once added, the data will be saved at
            'base_dir'/'dataset_name'.npz.
            - A tuple containing the features (X) and the target (y). If 'bed' is used as the ranking function,
            the target will be ignored. Once added, the data will be saved at 'base_dir'/'dataset_name'.npz.
        symbol_library: The symbol library to use.
        dataset_name: The name of the dataset. If None, a name will be generated automatically as
            'benchmark_name'_'index+1'.
        ranking_function: The ranking function used during evaluation. Can be: 'rmse', 'bed'.
        max_evaluations: The maximum number of expressions to evaluate. Less than 0 means no limit.
        ground_truth: The ground truth expression. Can either a list of symbols, a SRToolkit.utils.Node, or a
            numpy array representing behavior of an expressions. When 'bed' is used as the ranking function,
            ground truth must be provided.
        original_equation: The original equation from which the ground truth expression was generated.
        success_threshold: The threshold below which the experiment is considered successful. If None, the
            threshold will be calculated automatically. See SRToolkit.evaluation.SR_evaluator for more details.
        result_augmenters: The list of result augmenters to use.
        seed: The seed to use for random number generation. If None, number generation will be random.
        dataset_metadata: An optional dictionary containing metadata about this dataset. This could include
            information such as the name of the dataset, a citation for the dataset, number of variables, etc.

    Keyword Arguments:
        method (str): The method to be used for minimization. Currently, only "L-BFGS-B" is supported/tested.
            Default is "L-BFGS-B".
        tol (float): The tolerance for termination. Default is 1e-6.
        gtol (float): The tolerance for the gradient norm. Default is 1e-3.
        max_iter (int): The maximum number of iterations. Default is 100.
        constant_bounds (Tuple[float, float]): A tuple of two elements, specifying the lower and upper bounds for
            the constant values. Default is (-5, 5).
        initialization (str): The method to use for initializing the constant values. Currently, only "random" and
            "mean" are supported. "random" creates a vector with random values sampled within the bounds. "mean"
            creates a vector where all values are calculated as (lower_bound + upper_bound)/2. Default is "random".
        max_constants (int): The maximum number of constants allowed in the expression. Default is 8.
        max_expr_length (int): The maximum length of the expression. Default is -1 (no limit).
        num_points_sampled (int): The number of points to sample when estimating the behavior of an expression.
            Default is 64. If num_points_sampled==-1, then the number of points sampled is equal to the number of
            points in the dataset.
        bed_X (Optional[np.ndarray]): Points used for BED evaluation. If None and domain_bounds are given, points
            are sampled from the domain. If None and domain_bounds are not givem, points are randomly selected
            from X. Default is None.
        num_consts_sampled (int): Number of constants sampled for BED evaluation. Default is 32.
        domain_bounds (Optional[List[Tuple[float, float]]]): Bounds for the domain to be used if bed_X is None to
            sample random points. Default is None.
    """
    if dataset_name is None:
        dataset_name = f"{self.benchmark_name}_{len(self.datasets)}+1"

    self.datasets[dataset_name] = {}
    self.datasets[dataset_name]["symbol_library"] = symbol_library
    self.datasets[dataset_name]["ranking_function"] = ranking_function
    self.datasets[dataset_name]["max_evaluations"] = max_evaluations

    self.datasets[dataset_name]["success_threshold"] = success_threshold
    self.datasets[dataset_name]["result_augmenters"] = result_augmenters
    self.datasets[dataset_name]["seed"] = seed
    self.datasets[dataset_name]["dataset_metadata"] = copy.deepcopy(self.metadata).update(dataset_metadata)

    self.datasets[dataset_name]["kwargs"] = kwargs
    self.datasets[dataset_name]["original_equation"] = original_equation
    self.datasets[dataset_name]["ground_truth"] = ground_truth

    if ground_truth is None:
        if ranking_function == "bed":
            raise ValueError("[SR_benchmark.add_dataset] For 'bed' ranking, the ground truth must be provided. ")
        else:
            print(f"[SR_benchmark.add_dataset] 'ground_truth' argument not provided. We recommend providing it "
                  f"for more transparent evaluation.")
    else:
        if original_equation is None:
            if isinstance(ground_truth, str):
                self.datasets[dataset_name]["original_equation"] = "y = " + ground_truth
            elif isinstance(ground_truth, list):
                self.datasets[dataset_name]["original_equation"] = "y = " + "".join(ground_truth)

    if isinstance(dataset, str):
        dataset_path = None
        if os.path.exists(dataset):
            dataset_path = dataset
        elif dataset != "" and os.path.exists(f"{self.base_dir}/{dataset}"):
            dataset_path = f"{self.base_dir}/{dataset}"
        elif os.path.exists(f"{self.base_dir}/{dataset_name}.npz"):
            dataset_path = f"{self.base_dir}/{dataset_name}.npz"

        if dataset_path is None:
            error_msg = (
                f"[SR_benchmark.add_dataset] Could not find the dataset file. "
                f"Expected locations:\n"
                f"- Absolute path: '{dataset}'\n"
                f"- Relative to base_dir: '{self.base_dir}/{dataset}'\n"
                f"- NPZ with the name of the dataset in base_dir: '{self.base_dir}/{dataset_name}.npz'"
            )
            raise FileNotFoundError(error_msg)

        self.datasets[dataset_name]["dataset_path"] = dataset_path

        try:
            data = np.load(self.datasets[dataset_name]["dataset_path"], allow_pickle=False)
        except IOError as e:
            error_msg = (
                f"[SR_benchmark.add_dataset] Could not load dataset from path '{self.datasets[dataset_name]}' "
                f"using np.load. The file may be corrupt or not a valid NumPy archive (.npz, .npy). "
                f"Original error: {e}"
            )
            raise IOError(error_msg) from e

        if ranking_function == "rmse":
            if not (isinstance(data, np.lib.npyio.NpzFile) and "X" in data and "y" in data):
                error_msg = (
                    f"[SR_benchmark.add_dataset] For 'rmse' ranking, the dataset file "
                    f"('{self.datasets[dataset_name]['dataset_path']}') must be a .npz NumPy archive containing "
                    f"both 'X' (features) and 'y' (targets). It should be created via `np.savez(path, X=X, y=y)`."
                )
                raise ValueError(error_msg)

        elif ranking_function == "bed":
            if not (isinstance(data, np.lib.npyio.NpzFile) and "X" in data):
                error_msg = (
                    f"[SR_benchmark.add_dataset] For 'bed' ranking, the dataset file "
                    f"('{self.datasets[dataset_name]['dataset_path']}') must be a .npz NumPy archive "
                    f"containing 'X' (features). It should be created via `np.savez(path, X=X)`."
                )
                raise ValueError(error_msg)

        num_variables = data['X'].shape[1]

    elif isinstance(dataset, np.ndarray):
        if ranking_function == "rmse" and ground_truth is not None:
            try:
                expr = expr_to_executable_function(ground_truth, symbol_library)
                y = expr(dataset, None)
            except Exception as e:
                raise Exception(f"[SR_benchmark.add_dataset] Could not evaluate the ground truth. "
                                f"Original error: {e}")
            if not os.path.isdir(self.base_dir):
                os.makedirs(self.base_dir)
            np.savez(f"{self.base_dir}/{dataset_name}.npz", X=dataset, y=y, allow_pickle=False)
        elif ranking_function == "rmse" and ground_truth is None:
            raise ValueError("[SR_benchmark.add_dataset] For 'rmse' ranking, if the dataset argument is a numpy "
                             "array, the ground truth must be provided in order for the target values to be "
                             "calculated.")
        elif ranking_function == "bed":
            if not os.path.isdir(self.base_dir):
                os.makedirs(self.base_dir)
            np.savez(f"{self.base_dir}/{dataset_name}.npz", X=dataset, allow_pickle=False)

        self.datasets[dataset_name]["dataset_path"] = f"{self.base_dir}/{dataset_name}.npz"
        num_variables = dataset.shape[1]

    elif isinstance(dataset, tuple):
        if not isinstance(dataset[0], np.ndarray) or not isinstance(dataset[1], np.ndarray):
            raise ValueError("[SR_benchmark.add_dataset] When dataset argument is provided as a tuple, both "
                             "values must be a numpy array. The first array represents the features ('X'), "
                             "the second array represents the targets ('y').")
        if ranking_function == "bed":
            print(f"[SR_benchmark.add_dataset] 'bed' ranking only utilizes the array with feature. Array with "
                  f"targets will be ignored.")
        if not os.path.isdir(self.base_dir):
            os.makedirs(self.base_dir)
        np.savez(f"{self.base_dir}/{dataset_name}.npz", X=dataset[0], y=dataset[1], allow_pickle=False)
        self.datasets[dataset_name]["dataset_path"] = f"{self.base_dir}/{dataset_name}.npz"
        num_variables = dataset[0].shape[1]

    else:
        raise ValueError("[SR_benchmark.add_dataset] The dataset argument must be a string, a numpy array, "
                         "or a tuple containing two numpy arrays.")

    self.datasets[dataset_name]["num_variables"] = num_variables

create_dataset 

create_dataset(dataset_name: str) -> SR_dataset

Creates an instance of a dataset from the given dataset name.

Parameters:

Name Type Description Default
dataset_name str

The name of the dataset to create.

 required

Returns:

Type Description
SR_dataset

A SR_dataset instance containing the data, ground truth expression, and metadata for the given dataset.

Raises:

Type Description
ValueError

If the dataset name is not found in the available datasets.
Source code in SRToolkit/dataset/sr_benchmark.py 
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def create_dataset(self, dataset_name: str) -> SR_dataset:
    """
    Creates an instance of a dataset from the given dataset name.

    Args:
        dataset_name: The name of the dataset to create.

    Returns:
        A SR_dataset instance containing the data, ground truth expression, and metadata for the given dataset.

    Raises:
        ValueError: If the dataset name is not found in the available datasets.
    """
    if dataset_name in self.datasets:
        if "sr_dataset" in self.datasets[dataset_name]:
            return self.datasets[dataset_name]["sr_dataset"]
        else:
            try:
                return SR_dataset.from_dict(self.datasets[dataset_name], self.augmentation_map)
            except Exception as e:
                raise ValueError(f"[SR_benchmark.create_dataset] Could not create SR_dataset from the given "
                                 f"given dictionary. Original error: {e}")

    else:
        raise ValueError(f"Dataset {dataset_name} not found")

list_datasets 

list_datasets(verbose=True, num_variables: int = -1) -> List[str]

Lists the available datasets.

Parameters:

Name Type Description Default
verbose bool

If True, also prints out a description of each dataset.

 True
num_variables int

If not -1, only show datasets with the given number of variables.

 -1

Returns:

Type Description
List[str]

A list of dataset names.
Source code in SRToolkit/dataset/sr_benchmark.py 
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def list_datasets(self, verbose=True, num_variables: int = -1) -> List[str]:
    """
    Lists the available datasets.

    Args:
        verbose (bool): If True, also prints out a description of each dataset.
        num_variables (int): If not -1, only show datasets with the given number of variables.

    Returns:
        A list of dataset names.
    """
    datasets = [
        dataset_name
        for dataset_name in self.datasets
        if num_variables < 0
        or self.datasets[dataset_name]["num_variables"] == num_variables
    ]
    datasets = sorted(
        datasets,
        key=lambda dataset_name: (
            self.datasets[dataset_name]["num_variables"],
            dataset_name,
        ),
    )

    if verbose:
        # TODO: Make all names be of equal length for nicer output
        for d in datasets:
            if self.datasets[d]["num_variables"] == 1:
                variable_str = "1 variable"
            elif self.datasets[d]["num_variables"] < 1:
                variable_str = "Amount of variables unknown"
            else:
                variable_str = f"{self.datasets[d]['num_variables']} variables"

            print(
                f"{d}:\t{variable_str}, \tExpression: {self.datasets[d]['original_equation']}"
            )
    return datasets

download_benchmark_data staticmethod 

download_benchmark_data(url, directory_path)

Downloads a benchmark dataset from the given url to the given directory path.

This function will first check if the directory_path exists. If not, it will create it. Then it will check if the directory_path is empty. If it is not empty, it will not download the data. If it is empty, it will download the data from the given url and extract it to the directory_path.

Parameters:

Name Type Description Default
url str

The url of the benchmark dataset to download.

 required
directory_path str

The path of the directory where the dataset should be downloaded.

 required
Source code in SRToolkit/dataset/sr_benchmark.py 
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@staticmethod
def download_benchmark_data(url, directory_path):
    # Check if directory_path exist
    """
    Downloads a benchmark dataset from the given url to the given directory path.

    This function will first check if the directory_path exists. If not, it will create it. Then it will check if the directory_path is empty. If it is not empty, it will not download the data. If it is empty, it will download the data from the given url and extract it to the directory_path.

    Args:
        url (str): The url of the benchmark dataset to download.
        directory_path (str): The path of the directory where the dataset should be downloaded.
    """
    if not os.path.exists(directory_path):
        os.makedirs(directory_path)

    # Check if directory_path is empty
    if not os.listdir(directory_path):
        # Download data from the url to the directory_path
        http_response = urlopen(url)
        zipfile = ZipFile(BytesIO(http_response.read()))
        zipfile.extractall(path=directory_path)

feynman staticmethod 

feynman(dataset_directory: str, seed: Optional[int] = None) -> SR_benchmark

Downloads the Feynman benchmark dataset, sets up symbol libraries, and adds predefined datasets to the benchmark.

This method downloads the Feynman benchmark dataset from a specified URL, initializes symbol libraries for symbolic regression with varying numbers of variables, and adds multiple predefined datasets to the benchmark with their respective equations and metadata.

Examples:

>>> benchmark = SR_benchmark.feynman('data/feynman')
>>> for dataset in benchmark.list_datasets(verbose=False):
...     ds = benchmark.create_dataset(dataset)
...     rmse = ds.create_evaluator().evaluate_expr(ds.ground_truth)
...     if rmse > ds.success_threshold:
...         print(f'Failed dataset: {dataset} with RMSE {rmse}')

Parameters:

Name Type Description Default
dataset_directory str

The directory path where the benchmark dataset will be downloaded and stored or where it will be loaded from.

 required
seed Optional[int]

The seed to use for the random number generator. If None, the random number generation will not be seeded

 None

Returns:

Name Type Description
SR_benchmark SR_benchmark

An instance of the SR_benchmark class containing the predefined datasets.
Source code in SRToolkit/dataset/sr_benchmark.py 
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    @staticmethod
    def feynman(dataset_directory: str, seed: Optional[int] = None) -> "SR_benchmark":
        """
        Downloads the Feynman benchmark dataset, sets up symbol libraries, and adds predefined datasets to the benchmark.

        This method downloads the Feynman benchmark dataset from a specified URL, initializes symbol libraries for
        symbolic regression with varying numbers of variables, and adds multiple predefined datasets to the benchmark
        with their respective equations and metadata.

        Examples:
            >>> benchmark = SR_benchmark.feynman('data/feynman')
            >>> for dataset in benchmark.list_datasets(verbose=False):
            ...     ds = benchmark.create_dataset(dataset)
            ...     rmse = ds.create_evaluator().evaluate_expr(ds.ground_truth)
            ...     if rmse > ds.success_threshold:
            ...         print(f'Failed dataset: {dataset} with RMSE {rmse}')

        Args:
            dataset_directory: The directory path where the benchmark dataset will be downloaded and stored or where
                it will be loaded from.
            seed: The seed to use for the random number generator. If None, the random number generation will not
                be seeded

        Returns:
            SR_benchmark: An instance of the SR_benchmark class containing the predefined datasets.
        """
        url = "https://raw.githubusercontent.com/smeznar/SymbolicRegressionToolkit/master/data/feynman.zip"

        metadata = {"description": "Feynman benchmark containing 100 equations from the domain of physics. "
                                   "Expressions can contain up to 9 variables.",
                    "citation": """@article{Tegmark2020Feynman,
  title={{AI Feynman: A physics-inspired method for symbolic regression}},
  author={Udrescu, Silviu-Marian and Tegmark, Max},
  journal={Science Advances},
  volume={6},
  number={16},
  pages={eaay2631},
  year={2020},
  publisher={American Association for the Advancement of Science}
}
"""
                    }

        SR_benchmark.download_benchmark_data(url, dataset_directory)

        sl_1v = SymbolLibrary.from_symbol_list(["+", "-", "*", "/", "u-", "sqrt", "sin", "cos", "exp",
                                                "arcsin", "tanh", "ln", "^2", "^3", "pi", "C"], 1)
        sl_2v = SymbolLibrary.from_symbol_list(["+", "-", "*", "/", "u-", "sqrt", "sin", "cos", "exp",
                                                "arcsin", "tanh", "ln", "^2", "^3", "pi", "C"], 2)
        sl_3v = SymbolLibrary.from_symbol_list(["+", "-", "*", "/", "u-", "sqrt", "sin", "cos", "exp",
                                                "arcsin", "tanh", "ln", "^2", "^3", "pi", "C"], 3)
        sl_4v = SymbolLibrary.from_symbol_list(["+", "-", "*", "/", "u-", "sqrt", "sin", "cos", "exp",
                                                "arcsin", "tanh", "ln", "^2", "^3", "pi", "C"], 4)
        sl_5v = SymbolLibrary.from_symbol_list(["+", "-", "*", "/", "u-", "sqrt", "sin", "cos", "exp",
                                                "arcsin", "tanh", "ln", "^2", "^3", "pi", "C"], 5)
        sl_6v = SymbolLibrary.from_symbol_list(["+", "-", "*", "/", "u-", "sqrt", "sin", "cos", "exp",
                                                "arcsin", "tanh", "ln", "^2", "^3", "pi", "C"], 6)
        sl_8v = SymbolLibrary.from_symbol_list(["+", "-", "*", "/", "u-", "sqrt", "sin", "cos", "exp",
                                                "arcsin", "tanh", "ln", "^2", "^3", "pi", "C"], 8)
        sl_9v = SymbolLibrary.from_symbol_list(["+", "-", "*", "/", "u-", "sqrt", "sin", "cos", "exp",
                                                "arcsin", "tanh", "ln", "^2", "^3", "pi", "C"], 9)

        benchmark = SR_benchmark("feynman", dataset_directory)
        benchmark.metadata = metadata
        benchmark.add_dataset(
            "",
            sl_3v,
            dataset_name="I.16.6",
            ranking_function="rmse",
            max_evaluations=100000,
            ground_truth = ["(", "X_2", "+","X_1",")","/","(","1","+","(","X_2","*","X_1",")","/","(","X_0","^2",")",")"], # noqa: F401
            original_equation="v1 = (u+v)/(1+u*v/c^2)",
            success_threshold=1e-7,
            result_augmenters=[],
            seed = seed,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            max_expression_length=50,
        )
        benchmark.add_dataset(
            "",
            sl_3v,
            dataset_name="II.15.4",
            ranking_function="rmse",
            ground_truth = ["u-", "X_0", "*", "X_1", "*", "cos", "(", "X_2", ")"], # noqa: F401
            original_equation="E_n = -mom*B*cos(theta)",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_3v,
            dataset_name="II.27.16",
            ranking_function="rmse",
            ground_truth = ["X_0", "*", "X_1", "*", "X_2", "^2"], # noqa: F401
            original_equation="flux = epsilon*c*Ef^2",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_6v,
            dataset_name="I.11.19",
            ranking_function="rmse",
            ground_truth = ["X_0", "*", "X_3", "+", "X_1", "*", "X_4", "+", "X_2", "*", "X_5"], # noqa: F401
            original_equation="A = x1*y1+x2*y2+x3*y3",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_4v,
            dataset_name="I.15.3x",
            ranking_function="rmse",
            ground_truth = ["(", "X_0", "-", "X_1", "*", "X_3", ")", "/", "sqrt", "(", "1", "-", "X_1", "^2", "/", "X_2", "^2", ")"], # noqa: F401
            original_equation="x1 = (x-u*t)/sqrt(1-u^2/c^2)",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_3v,
            dataset_name="I.10.7",
            ranking_function="rmse",
            ground_truth = ["X_0", "/", "sqrt", "(", "1", "-", "X_1", "^2", "/", "X_2", "^2", ")"], # noqa: F401
            original_equation="m = m_0/sqrt(1-v^2/c^2)",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_9v,
            dataset_name="I.9.18",
            ranking_function="rmse",
            ground_truth = ["X_2", "*", "X_0", "*", "X_1", "/", "(", "(", "X_4", "-", "X_3", ")", "^2", "+", "(", "X_6", "-", "X_5", ")", "^2", "+", "(", "X_8", "-", "X_7", ")", "^2", ")"], # noqa: F401
            original_equation="F = G*m1*m2/((x2-x1)^2+(y2-y1)^2+(z2-z1)^2)",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_4v,
            dataset_name="I.15.3t",
            ranking_function="rmse",
            ground_truth = ["(", "X_3", "-", "X_2", "*", "X_0", "/", "X_1", "^2", ")", "/", "sqrt", "(", "1", "-", "X_2", "^2", "/", "X_1", "^2", ")"], # noqa: F401
            original_equation="t1 = (t-u*x/c^2)/sqrt(1-u^2/c^2)",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_8v,
            dataset_name="II.36.38",
            ranking_function="rmse",
            ground_truth = ["(", "X_0", "*", "X_1", ")", "/", "(", "X_2", "*", "X_3", ")", "+", "(", "(", "X_0", "*", "X_4", ")", "/", "(", "X_5", "*", "X_6", "^2", "*", "X_2", "*", "X_3", ")", ")", "*", "X_7"], # noqa: F401
            original_equation="f = mom*H/(kb*T)+(mom*alpha)/(epsilon*c**2*kb*T)*M",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_4v,
            dataset_name="I.43.43",
            ranking_function="rmse",
            ground_truth = ["(", "1", "/", "(", "X_0", "-", "1", ")", ")", "*", "X_1", "*", "X_3", "/", "X_2"], # noqa: F401
            original_equation="kappa = 1/(gamma-1)*kb*v/A",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_3v,
            dataset_name="II.15.5",
            ranking_function="rmse",
            ground_truth = ["u-", "X_0", "*", "X_1", "*", "cos", "(", "X_2", ")"], # noqa: F401
            original_equation="E_n = -p_d*Ef*cos(theta)",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_3v,
            dataset_name="I.37.4",
            ranking_function="rmse",
            ground_truth = ["X_0", "+", "X_1", "+", "2", "*", "sqrt", "(", "X_0", "*", "X_1", ")", "*", "cos", "(", "X_2", ")"], # noqa: F401
            original_equation="Int = I1+I2+2*sqrt(I1*I2)*cos(delta)",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_4v,
            dataset_name="II.6.11",
            ranking_function="rmse",
            ground_truth = ["(", "1", "/", "(", "4", "*", "pi", "*", "X_0", ")", ")", "*", "X_1", "*", "cos", "(", "X_2", ")", "/", "X_3", "^2"], # noqa: F401
            original_equation="Volt = 1/(4*pi*epsilon)*p_d*cos(theta)/r^2",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_3v,
            dataset_name="III.7.38",
            ranking_function="rmse",
            ground_truth = ["2", "*", "X_0", "*", "X_1", "/", "(", "X_2", "/", "(", "2", "*", "pi", ")", ")"], # noqa: F401
            original_equation="omega = 2*mom*B/(h/(2*pi))",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_3v,
            dataset_name="II.34.2a",
            ranking_function="rmse",
            ground_truth = ["X_0", "*", "X_1", "/", "(", "2", "*", "pi", "*", "X_2", ")"], # noqa: F401
            original_equation="l = q*v/(2*pi*r)",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_3v,
            dataset_name="II.13.23",
            ranking_function="rmse",
            ground_truth = ["X_0", "/", "sqrt", "(", "1", "-", "X_1", "^2", "/", "X_2", "^2", ")"], # noqa: F401
            original_equation="rho_c = rho_c_0/sqrt(1-v^2/c^2)",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_2v,
            dataset_name="I.29.4",
            ranking_function="rmse",
            ground_truth = ["X_0", "/", "X_1"], # noqa: F401
            original_equation="k = omega/c",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_4v,
            dataset_name="I.38.12",
            ranking_function="rmse",
            ground_truth = ["4", "*", "pi", "*", "X_3", "*", "(", "X_2", "/", "(", "2", "*", "pi", ")", ")", "^2", "/", "(", "X_0", "*", "X_1", "^2", ")"], # noqa: F401
            original_equation="r = 4*pi*epsilon*(h/(2*pi))^2/(m*q^2)",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_3v,
            dataset_name="III.15.27",
            ranking_function="rmse",
            ground_truth = ["2", "*", "pi", "*", "X_0", "/", "(", "X_1", "*", "X_2", ")"], # noqa: F401
            original_equation="k = 2*pi*alpha/(n*d)",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_5v,
            dataset_name="I.41.16",
            ranking_function="rmse",
            ground_truth = ["(", "X_2", "/", "(", "2", "*", "pi", ")", ")", "*", "X_0", "^3", "/", "(", "pi", "^2", "*", "X_4", "^2", "*", "(", "exp", "(", "(", "X_2", "/", "(", "2", "*", "pi", ")", ")", "*", "X_0", "/", "(", "X_3", "*", "X_1", ")", ")", "-", "1", ")", ")"], # noqa: F401
            original_equation="L_rad = h/(2*pi)*omega^3/(pi^2*c^2*(exp((h/(2*pi))*omega/(kb*T))-1))",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_3v,
            dataset_name="I.48.20",
            ranking_function="rmse",
            ground_truth = ["X_0", "*", "X_2", "^2", "/", "sqrt", "(", "1", "-", "X_1", "^2", "/", "X_2", "^2", ")"], # noqa: F401
            original_equation="E_n = m*c^2/sqrt(1-v^2/c^2)",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_5v,
            dataset_name="II.11.20",
            ranking_function="rmse",
            ground_truth = ["X_0", "*", "X_1", "^2", "*", "X_2", "/", "(", "3", "*", "X_3", "*", "X_4", ")"], # noqa: F401
            original_equation="Pol = n_rho*p_d^2*Ef/(3*kb*T)",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_2v,
            dataset_name="I.25.13",
            ranking_function="rmse",
            ground_truth = ["X_0", "/", "X_1"], # noqa: F401
            original_equation="Volt = q/C",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_3v,
            dataset_name="III.15.12",
            ranking_function="rmse",
            ground_truth = ["2", "*", "X_0", "*", "(", "1", "-", "cos", "(", "X_1", "*", "X_2", ")", ")"], # noqa: F401
            original_equation="E_n = 2*U*(1-cos(k*d))",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_4v,
            dataset_name="I.24.6",
            ranking_function="rmse",
            ground_truth = ["0.25", "*", "X_0", "*", "(", "X_1", "^2", "+", "X_2", "^2", ")", "*", "X_3", "^2"], # noqa: F401
            original_equation="E_n = 1/2*m*(omega^2+omega_0^2)*1/2*x^2",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_2v,
            dataset_name="I.34.27",
            ranking_function="rmse",
            ground_truth = ["(", "X_1", "/", "(", "2", "*", "pi", ")", ")", "*", "X_0"], # noqa: F401
            original_equation="E_n =(h/(2*pi))*omega",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_3v,
            dataset_name="I.43.31",
            ranking_function="rmse",
            ground_truth = ["X_0", "*", "X_2", "*", "X_1"], # noqa: F401
            original_equation="D = mob*kb*T",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_4v,
            dataset_name="I.29.16",
            ranking_function="rmse",
            ground_truth = ["sqrt", "(", "X_0", "^2", "+", "X_1", "^2", "-", "2", "*", "X_0", "*", "X_1", "*", "cos", "(", "X_2", "-", "X_3", ")", ")"], # noqa: F401
            original_equation="x = sqrt(x1^2+x2^2-2*x1*x2*cos(theta1-theta2))",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_4v,
            dataset_name="I.18.4",
            ranking_function="rmse",
            ground_truth = ["(", "X_0", "*", "X_2", "+", "X_1", "*", "X_3", ")", "/", "(", "X_0", "+", "X_1", ")"], # noqa: F401
            original_equation="r = (m1*r1+m2*r2)/(m1+m2)",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_6v,
            dataset_name="II.6.15a",
            ranking_function="rmse",
            ground_truth = ["(", "X_1", "/", "(", "4", "*", "pi", "*", "X_0", ")", ")", "*", "(", "3", "*", "X_5", "/", "(", "X_2", "^2", "*", "X_2", "^3", ")", ")", "*", "sqrt", "(", "X_3", "^2", "+", "X_4", "^2", ")"], # noqa: F401
            original_equation="Ef = p_d/(4*pi*epsilon)*3*z/r^5*sqrt(x^2+y^2)",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_3v,
            dataset_name="I.30.3",
            ranking_function="rmse",
            ground_truth = ["X_0", "*", "sin", "(", "X_2", "*", "X_1", "/", "2", ")", "^2", "/", "sin", "(", "X_1", "/", "2", ")", "^2"], # noqa: F401
            original_equation="Int = Int_0*sin(n*theta/2)^2/sin(theta/2)^2",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_6v,
            dataset_name="III.9.52",
            ranking_function="rmse",
            ground_truth = ["(", "X_0", "*", "X_1", "*", "X_2", "/", "(", "X_3", "/", "(", "2", "*", "pi", ")", ")", ")", "*", "sin", "(", "(", "X_4", "-", "X_5", ")", "*", "X_2", "/", "2", ")", "^2", "/", "(", "(", "X_4", "-", "X_5", ")", "*", "X_2", "/", "2", ")", "^2"], # noqa: F401
            original_equation="prob = (p_d*Ef*t/(h/(2*pi)))*sin((omega-omega_0)*t/2)^2/((omega-omega_0)*t/2)^2",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_3v,
            dataset_name="II.34.2",
            ranking_function="rmse",
            ground_truth = ["X_0", "*", "X_1", "*", "X_2", "/", "2"], # noqa: F401
            original_equation="mom = q*v*r/2",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_3v,
            dataset_name="I.39.11",
            ranking_function="rmse",
            ground_truth = ["(", "1", "/", "(", "X_0", "-", "1", ")", ")", "*", "X_1", "*", "X_2"], # noqa: F401
            original_equation="E_n = (1/(gamma-1))*pr*V",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_2v,
            dataset_name="II.11.28",
            ranking_function="rmse",
            ground_truth = ["1", "+", "X_0", "*", "X_1", "/", "(", "1", "-", "(", "X_0", "*", "X_1", "/", "3", ")", ")"], # noqa: F401
            original_equation="theta = 1+n*alpha/(1-(n*alpha/3))",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_2v,
            dataset_name="II.3.24",
            ranking_function="rmse",
            ground_truth = ["X_0", "/", "(", "4", "*", "pi", "*", "X_1", "^2", ")"], # noqa: F401
            original_equation="flux = Pwr/(4*pi*r^2)",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_3v,
            dataset_name="II.24.17",
            ranking_function="rmse",
            ground_truth = ["sqrt", "(", "X_0", "^2", "/", "X_1", "^2", "-", "pi", "^2", "/", "X_2", "^2", ")"], # noqa: F401
            original_equation="k = sqrt(omega^2/c^2-pi^2/d^2)",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_4v,
            dataset_name="II.13.17",
            ranking_function="rmse",
            ground_truth = ["(", "1", "/", "(", "4", "*", "pi", "*", "X_0", "*", "X_1", "^2", ")", ")", "*", "2", "*", "X_2", "/", "X_3"], # noqa: F401
            original_equation="B = 1/(4*pi*epsilon*c^2)*2*I/r",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_2v,
            dataset_name="I.12.5",
            ranking_function="rmse",
            ground_truth = ["X_0", "*", "X_1"], # noqa: F401
            original_equation="F = q2*Ef",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_5v,
            dataset_name="II.35.18",
            ranking_function="rmse",
            ground_truth = ["X_0", "/", "(", "exp", "(", "X_3", "*", "X_4", "/", "(", "X_1", "*", "X_2", ")", ")", "+", "exp", "(", "u-", "X_3", "*", "X_4", "/", "(", "X_1", "*", "X_2", ")", ")", ")"], # noqa: F401
            original_equation="n_0/(exp(mom*B/(kb*T))+exp(-mom*B/(kb*T)))",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_4v,
            dataset_name="II.34.11",
            ranking_function="rmse",
            ground_truth = ["X_0", "*", "X_1", "*", "X_2", "/", "(", "2", "*", "X_3", ")"], # noqa: F401
            original_equation="g_*q*B/(2*m)",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_3v,
            dataset_name="II.34.29a",
            ranking_function="rmse",
            ground_truth = ["X_0", "*", "X_1", "/", "(", "4", "*", "pi", "*", "X_2", ")"], # noqa: F401
            original_equation="q*h/(4*pi*m)",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_6v,
            dataset_name="I.32.17",
            ranking_function="rmse",
            ground_truth = ["(", "0.5", "*", "X_0", "*", "X_1", "*", "X_2", "^2", ")", "*", "(", "8", "*", "pi", "*", "X_3", "^2", "/", "3", ")", "*", "(", "(", "X_4", "^2", "*", "X_4", "^2", ")", "/", "(", "X_4", "^2", "-", "X_5", "^2", ")", "^2", ")"], # noqa: F401
            original_equation="(1/2*epsilon*c*Ef**2)*(8*pi*r**2/3)*(omega**4/(omega**2-omega_0**2)**2)",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_5v,
            dataset_name="II.35.21",
            ranking_function="rmse",
            ground_truth = ["X_0", "*", "X_1", "*", "tanh", "(", "X_1", "*", "X_2", "/", "(", "X_3", "*", "X_4", ")", ")"], # noqa: F401
            original_equation="n_rho*mom*tanh(mom*B/(kb*T))",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_5v,
            dataset_name="I.44.4",
            ranking_function="rmse",
            ground_truth = ["X_0", "*", "X_1", "*", "X_2", "*", "ln", "(", "X_4", "/", "X_3", ")"], # noqa: F401
            original_equation="n*kb*T*ln(V2/V1)",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_4v,
            dataset_name="III.4.32",
            ranking_function="rmse",
            ground_truth = ["1", "/", "(", "exp", "(", "(", "X_0", "/", "(", "2", "*", "pi", ")", ")", "*", "X_1", "/", "(", "X_2", "*", "X_3", ")", ")", "-", "1", ")"], # noqa: F401
            original_equation="1/(exp((h/(2*pi))*omega/(kb*T))-1)",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_3v,
            dataset_name="II.10.9",
            ranking_function="rmse",
            ground_truth = ["(", "X_0", "/", "X_1", ")", "*", "1", "/", "(", "1", "+", "X_2", ")"], # noqa: F401
            original_equation="sigma_den/epsilon*1/(1+chi)",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_4v,
            dataset_name="II.38.3",
            ranking_function="rmse",
            ground_truth = ["X_0", "*", "X_1", "*", "X_3", "/", "X_2"], # noqa: F401
            original_equation="Y*A*x/d",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_3v,
            dataset_name="I.6.2b",
            ranking_function="rmse",
            ground_truth = ["exp", "(", "u-", "(", "(", "(", "X_1", "-", "X_2", ")", "/", "X_0", ")", "^2", ")", "/", "2", ")", "/", "(", "sqrt", "(", "2", "*", "pi", ")", "*", "X_0", ")"], # noqa: F401
            original_equation="exp(-((theta-theta1)/sigma)**2/2)/(sqrt(2*pi)*sigma)",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_2v,
            dataset_name="II.8.31",
            ranking_function="rmse",
            ground_truth = ["X_0", "*", "X_1", "^2", "/", "2"], # noqa: F401
            original_equation="epsilon*Ef**2/2",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_1v,
            dataset_name="I.6.2a",
            ranking_function="rmse",
            ground_truth = ["exp", "(", "u-", "X_0", "^2", "/", "2", ")", "/", "sqrt", "(", "2", "*", "pi", ")"], # noqa: F401
            original_equation="exp(-theta**2/2)/sqrt(2*pi)",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_2v,
            dataset_name="III.12.43",
            ranking_function="rmse",
            ground_truth = ["X_0", "*", "(", "X_1", "/", "(", "2", "*", "pi", ")", ")"], # noqa: F401
            original_equation="n*(h/(2*pi))",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_3v,
            dataset_name="III.17.37",
            ranking_function="rmse",
            ground_truth = ["X_0", "*", "(", "1", "+", "X_1", "*", "cos", "(", "X_2", ")", ")"], # noqa: F401
            original_equation="beta*(1+alpha*cos(theta))",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_4v,
            dataset_name="III.10.19",
            ranking_function="rmse",
            ground_truth = ["X_0", "*", "sqrt", "(", "X_1", "^2", "+", "X_2", "^2", "+", "X_3", "^2", ")"], # noqa: F401
            original_equation="mom*sqrt(Bx**2+By**2+Bz**2)",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_6v,
            dataset_name="II.11.7",
            ranking_function="rmse",
            ground_truth = ["X_0", "*", "(", "1", "+", "X_4", "*", "X_5", "*", "cos", "(", "X_3", ")", "/", "(", "X_1", "*", "X_2", ")", ")"], # noqa: F401
            original_equation="n_0*(1+p_d*Ef*cos(theta)/(kb*T))",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_2v,
            dataset_name="I.39.1",
            ranking_function="rmse",
            ground_truth = ["1.5", "*", "X_0", "*", "X_1"], # noqa: F401
            original_equation="3/2*pr*V",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_3v,
            dataset_name="II.37.1",
            ranking_function="rmse",
            ground_truth = ["X_0", "*", "(", "1", "+", "X_2", ")", "*", "X_1"], # noqa: F401
            original_equation="mom*(1+chi)*B",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_3v,
            dataset_name="I.12.4",
            ranking_function="rmse",
            ground_truth = ["X_0", "*", "X_2", "/", "(", "4", "*", "pi", "*", "X_1", "*", "X_2", "^3", ")"], # noqa: F401
            original_equation="q1*r/(4*pi*epsilon*r**3)",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_2v,
            dataset_name="II.27.18",
            ranking_function="rmse",
            ground_truth = ["X_0", "*", "X_1", "^2"], # noqa: F401
            original_equation="epsilon*Ef**2",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_4v,
            dataset_name="I.12.2",
            ranking_function="rmse",
            ground_truth = ["X_0", "*", "X_1", "*", "X_3", "/", "(", "4", "*", "pi", "*", "X_2", "*", "X_3", "^3", ")"], # noqa: F401
            original_equation="q1*q2*r/(4*pi*epsilon*r**3)",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_4v,
            dataset_name="III.13.18",
            ranking_function="rmse",
            ground_truth = ["2", "*", "X_0", "*", "X_1", "^2", "*", "X_2", "/", "(", "X_3", "/", "(", "2", "*", "pi", ")", ")"], # noqa: F401
            original_equation="2*E_n*d**2*k/(h/(2*pi))",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_5v,
            dataset_name="II.11.3",
            ranking_function="rmse",
            ground_truth = ["X_0", "*", "X_1", "/", "(", "X_2", "*", "(", "X_3", "^2", "-", "X_4", "^2", ")", ")"], # noqa: F401
            original_equation="q*Ef/(m*(omega_0**2-omega**2))",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_6v,
            dataset_name="I.40.1",
            ranking_function="rmse",
            ground_truth = ["X_0", "*", "exp", "(", "u-", "X_1", "*", "X_4", "*", "X_2", "/", "(", "X_5", "*", "X_3", ")", ")"], # noqa: F401
            original_equation="n_0*exp(-m*g*x/(kb*T))",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_4v,
            dataset_name="III.21.20",
            ranking_function="rmse",
            ground_truth = ["u-", "X_0", "*", "X_1", "*", "X_2", "/", "X_3"], # noqa: F401
            original_equation="-rho_c_0*q*A_vec/m",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_4v,
            dataset_name="I.43.16",
            ranking_function="rmse",
            ground_truth = ["X_0", "*", "X_1", "*", "X_2", "/", "X_3"], # noqa: F401
            original_equation="mu_drift*q*Volt/d",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_3v,
            dataset_name="I.15.10",
            ranking_function="rmse",
            ground_truth = ["X_0", "*", "X_1", "/", "sqrt", "(", "1", "-", "X_1", "^2", "/", "X_2", "^2", ")"], # noqa: F401
            original_equation="m_0*v/sqrt(1-v**2/c**2)",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_3v,
            dataset_name="I.30.5",
            ranking_function="rmse",
            ground_truth = ["arcsin", "(", "X_0", "/", "(", "X_2", "*", "X_1", ")", ")"], # noqa: F401
            original_equation="arcsin(lambd/(n*d))",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_4v,
            dataset_name="I.50.26",
            ranking_function="rmse",
            ground_truth = ["X_0", "*", "(", "cos", "(", "X_1", "*", "X_2", ")", "+", "X_3", "*", "cos", "(", "X_1", "*", "X_2", ")", "^2", ")"], # noqa: F401
            original_equation="x1*(cos(omega*t)+alpha*cos(omega*t)**2)",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_5v,
            dataset_name="I.12.11",
            ranking_function="rmse",
            ground_truth = ["X_0", "*", "(", "X_1", "+", "X_2", "*", "X_3", "*", "sin", "(", "X_4", ")", ")"], # noqa: F401
            original_equation="q*(Ef+B*v*sin(theta))",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_2v,
            dataset_name="I.6.2",
            ranking_function="rmse",
            ground_truth = ["exp", "(", "u-", "(", "(", "X_1", "/", "X_0", ")", "^2", ")", "/", "2", ")", "/", "(", "sqrt", "(", "2", "*", "pi", ")", "*", "X_0", ")"], # noqa: F401
            original_equation="exp(-(theta/sigma)**2/2)/(sqrt(2*pi)*sigma)",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_2v,
            dataset_name="I.14.4",
            ranking_function="rmse",
            ground_truth = ["0.5", "*", "X_0", "*", "X_1", "^2"], # noqa: F401
            original_equation="1/2*k_spring*x**2",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_3v,
            dataset_name="I.47.23",
            ranking_function="rmse",
            ground_truth = ["sqrt", "(", "X_0", "*", "X_1", "/", "X_2", ")"], # noqa: F401
            original_equation="sqrt(gamma*pr/rho)",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_3v,
            dataset_name="II.8.7",
            ranking_function="rmse",
            ground_truth = ["0.6", "*", "X_0", "^2", "/", "(", "4", "*", "pi", "*", "X_1", "*", "X_2", ")"], # noqa: F401
            original_equation="3/5*q**2/(4*pi*epsilon*d)",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_3v,
            dataset_name="III.15.14",
            ranking_function="rmse",
            ground_truth = ["(", "X_0", "/", "(", "2", "*", "pi", ")", ")", "^2", "/", "(", "2", "*", "X_1", "*", "X_2", "^2", ")"], # noqa: F401
            original_equation="(h/(2*pi))**2/(2*E_n*d**2)",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_3v,
            dataset_name="I.34.14",
            ranking_function="rmse",
            ground_truth = ["(", "(", "1", "+", "(", "X_1", "/", "X_0", ")", ")", "/", "sqrt", "(", "1", "-", "X_1", "^2", "/", "X_0", "^2", ")", ")", "*", "X_2"], # noqa: F401
            original_equation="((1+v/c)/sqrt(1-v**2/c**2))*omega_0",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_3v,
            dataset_name="III.8.54",
            ranking_function="rmse",
            ground_truth = ["sin", "(", "X_0", "*", "X_1", "/", "(", "X_2", "/", "(", "2", "*", "pi", ")", ")", ")", "^2"], # noqa: F401
            original_equation="sin(E_n*t/(h/(2*pi)))**2",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_2v,
            dataset_name="I.26.2",
            ranking_function="rmse",
            ground_truth = ["arcsin", "(", "X_0", "*", "sin", "(", "X_1", ")", ")"], # noqa: F401
            original_equation="arcsin(n*sin(theta2))",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_5v,
            dataset_name="III.19.51",
            ranking_function="rmse",
            ground_truth = ["(", "u-", "X_0", "*", "(", "X_1", "^2", "*", "X_1", "^2", ")", "/", "(", "(", "2", "*", "(", "4", "*", "pi", "*", "X_4", ")", "^2", ")", "*", "(", "X_2", "/", "(", "2", "*", "pi", ")", ")", "^2", ")", "*", "(", "1", "/", "X_3", "^2", ")", ")"], # noqa: F401
            original_equation="-m*q**4/(2*(4*pi*epsilon)**2*(h/(2*pi))**2)*(1/n**2)",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_4v,
            dataset_name="III.4.33",
            ranking_function="rmse",
            ground_truth = ["(", "X_0", "/", "(", "2", "*", "pi", ")", ")", "*", "X_1", "/", "(", "exp", "(", "(", "X_0", "/", "(", "2", "*", "pi", ")", ")", "*", "X_1", "/", "(", "X_2", "*", "X_3", ")", ")", "-", "1", ")"], # noqa: F401
            original_equation="(h/(2*pi))*omega/(exp((h/(2*pi))*omega/(kb*T))-1)",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_3v,
            dataset_name="I.34.1",
            ranking_function="rmse",
            ground_truth = ["X_2", "/", "(", "1", "-", "X_1", "/", "X_0", ")"], # noqa: F401
            original_equation="omega_0/(1-v/c)",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_4v,
            dataset_name="II.11.27",
            ranking_function="rmse",
            ground_truth = ["(", "X_0", "*", "X_1", "/", "(", "1", "-", "(", "X_0", "*", "X_1", "/", "3", ")", ")", ")", "*", "X_2", "*", "X_3"], # noqa: F401
            original_equation="n*alpha/(1-(n*alpha/3))*epsilon*Ef",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_3v,
            dataset_name="II.13.34",
            ranking_function="rmse",
            ground_truth = ["X_0", "*", "X_1", "/", "sqrt", "(", "1", "-", "X_1", "^2", "/", "X_2", "^2", ")"], # noqa: F401
            original_equation="rho_c_0*v/sqrt(1-v**2/c**2)",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_3v,
            dataset_name="II.4.23",
            ranking_function="rmse",
            ground_truth = ["X_0", "/", "(", "4", "*", "pi", "*", "X_1", "*", "X_2", ")"], # noqa: F401
            original_equation="q/(4*pi*epsilon*r)",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_4v,
            dataset_name="I.32.5",
            ranking_function="rmse",
            ground_truth = ["X_0", "^2", "*", "X_1", "^2", "/", "(", "6", "*", "pi", "*", "X_2", "*", "X_3", "^3", ")"], # noqa: F401
            original_equation="q**2*a**2/(6*pi*epsilon*c**3)",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_5v,
            dataset_name="I.13.12",
            ranking_function="rmse",
            ground_truth = ["X_4", "*", "X_0", "*", "X_1", "*", "(", "1", "/", "X_3", "-", "1", "/", "X_2", ")"], # noqa: F401
            original_equation="G*m1*m2*(1/r2-1/r1)",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_5v,
            dataset_name="II.2.42",
            ranking_function="rmse",
            ground_truth = ["X_0", "*", "(", "X_2", "-", "X_1", ")", "*", "X_3", "/", "X_4"], # noqa: F401
            original_equation="kappa*(T2-T1)*A/d",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_3v,
            dataset_name="I.27.6",
            ranking_function="rmse",
            ground_truth = ["1", "/", "(", "1", "/", "X_0", "+", "X_2", "/", "X_1", ")"], # noqa: F401
            original_equation="1/(1/d1+n/d2)",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_5v,
            dataset_name="III.14.14",
            ranking_function="rmse",
            ground_truth = ["X_0", "*", "(", "exp", "(", "X_1", "*", "X_2", "/", "(", "X_3", "*", "X_4", ")", ")", "-", "1", ")"], # noqa: F401
            original_equation="I_0*(exp(q*Volt/(kb*T))-1)",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_3v,
            dataset_name="I.18.12",
            ranking_function="rmse",
            ground_truth = ["X_0", "*", "X_1", "*", "sin", "(", "X_2", ")"], # noqa: F401
            original_equation="r*F*sin(theta)",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_4v,
            dataset_name="I.18.14",
            ranking_function="rmse",
            ground_truth = ["X_0", "*", "X_1", "*", "X_2", "*", "sin", "(", "X_3", ")"], # noqa: F401
            original_equation="m*r*v*sin(theta)",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_5v,
            dataset_name="II.21.32",
            ranking_function="rmse",
            ground_truth = ["X_0", "/", "(", "4", "*", "pi", "*", "X_1", "*", "X_2", "*", "(", "1", "-", "X_3", "/", "X_4", ")", ")"], # noqa: F401
            original_equation="q/(4*pi*epsilon*r*(1-v/c))",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_2v,
            dataset_name="II.38.14",
            ranking_function="rmse",
            ground_truth = ["X_0", "/", "(", "2", "*", "(", "1", "+", "X_1", ")", ")"], # noqa: F401
            original_equation="Y/(2*(1+sigma))",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_4v,
            dataset_name="I.34.8",
            ranking_function="rmse",
            ground_truth = ["X_0", "*", "X_1", "*", "X_2", "/", "X_3"], # noqa: F401
            original_equation="q*v*B/p",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_4v,
            dataset_name="I.8.14",
            ranking_function="rmse",
            ground_truth = ["sqrt", "(", "(", "X_1", "-", "X_0", ")", "^2", "+", "(", "X_3", "-", "X_2", ")", "^2", ")"], # noqa: F401
            original_equation="sqrt((x2-x1)**2+(y2-y1)**2)",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_4v,
            dataset_name="II.6.15b",
            ranking_function="rmse",
            ground_truth = ["(", "X_1", "/", "(", "4", "*", "pi", "*", "X_0", ")", ")", "*", "3", "*", "cos", "(", "X_2", ")", "*", "sin", "(", "X_2", ")", "/", "X_3", "^3"], # noqa: F401
            original_equation="p_d/(4*pi*epsilon)*3*cos(theta)*sin(theta)/r**3",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_2v,
            dataset_name="I.12.1",
            ranking_function="rmse",
            ground_truth = ["X_0", "*", "X_1"], # noqa: F401
            original_equation="mu*Nn",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_5v,
            dataset_name="II.34.29b",
            ranking_function="rmse",
            ground_truth = ["X_0", "*", "X_3", "*", "X_4", "*", "X_2", "/", "(", "X_1", "/", "(", "2", "*", "pi", ")", ")"], # noqa: F401
            original_equation="g_*mom*B*Jz/(h/(2*pi))",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_4v,
            dataset_name="I.13.4",
            ranking_function="rmse",
            ground_truth = ["0.5", "*", "X_0", "*", "(", "X_1", "^2", "+", "X_2", "^2", "+", "X_3", "^2", ")"], # noqa: F401
            original_equation="1/2*m*(v**2+u**2+w**2)",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_4v,
            dataset_name="I.39.22",
            ranking_function="rmse",
            ground_truth = ["X_0", "*", "X_3", "*", "X_1", "/", "X_2"], # noqa: F401
            original_equation="n*kb*T/V",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )
        benchmark.add_dataset(
            "",
            sl_3v,
            dataset_name="I.14.3",
            ranking_function="rmse",
            ground_truth = ["X_0", "*", "X_1", "*", "X_2"], # noqa: F401
            original_equation="m*g*z",
            max_evaluations=100000,
            max_expression_length=50,
            success_threshold=1e-7,
            dataset_metadata=benchmark.metadata,
            constant_range=[-5.0, 5.0],
            result_augmenters=[],
            seed = seed
        )

        return benchmark

nguyen staticmethod 

nguyen(dataset_directory: str, seed: Optional[int] = None) -> SR_benchmark

Downloads and initializes the Nguyen benchmark datasets for symbolic regression.

This method downloads the Nguyen symbolic regression benchmark datasets from a specified URL and initializes a set of datasets using a provided dataset directory. It creates two symbol libraries for equations with one variable and two variables, respectively, and populates the benchmark with various Nguyen equations, each represented with its symbolic tokens and associated symbol library.

Examples:

>>> benchmark = SR_benchmark.nguyen('data/nguyen')
>>> for dataset in benchmark.list_datasets(verbose=False):
...     ds = benchmark.create_dataset(dataset)
...     rmse = ds.create_evaluator().evaluate_expr(ds.ground_truth)
...     if rmse > ds.success_threshold:
...         print(f'Failed dataset: {dataset} with RMSE {rmse}')

Parameters:

Name Type Description Default
dataset_directory str

The directory path where the benchmark dataset will be downloaded and stored or where it will be loaded from.

 required
seed Optional[int]

The seed to use for the random number generator. If None, the random number generation will not be seeded

 None

Returns:

Name Type Description
SR_benchmark SR_benchmark

An initialized SR_benchmark instance containing the Nguyen datasets.
Source code in SRToolkit/dataset/sr_benchmark.py 
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    @staticmethod
    def nguyen(dataset_directory: str, seed: Optional[int] = None) -> "SR_benchmark":
        """
        Downloads and initializes the Nguyen benchmark datasets for symbolic regression.

        This method downloads the Nguyen symbolic regression benchmark datasets from a specified URL
        and initializes a set of datasets using a provided dataset directory. It creates two symbol libraries
        for equations with one variable and two variables, respectively, and populates the benchmark with various
        Nguyen equations, each represented with its symbolic tokens and associated symbol library.

        Examples:
            >>> benchmark = SR_benchmark.nguyen('data/nguyen')
            >>> for dataset in benchmark.list_datasets(verbose=False):
            ...     ds = benchmark.create_dataset(dataset)
            ...     rmse = ds.create_evaluator().evaluate_expr(ds.ground_truth)
            ...     if rmse > ds.success_threshold:
            ...         print(f'Failed dataset: {dataset} with RMSE {rmse}')

        Args:
            dataset_directory: The directory path where the benchmark dataset will be downloaded and stored or where
                it will be loaded from.
            seed: The seed to use for the random number generator. If None, the random number generation will not
                be seeded

        Returns:
            SR_benchmark: An initialized SR_benchmark instance containing the Nguyen datasets.
        """
        url = "https://raw.githubusercontent.com/smeznar/SymbolicRegressionToolkit/master/data/nguyen.zip"
        SR_benchmark.download_benchmark_data(url, dataset_directory)
        # we create a SymbolLibrary with 1 and with 2 variables
        # Each library contains +, -, *, /, sin, cos, exp, log, sqrt, ^2, ^3
        sl_1v = SymbolLibrary.from_symbol_list(["+", "-", "*", "/", "sin", "cos", "exp", "log", "sqrt", "^2", "^3"], 1)
        sl_2v = SymbolLibrary.from_symbol_list(["+", "-", "*", "/", "sin", "cos", "exp", "log", "sqrt", "^2", "^3"], 2)

        metadata = {"description": "Symbolic regression benchmark with 10 expressions that don't contain constant "
                                   "parameters. First 4 are polynomials of different degrees. First eight expressions "
                                   "contain 1 variable, last two expressions contain two variables. This benchmark "
                                   "doesn't contain the original data, only expressions",
                    "citation": """@article{Uy2011,
    author={Uy, Nguyen Quang and Hoai, Nguyen Xuan and O'Neill, Michael and McKay, R. I. and Galv{\'a}n-L{\'o}pez, Edgar},
    title={Semantically-based crossover in genetic programming: application to real-valued symbolic regression},
    journal={Genetic Programming and Evolvable Machines},
    year={2011},
    month={Jun},
    day={01},
    volume={12},
    number={2},
    pages={91-119},
}"""}

        # Add datasets to the benchmark
        benchmark = SR_benchmark("Nguyen", dataset_directory, metadata=metadata)
        benchmark.add_dataset(
			"",
			sl_1v,
			dataset_name="NG-1",
			ranking_function="rmse",
			ground_truth = ["X_0", "+", "X_0", "^2", "+", "X_0", "^3"], # noqa: F401
			original_equation="x+x^2+x^3",
			max_evaluations=100000,
			max_expression_length=50,
			success_threshold=1e-7,
			dataset_metadata=benchmark.metadata,
			result_augmenters=[],
			seed = seed
		)

        benchmark.add_dataset(
			"",
			sl_1v,
			dataset_name="NG-2",
			ranking_function="rmse",
			ground_truth = ["X_0", "+", "X_0", "^2", "+", "X_0", "^3", "+", "X_0", "*", "X_0", "^3"], # noqa: F401
			original_equation="x+x^2+x^3+x^4",
			max_evaluations=100000,
			max_expression_length=50,
			success_threshold=1e-7,
			dataset_metadata=benchmark.metadata,
			result_augmenters=[],
			seed = seed
		)

        benchmark.add_dataset(
			"",
			sl_1v,
			dataset_name="NG-3",
			ranking_function="rmse",
			ground_truth = ["X_0", "+", "X_0", "^2", "+", "X_0", "^3", "+", "X_0", "*", "X_0", "^3", "+", "X_0", "^2", "*", "X_0", "^3"], # noqa: F401
			original_equation="x+x^2+x^3+x^4+x^5",
			max_evaluations=100000,
			max_expression_length=50,
			success_threshold=1e-7,
			dataset_metadata=benchmark.metadata,
			result_augmenters=[],
			seed = seed
		)

        benchmark.add_dataset(
			"",
			sl_1v,
			dataset_name="NG-4",
			ranking_function="rmse",
			ground_truth = ["X_0", "+", "X_0", "^2", "+", "X_0", "^3", "+", "X_0", "*", "X_0", "^3", "+", "X_0", "^2", "*", "X_0", "^3", "+", "X_0", "^3", "*", "X_0", "^3"], # noqa: F401
			original_equation="x+x^2+x^3+x^4+x^5+x^6",
			max_evaluations=100000,
			max_expression_length=50,
			success_threshold=1e-7,
			dataset_metadata=benchmark.metadata,
			result_augmenters=[],
			seed = seed
		)

        benchmark.add_dataset(
			"",
			sl_1v,
			dataset_name="NG-5",
			ranking_function="rmse",
			ground_truth = ["sin", "(", "X_0", "^2", ")", "*", "cos", "(", "X_0", ")", "-", "1"], # noqa: F401
			original_equation="sin(x^2)*cos(x)-1",
			max_evaluations=100000,
			max_expression_length=50,
			success_threshold=1e-7,
			dataset_metadata=benchmark.metadata,
			result_augmenters=[],
			seed = seed
		)

        benchmark.add_dataset(
			"",
			sl_1v,
			dataset_name="NG-6",
			ranking_function="rmse",
			ground_truth = ["sin", "(", "X_0", ")", "+", "sin", "(", "X_0", "+", "X_0", "^2", ")"], # noqa: F401
			original_equation="sin(x)+sin(x+x^2)",
			max_evaluations=100000,
			max_expression_length=50,
			success_threshold=1e-7,
			dataset_metadata=benchmark.metadata,
			result_augmenters=[],
			seed = seed
		)

        benchmark.add_dataset(
			"",
			sl_1v,
			dataset_name="NG-7",
			ranking_function="rmse",
			ground_truth = ["log", "(", "1", "+", "X_0", ")", "+", "log", "(", "1", "+", "X_0", "^2", ")"], # noqa: F401
			original_equation="log(1+x)+log(1+x^2)",
			max_evaluations=100000,
			max_expression_length=50,
			success_threshold=1e-7,
			dataset_metadata=benchmark.metadata,
			result_augmenters=[],
			seed = seed
		)

        benchmark.add_dataset(
			"",
			sl_1v,
			dataset_name="NG-8",
			ranking_function="rmse",
			ground_truth = ["sqrt", "(", "X_0", ")"], # noqa: F401
			original_equation="sqrt(x)",
			max_evaluations=100000,
			max_expression_length=50,
			success_threshold=1e-7,
			dataset_metadata=benchmark.metadata,
			result_augmenters=[],
			seed = seed
		)

        benchmark.add_dataset(
			"",
			sl_2v,
			dataset_name="NG-9",
			ranking_function="rmse",
			ground_truth = ["sin", "(", "X_0", ")", "+", "sin", "(", "X_1", "^2", ")"], # noqa: F401
			original_equation="sin(x)+sin(y^2)",
			max_evaluations=100000,
			max_expression_length=50,
			success_threshold=1e-7,
			dataset_metadata=benchmark.metadata,
			result_augmenters=[],
			seed = seed
		)

        benchmark.add_dataset(
			"",
			sl_2v,
			dataset_name="NG-10",
			ranking_function="rmse",
			ground_truth = ["2", "*", "sin", "(", "X_0", ")", "*", "cos", "(", "X_1", ")"], # noqa: F401
			original_equation="2*sin(x)*cos(y)",
			max_evaluations=100000,
			max_expression_length=50,
			success_threshold=1e-7,
			dataset_metadata=benchmark.metadata,
			result_augmenters=[],
			seed = seed
		)

        return benchmark