Dataset Module

SRToolkit.dataset

This module contains data sets and benchmarks for symbolic regression. A dataset represents a single equation with specific data, constraints for evaluation, etc. A benchmark is a collection of datasets. Our library provides the user with two modified version of popular equation discovery benchmarks. Specifically Feynman and Nguyen.

Modules:

Name	Description
sr_dataset	The module containing the SRDataset class, which can be used to create a dataset and easily evaluate equation discovery approaches.
sr_benchmark	The module containing the SRBenchmark class, which can be used to create a benchmark i.e. a collection of datasets.

SRDataset

Source code in SRToolkit/dataset/srdataset.py

class SRDataset:
    def __init__(self, X: np.ndarray, y: np.ndarray, ground_truth: List[str], original_equation: str,
                 symbols: SymbolLibrary, max_evaluations: int=-1, max_expression_length: int=-1, max_constants: int=8,
                 success_threshold: float=1e-7, constant_range: List[float]=None, dataset_metadata: dict=None):
        """
        Initializes an instance of the SRDataset class.

        Args:
            X: The input data to be used in parameter estimation for variables. We assume that X is a 2D array
                with shape (n_samples, n_features).
            y: The target values to be used in parameter estimation.
            ground_truth: The ground truth expression, represented as a list of tokens (strings) in the infix notation.
            original_equation: The original equation from which the ground truth expression was generated).
            symbols: The symbol library to use.
            max_evaluations: The maximum number of expressions to evaluate. Less than 0 means no limit.
            max_expression_length: The maximum length of the expression. Less than 0 means no limit.
            max_constants: The maximum number of constants allowed in the expression. Less than 0 means no limit.
            success_threshold: The RMSE threshold below which the experiment is considered successful.
            constant_range: A list of two floats, specifying the lower and upper bounds for the constant values.
                Default is [-5.0, 5.0]. If constant_range is None, we automatically set it to [-5.0, 5.0]
                if the symbol library contains a symbol for constants.
            dataset_metadata: An optional dictionary containing metadata about this evaluation. This could include
                information such as the name of the dataset, a citation for the dataset, number of variables, etc.
        """
        self.X = X
        self.y = y
        self.ground_truth = ground_truth
        self.original_equation = original_equation

        self.max_evaluations = max_evaluations
        self.max_expression_length = max_expression_length
        self.max_constants = max_constants

        self.success_threshold = success_threshold

        self.symbols = symbols

        # See if symbols contain a symbol for constants
        symbols_metadata = self.symbols.symbols.values()
        self.contains_constants = any([symbol["type"] == "const" for symbol in symbols_metadata])
        if constant_range is None and self.contains_constants:
            constant_range = [-5.0, 5.0]
        self.constant_range = constant_range

        self.dataset_metadata = dataset_metadata

    def __str__(self) -> str:
        """
        Returns a string describing this dataset.

        The string describes the target expression, symbols that should be used,
        and the success threshold. It also includes any constraints that should
        be followed when evaluating a model on this dataset, such as the maximum
        number of expressions to evaluate, the maximum length of the expression,
        and the maximum number of constants allowed in the expression. If the
        symbol library contains a symbol for constants, the string also includes
        the range of constants.

        For other metadata, please refer to the attribute self.dataset_metadata.

        Returns:
            A string describing this dataset.
        """
        description = f"Dataset for target expression {self.original_equation}. "
        description += (f" When evaluating your model on this dataset, you should limit your generative model to only"
                        f" produce expressions using the following symbols: {str(self.symbols)}. Expressions are deemed"
                        f" successful if the root mean squared error is less than {self.success_threshold}. However, we"
                        f" advise that you check the best performing expressions manually to ensure they are correct.")

        has_limitations = False
        limitations = "Constraints for this dataset are:"
        if self.max_evaluations > 0:
            has_limitations = True
            limitations += f" max_evaluations={self.max_evaluations}, "
        if self.max_expression_length > 0:
            has_limitations = True
            limitations += f" max_expression_length={self.max_expression_length}, "
        if self.max_constants > 0:
            has_limitations = True
            limitations += f" max_constants={self.max_constants}, "

        if has_limitations:
            limitations = limitations[:-2] + "."
            description += limitations

        if self.contains_constants:
            description += f" The dataset contains constants. The range of constants is {self.constant_range}."

        description += "For other metadata, please refer to the attribute self.dataset_metadata."

        return description

    def create_evaluator(self, metadata: dict=None) -> SR_evaluator:
        """
        Creates an instance of the SR_evaluator class from this dataset.

        Args:
            metadata: An optional dictionary containing metadata about this evaluation. This could include
                information such as the dataset used, the model used, seed, etc.

        Returns:
            An instance of the SR_evaluator class.
        """
        if metadata is None:
            metadata = dict()
        metadata["dataset_metadata"] = self.dataset_metadata
        return SR_evaluator(self.X, self.y, max_evaluations=self.max_evaluations, metadata=metadata,
                            symbol_library=self.symbols, max_constants=self.max_constants,
                            max_expression_length=self.max_expression_length,)

__init__(X, y, ground_truth, original_equation, symbols, max_evaluations=-1, max_expression_length=-1, max_constants=8, success_threshold=1e-07, constant_range=None, dataset_metadata=None)

Initializes an instance of the SRDataset class.

Parameters:

Name	Type	Description	Default
X	ndarray	The input data to be used in parameter estimation for variables. We assume that X is a 2D array with shape (n_samples, n_features).	required
y	ndarray	The target values to be used in parameter estimation.	required
ground_truth	List[str]	The ground truth expression, represented as a list of tokens (strings) in the infix notation.	required
original_equation	str	The original equation from which the ground truth expression was generated).	required
symbols	SymbolLibrary	The symbol library to use.	required
max_evaluations	int	The maximum number of expressions to evaluate. Less than 0 means no limit.	-1
max_expression_length	int	The maximum length of the expression. Less than 0 means no limit.	-1
max_constants	int	The maximum number of constants allowed in the expression. Less than 0 means no limit.	8
success_threshold	float	The RMSE threshold below which the experiment is considered successful.	1e-07
constant_range	List[float]	A list of two floats, specifying the lower and upper bounds for the constant values. Default is [-5.0, 5.0]. If constant_range is None, we automatically set it to [-5.0, 5.0] if the symbol library contains a symbol for constants.	None
dataset_metadata	dict	An optional dictionary containing metadata about this evaluation. This could include information such as the name of the dataset, a citation for the dataset, number of variables, etc.	None

Source code in SRToolkit/dataset/srdataset.py

def __init__(self, X: np.ndarray, y: np.ndarray, ground_truth: List[str], original_equation: str,
             symbols: SymbolLibrary, max_evaluations: int=-1, max_expression_length: int=-1, max_constants: int=8,
             success_threshold: float=1e-7, constant_range: List[float]=None, dataset_metadata: dict=None):
    """
    Initializes an instance of the SRDataset class.

    Args:
        X: The input data to be used in parameter estimation for variables. We assume that X is a 2D array
            with shape (n_samples, n_features).
        y: The target values to be used in parameter estimation.
        ground_truth: The ground truth expression, represented as a list of tokens (strings) in the infix notation.
        original_equation: The original equation from which the ground truth expression was generated).
        symbols: The symbol library to use.
        max_evaluations: The maximum number of expressions to evaluate. Less than 0 means no limit.
        max_expression_length: The maximum length of the expression. Less than 0 means no limit.
        max_constants: The maximum number of constants allowed in the expression. Less than 0 means no limit.
        success_threshold: The RMSE threshold below which the experiment is considered successful.
        constant_range: A list of two floats, specifying the lower and upper bounds for the constant values.
            Default is [-5.0, 5.0]. If constant_range is None, we automatically set it to [-5.0, 5.0]
            if the symbol library contains a symbol for constants.
        dataset_metadata: An optional dictionary containing metadata about this evaluation. This could include
            information such as the name of the dataset, a citation for the dataset, number of variables, etc.
    """
    self.X = X
    self.y = y
    self.ground_truth = ground_truth
    self.original_equation = original_equation

    self.max_evaluations = max_evaluations
    self.max_expression_length = max_expression_length
    self.max_constants = max_constants

    self.success_threshold = success_threshold

    self.symbols = symbols

    # See if symbols contain a symbol for constants
    symbols_metadata = self.symbols.symbols.values()
    self.contains_constants = any([symbol["type"] == "const" for symbol in symbols_metadata])
    if constant_range is None and self.contains_constants:
        constant_range = [-5.0, 5.0]
    self.constant_range = constant_range

    self.dataset_metadata = dataset_metadata

__str__()

Returns a string describing this dataset.

The string describes the target expression, symbols that should be used, and the success threshold. It also includes any constraints that should be followed when evaluating a model on this dataset, such as the maximum number of expressions to evaluate, the maximum length of the expression, and the maximum number of constants allowed in the expression. If the symbol library contains a symbol for constants, the string also includes the range of constants.

For other metadata, please refer to the attribute self.dataset_metadata.

Returns:

Type	Description
str	A string describing this dataset.

Source code in SRToolkit/dataset/srdataset.py

def __str__(self) -> str:
    """
    Returns a string describing this dataset.

    The string describes the target expression, symbols that should be used,
    and the success threshold. It also includes any constraints that should
    be followed when evaluating a model on this dataset, such as the maximum
    number of expressions to evaluate, the maximum length of the expression,
    and the maximum number of constants allowed in the expression. If the
    symbol library contains a symbol for constants, the string also includes
    the range of constants.

    For other metadata, please refer to the attribute self.dataset_metadata.

    Returns:
        A string describing this dataset.
    """
    description = f"Dataset for target expression {self.original_equation}. "
    description += (f" When evaluating your model on this dataset, you should limit your generative model to only"
                    f" produce expressions using the following symbols: {str(self.symbols)}. Expressions are deemed"
                    f" successful if the root mean squared error is less than {self.success_threshold}. However, we"
                    f" advise that you check the best performing expressions manually to ensure they are correct.")

    has_limitations = False
    limitations = "Constraints for this dataset are:"
    if self.max_evaluations > 0:
        has_limitations = True
        limitations += f" max_evaluations={self.max_evaluations}, "
    if self.max_expression_length > 0:
        has_limitations = True
        limitations += f" max_expression_length={self.max_expression_length}, "
    if self.max_constants > 0:
        has_limitations = True
        limitations += f" max_constants={self.max_constants}, "

    if has_limitations:
        limitations = limitations[:-2] + "."
        description += limitations

    if self.contains_constants:
        description += f" The dataset contains constants. The range of constants is {self.constant_range}."

    description += "For other metadata, please refer to the attribute self.dataset_metadata."

    return description

create_evaluator(metadata=None)

Creates an instance of the SR_evaluator class from this dataset.

Parameters:

Name	Type	Description	Default
metadata	dict	An optional dictionary containing metadata about this evaluation. This could include information such as the dataset used, the model used, seed, etc.	None

Returns:

Type	Description
SR_evaluator	An instance of the SR_evaluator class.

Source code in SRToolkit/dataset/srdataset.py

def create_evaluator(self, metadata: dict=None) -> SR_evaluator:
    """
    Creates an instance of the SR_evaluator class from this dataset.

    Args:
        metadata: An optional dictionary containing metadata about this evaluation. This could include
            information such as the dataset used, the model used, seed, etc.

    Returns:
        An instance of the SR_evaluator class.
    """
    if metadata is None:
        metadata = dict()
    metadata["dataset_metadata"] = self.dataset_metadata
    return SR_evaluator(self.X, self.y, max_evaluations=self.max_evaluations, metadata=metadata,
                        symbol_library=self.symbols, max_constants=self.max_constants,
                        max_expression_length=self.max_expression_length,)

SRBenchmark

Source code in SRToolkit/dataset/srbenchmark.py

class SRBenchmark:
    def __init__(self, benchmark_name: str, base_dir: str, metadata: dict = None):
        """
        Initializes an instance of the SRBenchmark class.

        Args:
            benchmark_name: The name of this benchmark.
            base_dir: The directory where the datasets will be stored.
            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.
        """
        self.benchmark_name = benchmark_name
        self.base_dir = base_dir
        self.datasets = {}
        self.metadata = {} if metadata is None else metadata

    def add_dataset(self, dataset_name: str, ground_truth: List[str],  symbol_library: SymbolLibrary,
                    original_equation: str = None, max_evaluations: int=-1, max_expression_length: int=-1,
                    max_constants: int=8, success_threshold: float=1e-7, constant_range: List[float]=None,
                    num_variables: int=-1, dataset_metadata: dict=None):

        """
        Adds a dataset to the benchmark.

        Args:
            dataset_name: The name of the dataset.
            ground_truth: The ground truth expression, represented as a list of tokens (strings) in the infix notation.
            symbol_library: The symbol library to use.
            original_equation: The original equation from which the ground truth expression was generated.
            max_evaluations: The maximum number of expressions to evaluate. Less than 0 means no limit.
            max_expression_length: The maximum length of the expression. Less than 0 means no limit.
            max_constants: The maximum number of constants allowed in the expression. Less than 0 means no limit.
            success_threshold: The RMSE threshold below which the experiment is considered successful.
            constant_range: A list of two floats, specifying the lower and upper bounds for the constant values.
                Default is [-5.0, 5.0]. If constant_range is None, we automatically set it to [-5.0, 5.0]
                if the symbol library contains a symbol for constants.
            num_variables: The number of variables in the expression. Default is -1, which means we don't know.
            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.
        """
        if original_equation is None:
            original_equation = "".join(ground_truth)

        self.datasets[dataset_name] = {
            "path": self.base_dir + "/" + dataset_name + ".npy",
            "ground_truth": ground_truth,
            "original_equation": original_equation,
            "symbols": symbol_library,
            "max_evaluations": max_evaluations,
            "max_expression_length": max_expression_length,
            "max_constants": max_constants,
            "success_threshold": success_threshold,
            "constant_range": constant_range,
            "dataset_metadata": self.metadata.update(dataset_metadata),
            "num_variables": num_variables
        }

    def create_dataset(self, dataset_name: str):
        """
        Creates an instance of a dataset from the given dataset name.

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

        Returns:
            A SRDataset 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:
            # Check if dataset exists otherwise download it from an url
            if os.path.exists(self.datasets[dataset_name]["path"]):
                data = np.load(self.datasets[dataset_name]["path"])
            else:
                raise ValueError(f"Could not find dataset {dataset_name} at {self.datasets[dataset_name]['path']}")

            X = data[:, :-1]
            y = data[:, -1]

            return SRDataset(X, y, ground_truth=self.datasets[dataset_name]["ground_truth"],
                             original_equation=self.datasets[dataset_name]["original_equation"],
                             symbols=self.datasets[dataset_name]["symbols"],
                             max_evaluations=self.datasets[dataset_name]["max_evaluations"],
                             max_expression_length=self.datasets[dataset_name]["max_expression_length"],
                             max_constants=self.datasets[dataset_name]["max_constants"],
                             success_threshold=self.datasets[dataset_name]["success_threshold"],
                             constant_range=self.datasets[dataset_name]["constant_range"],
                             dataset_metadata=self.datasets[dataset_name]["dataset_metadata"])
        else:
            raise ValueError(f"Dataset {dataset_name} not found")

    def list_datasets(self, verbose=True, num_variables: int=-1):
        """
        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


    @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.

        Returns:
            None
        """
        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)


    @staticmethod
    def feynman(dataset_directory: str):
        """
        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.

        Args:
            dataset_directory (str): The directory path where the benchmark dataset will be downloaded and stored.

        Returns:
            SRBenchmark: An instance of the SRBenchmark class containing the predefined datasets.
        """
        url = "https://raw.githubusercontent.com/smeznar/SymbolicRegressionToolkit/master/data/feynman.zip"
        SRBenchmark.download_benchmark_data(url, dataset_directory)

        sl_1v = SymbolLibrary()
        sl_1v.add_symbol("+", symbol_type="op", precedence=0, np_fn="{} = {} + {}", latex_str=r"{} + {}")
        sl_1v.add_symbol("-", symbol_type="op", precedence=0, np_fn="{} = {} - {}", latex_str=r"{} - {}")
        sl_1v.add_symbol("*", symbol_type="op", precedence=1, np_fn="{} = {} * {}", latex_str=r"{} \cdot {}")
        sl_1v.add_symbol("/", symbol_type="op", precedence=1, np_fn="{} = {} / {}", latex_str=r"\frac{{{}}}{{{}}}")
        sl_1v.add_symbol("u-", symbol_type="fn", precedence=5, np_fn="{} = -{}", latex_str=r"- {}")
        sl_1v.add_symbol("sqrt", symbol_type="fn", precedence=5, np_fn="{} = np.sqrt({})", latex_str=r"\sqrt {{{}}}")
        sl_1v.add_symbol("sin", symbol_type="fn", precedence=5, np_fn="{} = np.sin({})", latex_str=r"\sin {}")
        sl_1v.add_symbol("cos", symbol_type="fn", precedence=5, np_fn="{} = np.cos({})", latex_str=r"\cos {}")
        sl_1v.add_symbol("exp", symbol_type="fn", precedence=5, np_fn="{} = np.exp({})", latex_str=r"e^{{{}}}")
        sl_1v.add_symbol("arcsin", symbol_type="fn", precedence=5, np_fn="{} = np.arcsin({})", latex_str=r"\arcsin {}")
        sl_1v.add_symbol("tanh", symbol_type="fn", precedence=5, np_fn="{} = np.tanh({})", latex_str=r"\tanh {}")
        sl_1v.add_symbol("ln", symbol_type="fn", precedence=5, np_fn="{} = np.log({})", latex_str=r"\ln {}")
        sl_1v.add_symbol("^2", symbol_type="fn", precedence=-1, np_fn="{} = {}**2", latex_str=r"{}^2")
        sl_1v.add_symbol("^3", symbol_type="fn", precedence=-1, np_fn="{} = {}**3", latex_str=r"{}^3")
        sl_1v.add_symbol("pi", symbol_type="lit", precedence=5, np_fn="np.full(X.shape[0], np.pi)", latex_str=r"\pi")
        sl_1v.add_symbol("C", "const", 5, np_fn="np.full(X.shape[0], C[{}])", latex_str=r"C_{{{}}}")
        sl_1v.add_symbol("X_0", "var", 5, "X[:, 0]", r"X_{0}")

        sl_2v = copy.copy(sl_1v)
        sl_2v.add_symbol("X_1", "var", 5, "X[:, 1]", r"X_{1}")

        sl_3v = copy.copy(sl_2v)
        sl_3v.add_symbol("X_2", "var", 5, "X[:, 2]", r"X_{2}")

        sl_4v = copy.copy(sl_3v)
        sl_4v.add_symbol("X_3", "var", 5, "X[:, 3]", r"X_{3}")

        sl_5v = copy.copy(sl_4v)
        sl_5v.add_symbol("X_4", "var", 5, "X[:, 4]", r"X_{4}")

        sl_6v = copy.copy(sl_5v)
        sl_6v.add_symbol("X_5", "var", 5, "X[:, 5]", r"X_{5}")

        sl_8v = copy.copy(sl_6v)
        sl_8v.add_symbol("X_6", "var", 5, "X[:, 6]", r"X_{6}")
        sl_8v.add_symbol("X_7", "var", 5, "X[:, 7]", r"X_{7}")

        sl_9v = copy.copy(sl_8v)
        sl_9v.add_symbol("X_8", "var", 5, "X[:, 8]", r"X_{8}")

        benchmark = SRBenchmark("feynman", dataset_directory)
        benchmark.add_dataset("I.16.6", ["(", "X_2", "+", "X_1", ")", "/", "(", "1", "+", "(", "X_2", "*", "X_1", ")", "/", "(", "X_0", "^2", ")", ")"],
                              sl_3v, original_equation="v1 = (u+v)/(1+u*v/c^2)", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=3,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("II.15.4", ["u-", "X_0", "*", "X_1", "*", "cos", "(", "X_2", ")"], sl_3v, original_equation="E_n = -mom*B*cos(theta)", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=3,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("II.27.16", ["X_0", "*", "X_1", "*", "X_2", "^2"], sl_3v, original_equation="flux = epsilon*c*Ef^2", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=3,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("I.11.19", ["X_0", "*", "X_3", "+", "X_1", "*", "X_4", "+", "X_2", "*", "X_5"], sl_6v, original_equation="A = x1*y1+x2*y2+x3*y3", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=6,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("I.15.3x", ["(", "X_0", "-", "X_1", "*", "X_3", ")", "/", "sqrt", "(", "1", "-", "X_1", "^2", "/", "X_2", "^2", ")"], sl_4v, original_equation="x1 = (x-u*t)/sqrt(1-u^2/c^2)", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=4,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("I.10.7", ["X_0", "/", "sqrt", "(", "1", "-", "X_1", "^2", "/", "X_2", "^2", ")"], sl_3v, original_equation="m = m_0/sqrt(1-v^2/c^2)", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=3,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("I.9.18", ["X_2", "*", "X_0", "*", "X_1", "/", "(", "(", "X_4", "-", "X_3", ")", "^2", "+", "(", "X_6", "-", "X_5", ")", "^2", "+", "(", "X_8", "-", "X_7", ")", "^2",")"], sl_9v, 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, num_variables=9,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("I.15.3t", ["(", "X_3", "-", "X_2", "*", "X_0", "/", "X_1", "^2", ")", "/", "sqrt", "(", "1", "-", "X_2", "^2", "/", "X_1", "^2", ")"], sl_4v, 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, num_variables=4,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("II.36.38", ["(", "X_0", "*", "X_1", ")", "/", "(", "X_2", "*", "X_3",")", "+", "(", "(", "X_0", "*", "X_4", ")", "/", "(", "X_5", "*", "X_6", "^2", "*", "X_2", "*", "X_3", ")", ")", "*", "X_7"], sl_8v, 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, num_variables=8,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("I.43.43", ["(", "1", "/", "(", "X_0", "-", "1", ")", ")", "*", "X_1", "*", "X_3", "/", "X_2"], sl_4v, original_equation="kappa = 1/(gamma-1)*kb*v/A", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=4,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("II.15.5", ["u-", "X_0", "*", "X_1", "*", "cos", "(", "X_2", ")"], sl_3v, original_equation="E_n = -p_d*Ef*cos(theta)", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=3,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("I.37.4", ["X_0", "+", "X_1", "+", "2", "*", "sqrt", "(", "X_0", "*", "X_1", ")", "*", "cos", "(", "X_2", ")"], sl_3v, original_equation="Int = I1+I2+2*sqrt(I1*I2)*cos(delta)", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=3,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("II.6.11", ["(", "1", "/", "(", "4", "*", "pi", "*", "X_0", ")", ")", "*", "X_1", "*", "cos", "(", "X_2", ")", "/", "X_3", "^2"], sl_4v, original_equation="Volt = 1/(4*pi*epsilon)*p_d*cos(theta)/r^2", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=4,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("III.7.38", ["2", "*", "X_0", "*", "X_1", "/", "(", "X_2", "/", "(", "2", "*", "pi", ")", ")"], sl_3v, original_equation="omega = 2*mom*B/(h/(2*pi))", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=3,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("II.34.2a", ["X_0", "*", "X_1", "/", "(", "2", "*", "pi", "*", "X_2", ")"], sl_3v, original_equation="l = q*v/(2*pi*r)", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=3,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("II.13.23", ["X_0", "/", "sqrt", "(", "1", "-", "X_1", "^2", "/", "X_2", "^2", ")"], sl_3v, original_equation="rho_c = rho_c_0/sqrt(1-v^2/c^2)", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=3,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("I.29.4", ["X_0", "/", "X_1"], sl_2v, original_equation="k = omega/c", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=2,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("I.38.12", ["4", "*", "pi", "*", "X_3", "*", "(", "X_2", "/", "(", "2", "*", "pi", ")", ")", "^2", "/", "(", "X_0", "*", "X_1", "^2", ")"], sl_4v, original_equation="r = 4*pi*epsilon*(h/(2*pi))^2/(m*q^2)", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=4,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("III.15.27", ["2", "*", "pi", "*", "X_0", "/", "(", "X_1", "*", "X_2", ")"], sl_3v, original_equation="k = 2*pi*alpha/(n*d)", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=3,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("I.41.16", ["(", "X_2", "/", "(", "2", "*", "pi", ")", ")", "*", "X_0", "^3", "/", "(", "pi", "^2", "*", "X_4", "^2", "*", "(", "exp", "(", "(", "X_2", "/", "(", "2", "*", "pi", ")", ")", "*", "X_0", "/", "(", "X_3", "*", "X_1", ")", ")", "-", "1", ")", ")"], sl_5v, 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, num_variables=5,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("I.48.20", ["X_0", "*", "X_2", "^2", "/", "sqrt", "(", "1", "-", "X_1", "^2", "/", "X_2", "^2", ")"], sl_3v, original_equation="E_n = m*c^2/sqrt(1-v^2/c^2)", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=3,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("II.11.20", ["X_0", "*", "X_1", "^2", "*", "X_2", "/", "(", "3", "*", "X_3", "*", "X_4", ")"], sl_5v, original_equation="Pol = n_rho*p_d^2*Ef/(3*kb*T)", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=5,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("I.25.13", ["X_0", "/", "X_1"], sl_2v, original_equation="Volt = q/C", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=2,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("III.15.12", ["2", "*", "X_0", "*", "(", "1", "-", "cos", "(", "X_1", "*", "X_2", ")", ")"], sl_3v, original_equation="E_n = 2*U*(1-cos(k*d))", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=3,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("I.24.6", ["0.25", "*", "X_0", "*", "(", "X_1", "^2", "+", "X_2", "^2", ")", "*", "X_3", "^2"], sl_4v, 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, num_variables=4,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("I.34.27", ["(", "X_1", "/", "(", "2", "*", "pi", ")", ")", "*", "X_0"], sl_2v, original_equation="E_n =(h/(2*pi))*omega", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=2,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("I.43.31", ["X_0", "*", "X_2", "*", "X_1"], sl_3v, original_equation="D = mob*kb*T", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=3,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("I.29.16", ["sqrt", "(", "X_0", "^2", "+", "X_1", "^2", "-", "2", "*", "X_0", "*", "X_1", "*", "cos", "(", "X_2", "-", "X_3", ")", ")"], sl_4v, 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, num_variables=4,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("I.18.4", ["(","X_0", "*", "X_2", "+", "X_1", "*", "X_3", ")", "/", "(", "X_0", "+", "X_1", ")"], sl_4v, original_equation="r = (m1*r1+m2*r2)/(m1+m2)", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=4,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("II.6.15a", ["(", "X_1", "/", "(", "4", "*", "pi", "*", "X_0", ")", ")", "*", "(", "3", "*", "X_5", "/", "(", "X_2", "^2", "*", "X_2", "^3", ")", ")", "*", "sqrt", "(", "X_3", "^2", "+", "X_4", "^2", ")"],
                              sl_6v, 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, num_variables=6,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("I.30.3", ["X_0", "*", "sin", "(", "X_2", "*", "X_1", "/", "2", ")", "^2", "/", "sin", "(", "X_1", "/", "2", ")", "^2"], sl_3v, 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, num_variables=3,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("III.9.52", ["(", "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"], sl_6v, 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, num_variables=6,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("II.34.2", ["X_0", "*", "X_1", "*", "X_2", "/", "2"], sl_3v, original_equation="mom = q*v*r/2", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=3,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("I.39.11", ["(", "1", "/", "(", "X_0", "-", "1", ")", ")", "*", "X_1", "*", "X_2"], sl_3v, original_equation="E_n = (1/(gamma-1))*pr*V", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=3,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("II.11.28", ["1", "+", "X_0", "*", "X_1", "/", "(", "1", "-", "(", "X_0", "*", "X_1", "/", "3", ")", ")"], sl_2v, original_equation="theta = 1+n*alpha/(1-(n*alpha/3))", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=2,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("II.3.24", ["X_0", "/", "(", "4", "*", "pi", "*", "X_1", "^2", ")"], sl_2v, original_equation="flux = Pwr/(4*pi*r^2)", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=2,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("II.24.17", ["sqrt", "(", "X_0", "^2", "/", "X_1", "^2", "-", "pi", "^2", "/", "X_2", "^2", ")"], sl_3v, original_equation="k = sqrt(omega^2/c^2-pi^2/d^2)", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=3,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("II.13.17", ["(", "1", "/", "(", "4", "*", "pi", "*", "X_0", "*", "X_1", "^2", ")", ")", "*", "2", "*", "X_2", "/", "X_3"],
                              sl_4v, original_equation="B = 1/(4*pi*epsilon*c^2)*2*I/r", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=4,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("I.12.5", ["X_0", "*", "X_1"], sl_2v, original_equation="F = q2*Ef", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=2,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        # Check again if you find the time
        benchmark.add_dataset("II.35.18",
                              ["X_0", "/", "(", "exp", "(", "X_3", "*", "X_4", "/", "(", "X_1", "*", "X_2", ")", ")",
                               "+", "exp", "(", "u-", "X_3", "*", "X_4", "/", "(", "X_1", "*", "X_2", ")", ")", ")"],
                              sl_5v, 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, num_variables=5,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("II.34.11", ["X_0", "*", "X_1", "*", "X_2", "/", "(", "2", "*", "X_3", ")"], sl_4v,
                              original_equation="g_*q*B/(2*m)", max_evaluations=100000, max_expression_length=50,
                              success_threshold=1e-7, num_variables=4, dataset_metadata=benchmark.metadata,
                              constant_range=[-5.0, 5.0])
        benchmark.add_dataset("II.34.29a", ["X_0", "*", "X_1", "/", "(", "4", "*", "pi", "*", "X_2", ")"], sl_3v,
                              original_equation="q*h/(4*pi*m)", max_evaluations=100000, max_expression_length=50,
                              success_threshold=1e-7, num_variables=3, dataset_metadata=benchmark.metadata,
                              constant_range=[-5.0, 5.0])
        benchmark.add_dataset("I.32.17",
                              ["(", "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", ")"], sl_6v,
                              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, num_variables=6,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("II.35.21",
                              ["X_0", "*", "X_1", "*", "tanh", "(", "X_1", "*", "X_2", "/", "(", "X_3", "*", "X_4", ")",
                               ")"], sl_5v, original_equation="n_rho*mom*tanh(mom*B/(kb*T))", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=5,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("I.44.4", ["X_0", "*", "X_1", "*", "X_2", "*", "ln", "(", "X_4", "/", "X_3", ")"], sl_5v,
                              original_equation="n*kb*T*ln(V2/V1)", max_evaluations=100000, max_expression_length=50,
                              success_threshold=1e-7, num_variables=5, dataset_metadata=benchmark.metadata,
                              constant_range=[-5.0, 5.0])
        benchmark.add_dataset("III.4.32",
                              ["1", "/", "(", "exp", "(", "(", "X_0", "/", "(", "2", "*", "pi", ")", ")", "*", "X_1",
                               "/", "(", "X_2", "*", "X_3", ")", ")", "-", "1", ")"], sl_4v,
                              original_equation="1/(exp((h/(2*pi))*omega/(kb*T))-1)", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=4,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("II.10.9", ["(", "X_0", "/", "X_1", ")", "*", "1", "/", "(", "1", "+", "X_2", ")"], sl_3v,
                              original_equation="sigma_den/epsilon*1/(1+chi)", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=3,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("II.38.3", ["X_0", "*", "X_1", "*", "X_3", "/", "X_2"], sl_4v,
                              original_equation="Y*A*x/d", max_evaluations=100000, max_expression_length=50,
                              success_threshold=1e-7, num_variables=4, dataset_metadata=benchmark.metadata,
                              constant_range=[-5.0, 5.0])
        benchmark.add_dataset("I.6.2b",
                              ["exp", "(", "u-", "(", "(", "(", "X_1", "-", "X_2", ")", "/", "X_0", ")", "^2", ")", "/", "2", ")",
                               "/", "(", "sqrt", "(", "2", "*", "pi", ")", "*", "X_0", ")"], sl_3v,
                              original_equation="exp(-((theta-theta1)/sigma)**2/2)/(sqrt(2*pi)*sigma)",
                              max_evaluations=100000, max_expression_length=50, success_threshold=1e-7, num_variables=3,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("II.8.31", ["X_0", "*", "X_1", "^2", "/", "2"], sl_2v,
                              original_equation="epsilon*Ef**2/2", max_evaluations=100000, max_expression_length=50,
                              success_threshold=1e-7, num_variables=2, dataset_metadata=benchmark.metadata,
                              constant_range=[-5.0, 5.0])
        benchmark.add_dataset("I.6.2a",
                              ["exp", "(", "u-", "X_0", "^2", "/", "2", ")", "/", "sqrt", "(", "2", "*", "pi", ")"],
                              sl_1v, original_equation="exp(-theta**2/2)/sqrt(2*pi)", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=1,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("III.12.43", ["X_0", "*", "(", "X_1", "/", "(", "2", "*", "pi", ")", ")"], sl_2v,
                              original_equation="n*(h/(2*pi))", max_evaluations=100000, max_expression_length=50,
                              success_threshold=1e-7, num_variables=2, dataset_metadata=benchmark.metadata,
                              constant_range=[-5.0, 5.0])
        benchmark.add_dataset("III.17.37", ["X_0", "*", "(", "1", "+", "X_1", "*", "cos", "(", "X_2", ")", ")"], sl_3v,
                              original_equation="beta*(1+alpha*cos(theta))", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=3,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("III.10.19",
                              ["X_0", "*", "sqrt", "(", "X_1", "^2", "+", "X_2", "^2", "+", "X_3", "^2", ")"], sl_4v,
                              original_equation="mom*sqrt(Bx**2+By**2+Bz**2)", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=4,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("II.11.7",
                              ["X_0", "*", "(", "1", "+", "X_4", "*", "X_5", "*", "cos", "(", "X_3", ")", "/", "(",
                               "X_1", "*", "X_2", ")", ")"], sl_6v,
                              original_equation="n_0*(1+p_d*Ef*cos(theta)/(kb*T))", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=6,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("I.39.1", ["1.5", "*", "X_0", "*", "X_1"], sl_2v, original_equation="3/2*pr*V",
                              max_evaluations=100000, max_expression_length=50, success_threshold=1e-7, num_variables=2,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("II.37.1", ["X_0", "*", "(", "1", "+", "X_2", ")", "*", "X_1"], sl_3v,
                              original_equation="mom*(1+chi)*B", max_evaluations=100000, max_expression_length=50,
                              success_threshold=1e-7, num_variables=3, dataset_metadata=benchmark.metadata,
                              constant_range=[-5.0, 5.0])
        benchmark.add_dataset("I.12.4",
                              ["X_0", "*", "X_2", "/", "(", "4", "*", "pi", "*", "X_1", "*", "X_2", "^3", ")"],
                              sl_3v, original_equation="q1*r/(4*pi*epsilon*r**3)", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=3,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("II.27.18", ["X_0", "*", "X_1", "^2"], sl_2v, original_equation="epsilon*Ef**2",
                              max_evaluations=100000, max_expression_length=50, success_threshold=1e-7, num_variables=2,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("I.12.2",
                              ["X_0", "*", "X_1", "*", "X_3", "/", "(", "4", "*", "pi", "*", "X_2", "*", "X_3", "^3", ")"],
                              sl_4v, original_equation="q1*q2*r/(4*pi*epsilon*r**3)",
                              max_evaluations=100000, max_expression_length=50, success_threshold=1e-7, num_variables=4,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("III.13.18",
                              ["2", "*", "X_0", "*", "X_1", "^2", "*", "X_2", "/", "(", "X_3", "/", "(", "2", "*", "pi",
                               ")", ")"], sl_4v, original_equation="2*E_n*d**2*k/(h/(2*pi))", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=4,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("II.11.3",
                              ["X_0", "*", "X_1", "/", "(", "X_2", "*", "(", "X_3", "^2", "-", "X_4", "^2", ")", ")"],
                              sl_5v, original_equation="q*Ef/(m*(omega_0**2-omega**2))", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=5,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("I.40.1",
                              ["X_0", "*", "exp", "(", "u-", "X_1", "*", "X_4", "*", "X_2", "/", "(", "X_5", "*", "X_3",
                               ")", ")"], sl_6v, original_equation="n_0*exp(-m*g*x/(kb*T))", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=6,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("III.21.20", ["u-", "X_0", "*", "X_1", "*", "X_2", "/", "X_3"], sl_4v,
                              original_equation="-rho_c_0*q*A_vec/m", max_evaluations=100000, max_expression_length=50,
                              success_threshold=1e-7, num_variables=4, dataset_metadata=benchmark.metadata,
                              constant_range=[-5.0, 5.0])
        benchmark.add_dataset("I.43.16", ["X_0", "*", "X_1", "*", "X_2", "/", "X_3"], sl_4v,
                              original_equation="mu_drift*q*Volt/d", max_evaluations=100000, max_expression_length=50,
                              success_threshold=1e-7, num_variables=4, dataset_metadata=benchmark.metadata,
                              constant_range=[-5.0, 5.0])
        benchmark.add_dataset("I.15.10",
                              ["X_0", "*", "X_1", "/", "sqrt", "(", "1", "-", "X_1", "^2", "/", "X_2", "^2", ")"],
                              sl_3v, original_equation="m_0*v/sqrt(1-v**2/c**2)", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=3,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("I.30.5", ["arcsin", "(", "X_0", "/", "(", "X_2", "*", "X_1", ")", ")"], sl_3v,
                              original_equation="arcsin(lambd/(n*d))", max_evaluations=100000, max_expression_length=50,
                              success_threshold=1e-7, num_variables=3, dataset_metadata=benchmark.metadata,
                              constant_range=[-5.0, 5.0])
        benchmark.add_dataset("I.50.26",
                              ["X_0", "*", "(", "cos", "(", "X_1", "*", "X_2", ")", "+", "X_3", "*", "cos", "(", "X_1",
                               "*", "X_2", ")", "^2", ")"], sl_4v,
                              original_equation="x1*(cos(omega*t)+alpha*cos(omega*t)**2)", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=4,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("I.12.11",
                              ["X_0", "*", "(", "X_1", "+", "X_2", "*", "X_3", "*", "sin", "(", "X_4", ")", ")"], sl_5v,
                              original_equation="q*(Ef+B*v*sin(theta))", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=5,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("I.6.2",
                              ["exp", "(", "u-", "(", "(", "X_1", "/", "X_0", ")", "^2", ")",  "/", "2", ")", "/", "(", "sqrt",
                               "(", "2", "*", "pi", ")", "*", "X_0", ")"], sl_2v,
                              original_equation="exp(-(theta/sigma)**2/2)/(sqrt(2*pi)*sigma)", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=2,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("I.14.4", ["0.5", "*", "X_0", "*", "X_1", "^2"], sl_2v,
                              original_equation="1/2*k_spring*x**2", max_evaluations=100000, max_expression_length=50,
                              success_threshold=1e-7, num_variables=2, dataset_metadata=benchmark.metadata,
                              constant_range=[-5.0, 5.0])
        benchmark.add_dataset("I.47.23", ["sqrt", "(", "X_0", "*", "X_1", "/", "X_2", ")"], sl_3v,
                              original_equation="sqrt(gamma*pr/rho)", max_evaluations=100000, max_expression_length=50,
                              success_threshold=1e-7, num_variables=3, dataset_metadata=benchmark.metadata,
                              constant_range=[-5.0, 5.0])
        benchmark.add_dataset("II.8.7",
                              ["0.6", "*", "X_0", "^2", "/", "(", "4", "*", "pi", "*", "X_1", "*", "X_2", ")"],
                              sl_3v, original_equation="3/5*q**2/(4*pi*epsilon*d)", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=3,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("III.15.14",
                              ["(", "X_0", "/", "(", "2", "*", "pi", ")", ")", "^2", "/", "(", "2", "*", "X_1", "*",
                               "X_2", "^2", ")"], sl_3v, original_equation="(h/(2*pi))**2/(2*E_n*d**2)",
                              max_evaluations=100000, max_expression_length=50, success_threshold=1e-7, num_variables=3,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("I.34.14",
                              ["(", "(", "1", "+", "(", "X_1", "/", "X_0", ")", ")", "/", "sqrt", "(", "1", "-", "X_1", "^2", "/",
                               "X_0", "^2", ")", ")", "*", "X_2"], sl_3v,
                              original_equation="((1+v/c)/sqrt(1-v**2/c**2))*omega_0", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=3,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("III.8.54",
                              ["sin", "(", "X_0", "*", "X_1", "/", "(", "X_2", "/", "(", "2", "*", "pi", ")", ")", ")",
                               "^2"], sl_3v, original_equation="sin(E_n*t/(h/(2*pi)))**2", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=3,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("I.26.2", ["arcsin", "(", "X_0", "*", "sin", "(", "X_1", ")", ")"], sl_2v,
                              original_equation="arcsin(n*sin(theta2))", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=2,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("III.19.51",
                              ['(', "u-", "X_0", "*", "(", "X_1", "^2", "*", "X_1", "^2", ")", "/", "(", "2", "*", "(", "4", "*", "pi", "*", "X_4",
                               ")", "^2", ")", "*", "(", "X_2", "/", "(", "2", "*", "pi", ")", ")", "^2", ")", "*", "(", "1",
                               "/", "X_3", "^2", ")"], sl_5v,
                              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, num_variables=5,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("III.4.33",
                              ["(", "X_0", "/", "(", "2", "*", "pi", ")", ")", "*", "X_1", "/", "(", "exp", "(", "(",
                               "X_0", "/", "(", "2", "*", "pi", ")", ")", "*", "X_1", "/", "(", "X_2", "*", "X_3", ")",
                               ")", "-", "1", ")"], sl_4v,
                              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, num_variables=4,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("I.34.1", ["X_2", "/", "(", "1", "-", "X_1", "/", "X_0", ")"], sl_3v,
                              original_equation="omega_0/(1-v/c)", max_evaluations=100000, max_expression_length=50,
                              success_threshold=1e-7, num_variables=3, dataset_metadata=benchmark.metadata,
                              constant_range=[-5.0, 5.0])
        benchmark.add_dataset("II.11.27",
                              ["(", "X_0", "*", "X_1", "/", "(", "1", "-", "(", "X_0", "*", "X_1", "/", "3", ")", ")", ")", "*",
                               "X_2", "*", "X_3"], sl_4v, original_equation="n*alpha/(1-(n*alpha/3))*epsilon*Ef",
                              max_evaluations=100000, max_expression_length=50, success_threshold=1e-7, num_variables=4,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("II.13.34",
                              ["X_0", "*", "X_1", "/", "sqrt", "(", "1", "-", "X_1", "^2", "/", "X_2", "^2", ")"],
                              sl_3v, original_equation="rho_c_0*v/sqrt(1-v**2/c**2)", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=3,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("II.4.23", ["X_0", "/", "(", "4", "*", "pi", "*", "X_1", "*", "X_2", ")"], sl_3v,
                              original_equation="q/(4*pi*epsilon*r)", max_evaluations=100000, max_expression_length=50,
                              success_threshold=1e-7, num_variables=3, dataset_metadata=benchmark.metadata,
                              constant_range=[-5.0, 5.0])
        benchmark.add_dataset("I.32.5",
                              ["X_0", "^2", "*", "X_1", "^2", "/", "(", "6", "*", "pi", "*", "X_2", "*", "X_3", "^3", ")"],
                              sl_4v, original_equation="q**2*a**2/(6*pi*epsilon*c**3)",
                              max_evaluations=100000, max_expression_length=50, success_threshold=1e-7, num_variables=4,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("I.13.12",
                              ["X_4", "*", "X_0", "*", "X_1", "*", "(", "1", "/", "X_3", "-", "1", "/", "X_2", ")"],
                              sl_5v, original_equation="G*m1*m2*(1/r2-1/r1)", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=5,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("II.2.42", ["X_0", "*", "(", "X_2", "-", "X_1", ")", "*", "X_3", "/", "X_4"], sl_5v,
                              original_equation="kappa*(T2-T1)*A/d", max_evaluations=100000, max_expression_length=50,
                              success_threshold=1e-7, num_variables=5, dataset_metadata=benchmark.metadata,
                              constant_range=[-5.0, 5.0])
        benchmark.add_dataset("I.27.6", ["1", "/", "(", "1", "/", "X_0", "+", "X_2", "/", "X_1", ")"], sl_3v,
                              original_equation="1/(1/d1+n/d2)", max_evaluations=100000, max_expression_length=50,
                              success_threshold=1e-7, num_variables=3, dataset_metadata=benchmark.metadata,
                              constant_range=[-5.0, 5.0])
        benchmark.add_dataset("III.14.14",
                              ["X_0", "*", "(", "exp", "(", "X_1", "*", "X_2", "/", "(", "X_3", "*", "X_4", ")", ")",
                               "-", "1", ")"], sl_5v, original_equation="I_0*(exp(q*Volt/(kb*T))-1)",
                              max_evaluations=100000, max_expression_length=50, success_threshold=1e-7, num_variables=5,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("I.18.12", ["X_0", "*", "X_1", "*", "sin", "(", "X_2", ")"], sl_3v,
                              original_equation="r*F*sin(theta)", max_evaluations=100000, max_expression_length=50,
                              success_threshold=1e-7, num_variables=3, dataset_metadata=benchmark.metadata,
                              constant_range=[-5.0, 5.0])
        benchmark.add_dataset("I.18.14", ["X_0", "*", "X_1", "*", "X_2", "*", "sin", "(", "X_3", ")"], sl_4v,
                              original_equation="m*r*v*sin(theta)", max_evaluations=100000, max_expression_length=50,
                              success_threshold=1e-7, num_variables=4, dataset_metadata=benchmark.metadata,
                              constant_range=[-5.0, 5.0])
        benchmark.add_dataset("II.21.32",
                              ["X_0", "/", "(", "4", "*", "pi", "*", "X_1", "*", "X_2", "*", "(", "1", "-", "X_3", "/",
                               "X_4", ")", ")"], sl_5v, original_equation="q/(4*pi*epsilon*r*(1-v/c))",
                              max_evaluations=100000, max_expression_length=50, success_threshold=1e-7, num_variables=5,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("II.38.14", ["X_0", "/", "(", "2", "*", "(", "1", "+", "X_1", ")", ")"], sl_2v,
                              original_equation="Y/(2*(1+sigma))", max_evaluations=100000, max_expression_length=50,
                              success_threshold=1e-7, num_variables=2, dataset_metadata=benchmark.metadata,
                              constant_range=[-5.0, 5.0])
        benchmark.add_dataset("I.34.8", ["X_0", "*", "X_1", "*", "X_2", "/", "X_3"], sl_4v, original_equation="q*v*B/p",
                              max_evaluations=100000, max_expression_length=50, success_threshold=1e-7, num_variables=4,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("I.8.14",
                              ["sqrt", "(", "(", "X_1", "-", "X_0", ")", "^2", "+", "(", "X_3", "-", "X_2", ")", "^2",
                               ")"], sl_4v, original_equation="sqrt((x2-x1)**2+(y2-y1)**2)", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=4,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("II.6.15b",
                              ["(", "X_1", "/", "(", "4", "*", "pi", "*", "X_0", ")", ")", "*", "3", "*", "cos", "(", "X_2", ")",
                               "*", "sin", "(", "X_2", ")", "/", "X_3", "^3"], sl_4v,
                              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, num_variables=4,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("I.12.1", ["X_0", "*", "X_1"], sl_2v, original_equation="mu*Nn", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=2,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("II.34.29b",
                              ["X_0", "*", "X_3", "*", "X_4", "*", "X_2", "/", "(", "X_1", "/", "(", "2", "*", "pi",
                               ")", ")"], sl_5v, original_equation="g_*mom*B*Jz/(h/(2*pi))", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=5,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("I.13.4",
                              ["0.5", "*", "X_0", "*", "(", "X_1", "^2", "+", "X_2", "^2", "+", "X_3", "^2",
                               ")"], sl_4v, original_equation="1/2*m*(v**2+u**2+w**2)", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=4,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
        benchmark.add_dataset("I.39.22", ["X_0", "*", "X_3", "*", "X_1", "/", "X_2"], sl_4v,
                              original_equation="n*kb*T/V", max_evaluations=100000, max_expression_length=50,
                              success_threshold=1e-7, num_variables=4, dataset_metadata=benchmark.metadata,
                              constant_range=[-5.0, 5.0])
        benchmark.add_dataset("I.14.3", ["X_0", "*", "X_1", "*", "X_2"], sl_3v, original_equation="m*g*z",
                              max_evaluations=100000, max_expression_length=50, success_threshold=1e-7, num_variables=3,
                              dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])

        return benchmark

    @staticmethod
    def nguyen(dataset_directory: str):
        """
        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.

        Args:
            dataset_directory (str): The directory where the benchmark datasets will be stored and accessed.

        Returns:
            SRBenchmark: An initialized SRBenchmark instance containing the Nguyen datasets.
        """
        url = "https://raw.githubusercontent.com/smeznar/SymbolicRegressionToolkit/master/data/nguyen.zip"
        SRBenchmark.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()
        sl_1v.add_symbol("+", symbol_type="op", precedence=0, np_fn="{} = {} + {}")
        sl_1v.add_symbol("-", symbol_type="op", precedence=0, np_fn="{} = {} - {}")
        sl_1v.add_symbol("*", symbol_type="op", precedence=1, np_fn="{} = {} * {}")
        sl_1v.add_symbol("/", symbol_type="op", precedence=1, np_fn="{} = {} / {}")
        sl_1v.add_symbol("sin", symbol_type="fn", precedence=5, np_fn="{} = np.sin({})")
        sl_1v.add_symbol("cos", symbol_type="fn", precedence=5, np_fn="{} = np.cos({})")
        sl_1v.add_symbol("exp", symbol_type="fn", precedence=5, np_fn="{} = np.exp({})")
        sl_1v.add_symbol("log", symbol_type="fn", precedence=5, np_fn="{} = np.log10({})")
        sl_1v.add_symbol("sqrt", symbol_type="fn", precedence=5, np_fn="{} = np.sqrt({})")
        sl_1v.add_symbol("^2", symbol_type="fn", precedence=5, np_fn="{} = np.power({}, 2)")
        sl_1v.add_symbol("^3", symbol_type="fn", precedence=5, np_fn="{} = np.power({}, 3)")
        sl_1v.add_symbol("X_0", "var", 5, "X[:, 0]")

        sl_2v = copy.copy(sl_1v)
        sl_2v.add_symbol("X_1", "var", 5, "X[:, 1]")

        # Add datasets to the benchmark
        benchmark = SRBenchmark("Nguyen", dataset_directory)
        benchmark.add_dataset("NG-1", ["X_0", "+", "X_0", "^2", "+", "X_0", "^3"], sl_1v,
                              original_equation="x+x^2+x^3", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=1,
                              dataset_metadata=benchmark.metadata)
        benchmark.add_dataset("NG-2", ["X_0", "+", "X_0", "^2", "+", "X_0", "^3", "+", "X_0","*", "X_0", "^3"], sl_1v,
                              original_equation="x+x^2+x^3+x^4", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=1,
                              dataset_metadata=benchmark.metadata)
        benchmark.add_dataset("NG-3", ["X_0", "+", "X_0", "^2", "+", "X_0", "^3", "+", "X_0","*", "X_0", "^3", "+", "X_0","^2", "*", "X_0", "^3"], sl_1v,
                              original_equation="x+x^2+x^3+x^4+x^5", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=1,
                              dataset_metadata=benchmark.metadata)
        benchmark.add_dataset("NG-4", ["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"], sl_1v,
                              original_equation="x+x^2+x^3+x^4+x^5+x^6", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=1,
                              dataset_metadata=benchmark.metadata)
        benchmark.add_dataset("NG-5", ["sin", "(", "X_0", "^2", ")", "*", "cos", "(", "X_0", ")", "-", "1"], sl_1v,
                              original_equation="sin(x^2)*cos(x)-1", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=1,
                              dataset_metadata=benchmark.metadata)
        benchmark.add_dataset("NG-6", ["sin", "(", "X_0", ")", "+", "sin", "(", "X_0", "+", "X_0", "^2", ")"], sl_1v,
                              original_equation="sin(x)+sin(x+x^2)", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=1,
                              dataset_metadata=benchmark.metadata)
        benchmark.add_dataset("NG-7", ["log", "(", "1", "+", "X_0", ")", "+", "log", "(", "1", "+", "X_0", "^2", ")"], sl_1v,
                              original_equation="log(1+x)+log(1+x^2)", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=1,
                              dataset_metadata=benchmark.metadata)
        benchmark.add_dataset("NG-8", ["sqrt", "(", "X_0", ")"], sl_1v,
                              original_equation="sqrt(x)", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=1,
                              dataset_metadata=benchmark.metadata)
        benchmark.add_dataset("NG-9", ["sin", "(", "X_0", ")", "+", "sin", "(", "X_1", "^2", ")"], sl_2v,
                              original_equation="sin(x)+sin(y^2)", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=2,
                              dataset_metadata=benchmark.metadata)
        benchmark.add_dataset("NG-10", ["2", "*", "sin", "(", "X_0", ")", "*", "cos", "(", "X_1", ")"], sl_2v,
                              original_equation="2*sin(x)*cos(y)", max_evaluations=100000,
                              max_expression_length=50, success_threshold=1e-7, num_variables=2,
                              dataset_metadata=benchmark.metadata)

        return benchmark

__init__(benchmark_name, base_dir, metadata=None)

Initializes an instance of the SRBenchmark 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
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

Source code in SRToolkit/dataset/srbenchmark.py

def __init__(self, benchmark_name: str, base_dir: str, metadata: dict = None):
    """
    Initializes an instance of the SRBenchmark class.

    Args:
        benchmark_name: The name of this benchmark.
        base_dir: The directory where the datasets will be stored.
        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.
    """
    self.benchmark_name = benchmark_name
    self.base_dir = base_dir
    self.datasets = {}
    self.metadata = {} if metadata is None else metadata

add_dataset(dataset_name, ground_truth, symbol_library, original_equation=None, max_evaluations=-1, max_expression_length=-1, max_constants=8, success_threshold=1e-07, constant_range=None, num_variables=-1, dataset_metadata=None)

Adds a dataset to the benchmark.

Parameters:

Name	Type	Description	Default
dataset_name	str	The name of the dataset.	required
ground_truth	List[str]	The ground truth expression, represented as a list of tokens (strings) in the infix notation.	required
symbol_library	SymbolLibrary	The symbol library to use.	required
original_equation	str	The original equation from which the ground truth expression was generated.	None
max_evaluations	int	The maximum number of expressions to evaluate. Less than 0 means no limit.	-1
max_expression_length	int	The maximum length of the expression. Less than 0 means no limit.	-1
max_constants	int	The maximum number of constants allowed in the expression. Less than 0 means no limit.	8
success_threshold	float	The RMSE threshold below which the experiment is considered successful.	1e-07
constant_range	List[float]	A list of two floats, specifying the lower and upper bounds for the constant values. Default is [-5.0, 5.0]. If constant_range is None, we automatically set it to [-5.0, 5.0] if the symbol library contains a symbol for constants.	None
num_variables	int	The number of variables in the expression. Default is -1, which means we don't know.	-1
dataset_metadata	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

Source code in SRToolkit/dataset/srbenchmark.py

def add_dataset(self, dataset_name: str, ground_truth: List[str],  symbol_library: SymbolLibrary,
                original_equation: str = None, max_evaluations: int=-1, max_expression_length: int=-1,
                max_constants: int=8, success_threshold: float=1e-7, constant_range: List[float]=None,
                num_variables: int=-1, dataset_metadata: dict=None):

    """
    Adds a dataset to the benchmark.

    Args:
        dataset_name: The name of the dataset.
        ground_truth: The ground truth expression, represented as a list of tokens (strings) in the infix notation.
        symbol_library: The symbol library to use.
        original_equation: The original equation from which the ground truth expression was generated.
        max_evaluations: The maximum number of expressions to evaluate. Less than 0 means no limit.
        max_expression_length: The maximum length of the expression. Less than 0 means no limit.
        max_constants: The maximum number of constants allowed in the expression. Less than 0 means no limit.
        success_threshold: The RMSE threshold below which the experiment is considered successful.
        constant_range: A list of two floats, specifying the lower and upper bounds for the constant values.
            Default is [-5.0, 5.0]. If constant_range is None, we automatically set it to [-5.0, 5.0]
            if the symbol library contains a symbol for constants.
        num_variables: The number of variables in the expression. Default is -1, which means we don't know.
        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.
    """
    if original_equation is None:
        original_equation = "".join(ground_truth)

    self.datasets[dataset_name] = {
        "path": self.base_dir + "/" + dataset_name + ".npy",
        "ground_truth": ground_truth,
        "original_equation": original_equation,
        "symbols": symbol_library,
        "max_evaluations": max_evaluations,
        "max_expression_length": max_expression_length,
        "max_constants": max_constants,
        "success_threshold": success_threshold,
        "constant_range": constant_range,
        "dataset_metadata": self.metadata.update(dataset_metadata),
        "num_variables": num_variables
    }

create_dataset(dataset_name)

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
	A SRDataset 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/srbenchmark.py

def create_dataset(self, dataset_name: str):
    """
    Creates an instance of a dataset from the given dataset name.

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

    Returns:
        A SRDataset 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:
        # Check if dataset exists otherwise download it from an url
        if os.path.exists(self.datasets[dataset_name]["path"]):
            data = np.load(self.datasets[dataset_name]["path"])
        else:
            raise ValueError(f"Could not find dataset {dataset_name} at {self.datasets[dataset_name]['path']}")

        X = data[:, :-1]
        y = data[:, -1]

        return SRDataset(X, y, ground_truth=self.datasets[dataset_name]["ground_truth"],
                         original_equation=self.datasets[dataset_name]["original_equation"],
                         symbols=self.datasets[dataset_name]["symbols"],
                         max_evaluations=self.datasets[dataset_name]["max_evaluations"],
                         max_expression_length=self.datasets[dataset_name]["max_expression_length"],
                         max_constants=self.datasets[dataset_name]["max_constants"],
                         success_threshold=self.datasets[dataset_name]["success_threshold"],
                         constant_range=self.datasets[dataset_name]["constant_range"],
                         dataset_metadata=self.datasets[dataset_name]["dataset_metadata"])
    else:
        raise ValueError(f"Dataset {dataset_name} not found")

list_datasets(verbose=True, num_variables=-1)

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
	A list of dataset names.

Source code in SRToolkit/dataset/srbenchmark.py

def list_datasets(self, verbose=True, num_variables: int=-1):
    """
    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(url, directory_path) staticmethod

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

Returns:

Type	Description
	None

Source code in SRToolkit/dataset/srbenchmark.py

@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.

    Returns:
        None
    """
    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(dataset_directory) staticmethod

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.

Parameters:

Name	Type	Description	Default
dataset_directory	str	The directory path where the benchmark dataset will be downloaded and stored.	required

Returns:

Name	Type	Description
SRBenchmark		An instance of the SRBenchmark class containing the predefined datasets.

Source code in SRToolkit/dataset/srbenchmark.py

@staticmethod
def feynman(dataset_directory: str):
    """
    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.

    Args:
        dataset_directory (str): The directory path where the benchmark dataset will be downloaded and stored.

    Returns:
        SRBenchmark: An instance of the SRBenchmark class containing the predefined datasets.
    """
    url = "https://raw.githubusercontent.com/smeznar/SymbolicRegressionToolkit/master/data/feynman.zip"
    SRBenchmark.download_benchmark_data(url, dataset_directory)

    sl_1v = SymbolLibrary()
    sl_1v.add_symbol("+", symbol_type="op", precedence=0, np_fn="{} = {} + {}", latex_str=r"{} + {}")
    sl_1v.add_symbol("-", symbol_type="op", precedence=0, np_fn="{} = {} - {}", latex_str=r"{} - {}")
    sl_1v.add_symbol("*", symbol_type="op", precedence=1, np_fn="{} = {} * {}", latex_str=r"{} \cdot {}")
    sl_1v.add_symbol("/", symbol_type="op", precedence=1, np_fn="{} = {} / {}", latex_str=r"\frac{{{}}}{{{}}}")
    sl_1v.add_symbol("u-", symbol_type="fn", precedence=5, np_fn="{} = -{}", latex_str=r"- {}")
    sl_1v.add_symbol("sqrt", symbol_type="fn", precedence=5, np_fn="{} = np.sqrt({})", latex_str=r"\sqrt {{{}}}")
    sl_1v.add_symbol("sin", symbol_type="fn", precedence=5, np_fn="{} = np.sin({})", latex_str=r"\sin {}")
    sl_1v.add_symbol("cos", symbol_type="fn", precedence=5, np_fn="{} = np.cos({})", latex_str=r"\cos {}")
    sl_1v.add_symbol("exp", symbol_type="fn", precedence=5, np_fn="{} = np.exp({})", latex_str=r"e^{{{}}}")
    sl_1v.add_symbol("arcsin", symbol_type="fn", precedence=5, np_fn="{} = np.arcsin({})", latex_str=r"\arcsin {}")
    sl_1v.add_symbol("tanh", symbol_type="fn", precedence=5, np_fn="{} = np.tanh({})", latex_str=r"\tanh {}")
    sl_1v.add_symbol("ln", symbol_type="fn", precedence=5, np_fn="{} = np.log({})", latex_str=r"\ln {}")
    sl_1v.add_symbol("^2", symbol_type="fn", precedence=-1, np_fn="{} = {}**2", latex_str=r"{}^2")
    sl_1v.add_symbol("^3", symbol_type="fn", precedence=-1, np_fn="{} = {}**3", latex_str=r"{}^3")
    sl_1v.add_symbol("pi", symbol_type="lit", precedence=5, np_fn="np.full(X.shape[0], np.pi)", latex_str=r"\pi")
    sl_1v.add_symbol("C", "const", 5, np_fn="np.full(X.shape[0], C[{}])", latex_str=r"C_{{{}}}")
    sl_1v.add_symbol("X_0", "var", 5, "X[:, 0]", r"X_{0}")

    sl_2v = copy.copy(sl_1v)
    sl_2v.add_symbol("X_1", "var", 5, "X[:, 1]", r"X_{1}")

    sl_3v = copy.copy(sl_2v)
    sl_3v.add_symbol("X_2", "var", 5, "X[:, 2]", r"X_{2}")

    sl_4v = copy.copy(sl_3v)
    sl_4v.add_symbol("X_3", "var", 5, "X[:, 3]", r"X_{3}")

    sl_5v = copy.copy(sl_4v)
    sl_5v.add_symbol("X_4", "var", 5, "X[:, 4]", r"X_{4}")

    sl_6v = copy.copy(sl_5v)
    sl_6v.add_symbol("X_5", "var", 5, "X[:, 5]", r"X_{5}")

    sl_8v = copy.copy(sl_6v)
    sl_8v.add_symbol("X_6", "var", 5, "X[:, 6]", r"X_{6}")
    sl_8v.add_symbol("X_7", "var", 5, "X[:, 7]", r"X_{7}")

    sl_9v = copy.copy(sl_8v)
    sl_9v.add_symbol("X_8", "var", 5, "X[:, 8]", r"X_{8}")

    benchmark = SRBenchmark("feynman", dataset_directory)
    benchmark.add_dataset("I.16.6", ["(", "X_2", "+", "X_1", ")", "/", "(", "1", "+", "(", "X_2", "*", "X_1", ")", "/", "(", "X_0", "^2", ")", ")"],
                          sl_3v, original_equation="v1 = (u+v)/(1+u*v/c^2)", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=3,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("II.15.4", ["u-", "X_0", "*", "X_1", "*", "cos", "(", "X_2", ")"], sl_3v, original_equation="E_n = -mom*B*cos(theta)", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=3,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("II.27.16", ["X_0", "*", "X_1", "*", "X_2", "^2"], sl_3v, original_equation="flux = epsilon*c*Ef^2", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=3,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("I.11.19", ["X_0", "*", "X_3", "+", "X_1", "*", "X_4", "+", "X_2", "*", "X_5"], sl_6v, original_equation="A = x1*y1+x2*y2+x3*y3", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=6,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("I.15.3x", ["(", "X_0", "-", "X_1", "*", "X_3", ")", "/", "sqrt", "(", "1", "-", "X_1", "^2", "/", "X_2", "^2", ")"], sl_4v, original_equation="x1 = (x-u*t)/sqrt(1-u^2/c^2)", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=4,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("I.10.7", ["X_0", "/", "sqrt", "(", "1", "-", "X_1", "^2", "/", "X_2", "^2", ")"], sl_3v, original_equation="m = m_0/sqrt(1-v^2/c^2)", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=3,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("I.9.18", ["X_2", "*", "X_0", "*", "X_1", "/", "(", "(", "X_4", "-", "X_3", ")", "^2", "+", "(", "X_6", "-", "X_5", ")", "^2", "+", "(", "X_8", "-", "X_7", ")", "^2",")"], sl_9v, 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, num_variables=9,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("I.15.3t", ["(", "X_3", "-", "X_2", "*", "X_0", "/", "X_1", "^2", ")", "/", "sqrt", "(", "1", "-", "X_2", "^2", "/", "X_1", "^2", ")"], sl_4v, 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, num_variables=4,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("II.36.38", ["(", "X_0", "*", "X_1", ")", "/", "(", "X_2", "*", "X_3",")", "+", "(", "(", "X_0", "*", "X_4", ")", "/", "(", "X_5", "*", "X_6", "^2", "*", "X_2", "*", "X_3", ")", ")", "*", "X_7"], sl_8v, 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, num_variables=8,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("I.43.43", ["(", "1", "/", "(", "X_0", "-", "1", ")", ")", "*", "X_1", "*", "X_3", "/", "X_2"], sl_4v, original_equation="kappa = 1/(gamma-1)*kb*v/A", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=4,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("II.15.5", ["u-", "X_0", "*", "X_1", "*", "cos", "(", "X_2", ")"], sl_3v, original_equation="E_n = -p_d*Ef*cos(theta)", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=3,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("I.37.4", ["X_0", "+", "X_1", "+", "2", "*", "sqrt", "(", "X_0", "*", "X_1", ")", "*", "cos", "(", "X_2", ")"], sl_3v, original_equation="Int = I1+I2+2*sqrt(I1*I2)*cos(delta)", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=3,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("II.6.11", ["(", "1", "/", "(", "4", "*", "pi", "*", "X_0", ")", ")", "*", "X_1", "*", "cos", "(", "X_2", ")", "/", "X_3", "^2"], sl_4v, original_equation="Volt = 1/(4*pi*epsilon)*p_d*cos(theta)/r^2", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=4,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("III.7.38", ["2", "*", "X_0", "*", "X_1", "/", "(", "X_2", "/", "(", "2", "*", "pi", ")", ")"], sl_3v, original_equation="omega = 2*mom*B/(h/(2*pi))", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=3,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("II.34.2a", ["X_0", "*", "X_1", "/", "(", "2", "*", "pi", "*", "X_2", ")"], sl_3v, original_equation="l = q*v/(2*pi*r)", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=3,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("II.13.23", ["X_0", "/", "sqrt", "(", "1", "-", "X_1", "^2", "/", "X_2", "^2", ")"], sl_3v, original_equation="rho_c = rho_c_0/sqrt(1-v^2/c^2)", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=3,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("I.29.4", ["X_0", "/", "X_1"], sl_2v, original_equation="k = omega/c", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=2,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("I.38.12", ["4", "*", "pi", "*", "X_3", "*", "(", "X_2", "/", "(", "2", "*", "pi", ")", ")", "^2", "/", "(", "X_0", "*", "X_1", "^2", ")"], sl_4v, original_equation="r = 4*pi*epsilon*(h/(2*pi))^2/(m*q^2)", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=4,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("III.15.27", ["2", "*", "pi", "*", "X_0", "/", "(", "X_1", "*", "X_2", ")"], sl_3v, original_equation="k = 2*pi*alpha/(n*d)", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=3,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("I.41.16", ["(", "X_2", "/", "(", "2", "*", "pi", ")", ")", "*", "X_0", "^3", "/", "(", "pi", "^2", "*", "X_4", "^2", "*", "(", "exp", "(", "(", "X_2", "/", "(", "2", "*", "pi", ")", ")", "*", "X_0", "/", "(", "X_3", "*", "X_1", ")", ")", "-", "1", ")", ")"], sl_5v, 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, num_variables=5,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("I.48.20", ["X_0", "*", "X_2", "^2", "/", "sqrt", "(", "1", "-", "X_1", "^2", "/", "X_2", "^2", ")"], sl_3v, original_equation="E_n = m*c^2/sqrt(1-v^2/c^2)", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=3,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("II.11.20", ["X_0", "*", "X_1", "^2", "*", "X_2", "/", "(", "3", "*", "X_3", "*", "X_4", ")"], sl_5v, original_equation="Pol = n_rho*p_d^2*Ef/(3*kb*T)", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=5,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("I.25.13", ["X_0", "/", "X_1"], sl_2v, original_equation="Volt = q/C", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=2,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("III.15.12", ["2", "*", "X_0", "*", "(", "1", "-", "cos", "(", "X_1", "*", "X_2", ")", ")"], sl_3v, original_equation="E_n = 2*U*(1-cos(k*d))", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=3,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("I.24.6", ["0.25", "*", "X_0", "*", "(", "X_1", "^2", "+", "X_2", "^2", ")", "*", "X_3", "^2"], sl_4v, 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, num_variables=4,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("I.34.27", ["(", "X_1", "/", "(", "2", "*", "pi", ")", ")", "*", "X_0"], sl_2v, original_equation="E_n =(h/(2*pi))*omega", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=2,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("I.43.31", ["X_0", "*", "X_2", "*", "X_1"], sl_3v, original_equation="D = mob*kb*T", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=3,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("I.29.16", ["sqrt", "(", "X_0", "^2", "+", "X_1", "^2", "-", "2", "*", "X_0", "*", "X_1", "*", "cos", "(", "X_2", "-", "X_3", ")", ")"], sl_4v, 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, num_variables=4,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("I.18.4", ["(","X_0", "*", "X_2", "+", "X_1", "*", "X_3", ")", "/", "(", "X_0", "+", "X_1", ")"], sl_4v, original_equation="r = (m1*r1+m2*r2)/(m1+m2)", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=4,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("II.6.15a", ["(", "X_1", "/", "(", "4", "*", "pi", "*", "X_0", ")", ")", "*", "(", "3", "*", "X_5", "/", "(", "X_2", "^2", "*", "X_2", "^3", ")", ")", "*", "sqrt", "(", "X_3", "^2", "+", "X_4", "^2", ")"],
                          sl_6v, 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, num_variables=6,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("I.30.3", ["X_0", "*", "sin", "(", "X_2", "*", "X_1", "/", "2", ")", "^2", "/", "sin", "(", "X_1", "/", "2", ")", "^2"], sl_3v, 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, num_variables=3,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("III.9.52", ["(", "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"], sl_6v, 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, num_variables=6,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("II.34.2", ["X_0", "*", "X_1", "*", "X_2", "/", "2"], sl_3v, original_equation="mom = q*v*r/2", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=3,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("I.39.11", ["(", "1", "/", "(", "X_0", "-", "1", ")", ")", "*", "X_1", "*", "X_2"], sl_3v, original_equation="E_n = (1/(gamma-1))*pr*V", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=3,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("II.11.28", ["1", "+", "X_0", "*", "X_1", "/", "(", "1", "-", "(", "X_0", "*", "X_1", "/", "3", ")", ")"], sl_2v, original_equation="theta = 1+n*alpha/(1-(n*alpha/3))", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=2,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("II.3.24", ["X_0", "/", "(", "4", "*", "pi", "*", "X_1", "^2", ")"], sl_2v, original_equation="flux = Pwr/(4*pi*r^2)", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=2,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("II.24.17", ["sqrt", "(", "X_0", "^2", "/", "X_1", "^2", "-", "pi", "^2", "/", "X_2", "^2", ")"], sl_3v, original_equation="k = sqrt(omega^2/c^2-pi^2/d^2)", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=3,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("II.13.17", ["(", "1", "/", "(", "4", "*", "pi", "*", "X_0", "*", "X_1", "^2", ")", ")", "*", "2", "*", "X_2", "/", "X_3"],
                          sl_4v, original_equation="B = 1/(4*pi*epsilon*c^2)*2*I/r", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=4,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("I.12.5", ["X_0", "*", "X_1"], sl_2v, original_equation="F = q2*Ef", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=2,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    # Check again if you find the time
    benchmark.add_dataset("II.35.18",
                          ["X_0", "/", "(", "exp", "(", "X_3", "*", "X_4", "/", "(", "X_1", "*", "X_2", ")", ")",
                           "+", "exp", "(", "u-", "X_3", "*", "X_4", "/", "(", "X_1", "*", "X_2", ")", ")", ")"],
                          sl_5v, 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, num_variables=5,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("II.34.11", ["X_0", "*", "X_1", "*", "X_2", "/", "(", "2", "*", "X_3", ")"], sl_4v,
                          original_equation="g_*q*B/(2*m)", max_evaluations=100000, max_expression_length=50,
                          success_threshold=1e-7, num_variables=4, dataset_metadata=benchmark.metadata,
                          constant_range=[-5.0, 5.0])
    benchmark.add_dataset("II.34.29a", ["X_0", "*", "X_1", "/", "(", "4", "*", "pi", "*", "X_2", ")"], sl_3v,
                          original_equation="q*h/(4*pi*m)", max_evaluations=100000, max_expression_length=50,
                          success_threshold=1e-7, num_variables=3, dataset_metadata=benchmark.metadata,
                          constant_range=[-5.0, 5.0])
    benchmark.add_dataset("I.32.17",
                          ["(", "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", ")"], sl_6v,
                          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, num_variables=6,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("II.35.21",
                          ["X_0", "*", "X_1", "*", "tanh", "(", "X_1", "*", "X_2", "/", "(", "X_3", "*", "X_4", ")",
                           ")"], sl_5v, original_equation="n_rho*mom*tanh(mom*B/(kb*T))", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=5,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("I.44.4", ["X_0", "*", "X_1", "*", "X_2", "*", "ln", "(", "X_4", "/", "X_3", ")"], sl_5v,
                          original_equation="n*kb*T*ln(V2/V1)", max_evaluations=100000, max_expression_length=50,
                          success_threshold=1e-7, num_variables=5, dataset_metadata=benchmark.metadata,
                          constant_range=[-5.0, 5.0])
    benchmark.add_dataset("III.4.32",
                          ["1", "/", "(", "exp", "(", "(", "X_0", "/", "(", "2", "*", "pi", ")", ")", "*", "X_1",
                           "/", "(", "X_2", "*", "X_3", ")", ")", "-", "1", ")"], sl_4v,
                          original_equation="1/(exp((h/(2*pi))*omega/(kb*T))-1)", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=4,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("II.10.9", ["(", "X_0", "/", "X_1", ")", "*", "1", "/", "(", "1", "+", "X_2", ")"], sl_3v,
                          original_equation="sigma_den/epsilon*1/(1+chi)", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=3,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("II.38.3", ["X_0", "*", "X_1", "*", "X_3", "/", "X_2"], sl_4v,
                          original_equation="Y*A*x/d", max_evaluations=100000, max_expression_length=50,
                          success_threshold=1e-7, num_variables=4, dataset_metadata=benchmark.metadata,
                          constant_range=[-5.0, 5.0])
    benchmark.add_dataset("I.6.2b",
                          ["exp", "(", "u-", "(", "(", "(", "X_1", "-", "X_2", ")", "/", "X_0", ")", "^2", ")", "/", "2", ")",
                           "/", "(", "sqrt", "(", "2", "*", "pi", ")", "*", "X_0", ")"], sl_3v,
                          original_equation="exp(-((theta-theta1)/sigma)**2/2)/(sqrt(2*pi)*sigma)",
                          max_evaluations=100000, max_expression_length=50, success_threshold=1e-7, num_variables=3,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("II.8.31", ["X_0", "*", "X_1", "^2", "/", "2"], sl_2v,
                          original_equation="epsilon*Ef**2/2", max_evaluations=100000, max_expression_length=50,
                          success_threshold=1e-7, num_variables=2, dataset_metadata=benchmark.metadata,
                          constant_range=[-5.0, 5.0])
    benchmark.add_dataset("I.6.2a",
                          ["exp", "(", "u-", "X_0", "^2", "/", "2", ")", "/", "sqrt", "(", "2", "*", "pi", ")"],
                          sl_1v, original_equation="exp(-theta**2/2)/sqrt(2*pi)", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=1,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("III.12.43", ["X_0", "*", "(", "X_1", "/", "(", "2", "*", "pi", ")", ")"], sl_2v,
                          original_equation="n*(h/(2*pi))", max_evaluations=100000, max_expression_length=50,
                          success_threshold=1e-7, num_variables=2, dataset_metadata=benchmark.metadata,
                          constant_range=[-5.0, 5.0])
    benchmark.add_dataset("III.17.37", ["X_0", "*", "(", "1", "+", "X_1", "*", "cos", "(", "X_2", ")", ")"], sl_3v,
                          original_equation="beta*(1+alpha*cos(theta))", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=3,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("III.10.19",
                          ["X_0", "*", "sqrt", "(", "X_1", "^2", "+", "X_2", "^2", "+", "X_3", "^2", ")"], sl_4v,
                          original_equation="mom*sqrt(Bx**2+By**2+Bz**2)", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=4,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("II.11.7",
                          ["X_0", "*", "(", "1", "+", "X_4", "*", "X_5", "*", "cos", "(", "X_3", ")", "/", "(",
                           "X_1", "*", "X_2", ")", ")"], sl_6v,
                          original_equation="n_0*(1+p_d*Ef*cos(theta)/(kb*T))", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=6,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("I.39.1", ["1.5", "*", "X_0", "*", "X_1"], sl_2v, original_equation="3/2*pr*V",
                          max_evaluations=100000, max_expression_length=50, success_threshold=1e-7, num_variables=2,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("II.37.1", ["X_0", "*", "(", "1", "+", "X_2", ")", "*", "X_1"], sl_3v,
                          original_equation="mom*(1+chi)*B", max_evaluations=100000, max_expression_length=50,
                          success_threshold=1e-7, num_variables=3, dataset_metadata=benchmark.metadata,
                          constant_range=[-5.0, 5.0])
    benchmark.add_dataset("I.12.4",
                          ["X_0", "*", "X_2", "/", "(", "4", "*", "pi", "*", "X_1", "*", "X_2", "^3", ")"],
                          sl_3v, original_equation="q1*r/(4*pi*epsilon*r**3)", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=3,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("II.27.18", ["X_0", "*", "X_1", "^2"], sl_2v, original_equation="epsilon*Ef**2",
                          max_evaluations=100000, max_expression_length=50, success_threshold=1e-7, num_variables=2,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("I.12.2",
                          ["X_0", "*", "X_1", "*", "X_3", "/", "(", "4", "*", "pi", "*", "X_2", "*", "X_3", "^3", ")"],
                          sl_4v, original_equation="q1*q2*r/(4*pi*epsilon*r**3)",
                          max_evaluations=100000, max_expression_length=50, success_threshold=1e-7, num_variables=4,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("III.13.18",
                          ["2", "*", "X_0", "*", "X_1", "^2", "*", "X_2", "/", "(", "X_3", "/", "(", "2", "*", "pi",
                           ")", ")"], sl_4v, original_equation="2*E_n*d**2*k/(h/(2*pi))", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=4,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("II.11.3",
                          ["X_0", "*", "X_1", "/", "(", "X_2", "*", "(", "X_3", "^2", "-", "X_4", "^2", ")", ")"],
                          sl_5v, original_equation="q*Ef/(m*(omega_0**2-omega**2))", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=5,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("I.40.1",
                          ["X_0", "*", "exp", "(", "u-", "X_1", "*", "X_4", "*", "X_2", "/", "(", "X_5", "*", "X_3",
                           ")", ")"], sl_6v, original_equation="n_0*exp(-m*g*x/(kb*T))", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=6,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("III.21.20", ["u-", "X_0", "*", "X_1", "*", "X_2", "/", "X_3"], sl_4v,
                          original_equation="-rho_c_0*q*A_vec/m", max_evaluations=100000, max_expression_length=50,
                          success_threshold=1e-7, num_variables=4, dataset_metadata=benchmark.metadata,
                          constant_range=[-5.0, 5.0])
    benchmark.add_dataset("I.43.16", ["X_0", "*", "X_1", "*", "X_2", "/", "X_3"], sl_4v,
                          original_equation="mu_drift*q*Volt/d", max_evaluations=100000, max_expression_length=50,
                          success_threshold=1e-7, num_variables=4, dataset_metadata=benchmark.metadata,
                          constant_range=[-5.0, 5.0])
    benchmark.add_dataset("I.15.10",
                          ["X_0", "*", "X_1", "/", "sqrt", "(", "1", "-", "X_1", "^2", "/", "X_2", "^2", ")"],
                          sl_3v, original_equation="m_0*v/sqrt(1-v**2/c**2)", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=3,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("I.30.5", ["arcsin", "(", "X_0", "/", "(", "X_2", "*", "X_1", ")", ")"], sl_3v,
                          original_equation="arcsin(lambd/(n*d))", max_evaluations=100000, max_expression_length=50,
                          success_threshold=1e-7, num_variables=3, dataset_metadata=benchmark.metadata,
                          constant_range=[-5.0, 5.0])
    benchmark.add_dataset("I.50.26",
                          ["X_0", "*", "(", "cos", "(", "X_1", "*", "X_2", ")", "+", "X_3", "*", "cos", "(", "X_1",
                           "*", "X_2", ")", "^2", ")"], sl_4v,
                          original_equation="x1*(cos(omega*t)+alpha*cos(omega*t)**2)", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=4,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("I.12.11",
                          ["X_0", "*", "(", "X_1", "+", "X_2", "*", "X_3", "*", "sin", "(", "X_4", ")", ")"], sl_5v,
                          original_equation="q*(Ef+B*v*sin(theta))", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=5,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("I.6.2",
                          ["exp", "(", "u-", "(", "(", "X_1", "/", "X_0", ")", "^2", ")",  "/", "2", ")", "/", "(", "sqrt",
                           "(", "2", "*", "pi", ")", "*", "X_0", ")"], sl_2v,
                          original_equation="exp(-(theta/sigma)**2/2)/(sqrt(2*pi)*sigma)", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=2,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("I.14.4", ["0.5", "*", "X_0", "*", "X_1", "^2"], sl_2v,
                          original_equation="1/2*k_spring*x**2", max_evaluations=100000, max_expression_length=50,
                          success_threshold=1e-7, num_variables=2, dataset_metadata=benchmark.metadata,
                          constant_range=[-5.0, 5.0])
    benchmark.add_dataset("I.47.23", ["sqrt", "(", "X_0", "*", "X_1", "/", "X_2", ")"], sl_3v,
                          original_equation="sqrt(gamma*pr/rho)", max_evaluations=100000, max_expression_length=50,
                          success_threshold=1e-7, num_variables=3, dataset_metadata=benchmark.metadata,
                          constant_range=[-5.0, 5.0])
    benchmark.add_dataset("II.8.7",
                          ["0.6", "*", "X_0", "^2", "/", "(", "4", "*", "pi", "*", "X_1", "*", "X_2", ")"],
                          sl_3v, original_equation="3/5*q**2/(4*pi*epsilon*d)", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=3,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("III.15.14",
                          ["(", "X_0", "/", "(", "2", "*", "pi", ")", ")", "^2", "/", "(", "2", "*", "X_1", "*",
                           "X_2", "^2", ")"], sl_3v, original_equation="(h/(2*pi))**2/(2*E_n*d**2)",
                          max_evaluations=100000, max_expression_length=50, success_threshold=1e-7, num_variables=3,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("I.34.14",
                          ["(", "(", "1", "+", "(", "X_1", "/", "X_0", ")", ")", "/", "sqrt", "(", "1", "-", "X_1", "^2", "/",
                           "X_0", "^2", ")", ")", "*", "X_2"], sl_3v,
                          original_equation="((1+v/c)/sqrt(1-v**2/c**2))*omega_0", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=3,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("III.8.54",
                          ["sin", "(", "X_0", "*", "X_1", "/", "(", "X_2", "/", "(", "2", "*", "pi", ")", ")", ")",
                           "^2"], sl_3v, original_equation="sin(E_n*t/(h/(2*pi)))**2", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=3,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("I.26.2", ["arcsin", "(", "X_0", "*", "sin", "(", "X_1", ")", ")"], sl_2v,
                          original_equation="arcsin(n*sin(theta2))", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=2,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("III.19.51",
                          ['(', "u-", "X_0", "*", "(", "X_1", "^2", "*", "X_1", "^2", ")", "/", "(", "2", "*", "(", "4", "*", "pi", "*", "X_4",
                           ")", "^2", ")", "*", "(", "X_2", "/", "(", "2", "*", "pi", ")", ")", "^2", ")", "*", "(", "1",
                           "/", "X_3", "^2", ")"], sl_5v,
                          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, num_variables=5,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("III.4.33",
                          ["(", "X_0", "/", "(", "2", "*", "pi", ")", ")", "*", "X_1", "/", "(", "exp", "(", "(",
                           "X_0", "/", "(", "2", "*", "pi", ")", ")", "*", "X_1", "/", "(", "X_2", "*", "X_3", ")",
                           ")", "-", "1", ")"], sl_4v,
                          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, num_variables=4,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("I.34.1", ["X_2", "/", "(", "1", "-", "X_1", "/", "X_0", ")"], sl_3v,
                          original_equation="omega_0/(1-v/c)", max_evaluations=100000, max_expression_length=50,
                          success_threshold=1e-7, num_variables=3, dataset_metadata=benchmark.metadata,
                          constant_range=[-5.0, 5.0])
    benchmark.add_dataset("II.11.27",
                          ["(", "X_0", "*", "X_1", "/", "(", "1", "-", "(", "X_0", "*", "X_1", "/", "3", ")", ")", ")", "*",
                           "X_2", "*", "X_3"], sl_4v, original_equation="n*alpha/(1-(n*alpha/3))*epsilon*Ef",
                          max_evaluations=100000, max_expression_length=50, success_threshold=1e-7, num_variables=4,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("II.13.34",
                          ["X_0", "*", "X_1", "/", "sqrt", "(", "1", "-", "X_1", "^2", "/", "X_2", "^2", ")"],
                          sl_3v, original_equation="rho_c_0*v/sqrt(1-v**2/c**2)", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=3,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("II.4.23", ["X_0", "/", "(", "4", "*", "pi", "*", "X_1", "*", "X_2", ")"], sl_3v,
                          original_equation="q/(4*pi*epsilon*r)", max_evaluations=100000, max_expression_length=50,
                          success_threshold=1e-7, num_variables=3, dataset_metadata=benchmark.metadata,
                          constant_range=[-5.0, 5.0])
    benchmark.add_dataset("I.32.5",
                          ["X_0", "^2", "*", "X_1", "^2", "/", "(", "6", "*", "pi", "*", "X_2", "*", "X_3", "^3", ")"],
                          sl_4v, original_equation="q**2*a**2/(6*pi*epsilon*c**3)",
                          max_evaluations=100000, max_expression_length=50, success_threshold=1e-7, num_variables=4,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("I.13.12",
                          ["X_4", "*", "X_0", "*", "X_1", "*", "(", "1", "/", "X_3", "-", "1", "/", "X_2", ")"],
                          sl_5v, original_equation="G*m1*m2*(1/r2-1/r1)", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=5,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("II.2.42", ["X_0", "*", "(", "X_2", "-", "X_1", ")", "*", "X_3", "/", "X_4"], sl_5v,
                          original_equation="kappa*(T2-T1)*A/d", max_evaluations=100000, max_expression_length=50,
                          success_threshold=1e-7, num_variables=5, dataset_metadata=benchmark.metadata,
                          constant_range=[-5.0, 5.0])
    benchmark.add_dataset("I.27.6", ["1", "/", "(", "1", "/", "X_0", "+", "X_2", "/", "X_1", ")"], sl_3v,
                          original_equation="1/(1/d1+n/d2)", max_evaluations=100000, max_expression_length=50,
                          success_threshold=1e-7, num_variables=3, dataset_metadata=benchmark.metadata,
                          constant_range=[-5.0, 5.0])
    benchmark.add_dataset("III.14.14",
                          ["X_0", "*", "(", "exp", "(", "X_1", "*", "X_2", "/", "(", "X_3", "*", "X_4", ")", ")",
                           "-", "1", ")"], sl_5v, original_equation="I_0*(exp(q*Volt/(kb*T))-1)",
                          max_evaluations=100000, max_expression_length=50, success_threshold=1e-7, num_variables=5,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("I.18.12", ["X_0", "*", "X_1", "*", "sin", "(", "X_2", ")"], sl_3v,
                          original_equation="r*F*sin(theta)", max_evaluations=100000, max_expression_length=50,
                          success_threshold=1e-7, num_variables=3, dataset_metadata=benchmark.metadata,
                          constant_range=[-5.0, 5.0])
    benchmark.add_dataset("I.18.14", ["X_0", "*", "X_1", "*", "X_2", "*", "sin", "(", "X_3", ")"], sl_4v,
                          original_equation="m*r*v*sin(theta)", max_evaluations=100000, max_expression_length=50,
                          success_threshold=1e-7, num_variables=4, dataset_metadata=benchmark.metadata,
                          constant_range=[-5.0, 5.0])
    benchmark.add_dataset("II.21.32",
                          ["X_0", "/", "(", "4", "*", "pi", "*", "X_1", "*", "X_2", "*", "(", "1", "-", "X_3", "/",
                           "X_4", ")", ")"], sl_5v, original_equation="q/(4*pi*epsilon*r*(1-v/c))",
                          max_evaluations=100000, max_expression_length=50, success_threshold=1e-7, num_variables=5,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("II.38.14", ["X_0", "/", "(", "2", "*", "(", "1", "+", "X_1", ")", ")"], sl_2v,
                          original_equation="Y/(2*(1+sigma))", max_evaluations=100000, max_expression_length=50,
                          success_threshold=1e-7, num_variables=2, dataset_metadata=benchmark.metadata,
                          constant_range=[-5.0, 5.0])
    benchmark.add_dataset("I.34.8", ["X_0", "*", "X_1", "*", "X_2", "/", "X_3"], sl_4v, original_equation="q*v*B/p",
                          max_evaluations=100000, max_expression_length=50, success_threshold=1e-7, num_variables=4,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("I.8.14",
                          ["sqrt", "(", "(", "X_1", "-", "X_0", ")", "^2", "+", "(", "X_3", "-", "X_2", ")", "^2",
                           ")"], sl_4v, original_equation="sqrt((x2-x1)**2+(y2-y1)**2)", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=4,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("II.6.15b",
                          ["(", "X_1", "/", "(", "4", "*", "pi", "*", "X_0", ")", ")", "*", "3", "*", "cos", "(", "X_2", ")",
                           "*", "sin", "(", "X_2", ")", "/", "X_3", "^3"], sl_4v,
                          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, num_variables=4,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("I.12.1", ["X_0", "*", "X_1"], sl_2v, original_equation="mu*Nn", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=2,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("II.34.29b",
                          ["X_0", "*", "X_3", "*", "X_4", "*", "X_2", "/", "(", "X_1", "/", "(", "2", "*", "pi",
                           ")", ")"], sl_5v, original_equation="g_*mom*B*Jz/(h/(2*pi))", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=5,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("I.13.4",
                          ["0.5", "*", "X_0", "*", "(", "X_1", "^2", "+", "X_2", "^2", "+", "X_3", "^2",
                           ")"], sl_4v, original_equation="1/2*m*(v**2+u**2+w**2)", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=4,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])
    benchmark.add_dataset("I.39.22", ["X_0", "*", "X_3", "*", "X_1", "/", "X_2"], sl_4v,
                          original_equation="n*kb*T/V", max_evaluations=100000, max_expression_length=50,
                          success_threshold=1e-7, num_variables=4, dataset_metadata=benchmark.metadata,
                          constant_range=[-5.0, 5.0])
    benchmark.add_dataset("I.14.3", ["X_0", "*", "X_1", "*", "X_2"], sl_3v, original_equation="m*g*z",
                          max_evaluations=100000, max_expression_length=50, success_threshold=1e-7, num_variables=3,
                          dataset_metadata=benchmark.metadata, constant_range=[-5.0, 5.0])

    return benchmark

nguyen(dataset_directory) staticmethod

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.

Parameters:

Name	Type	Description	Default
dataset_directory	str	The directory where the benchmark datasets will be stored and accessed.	required

Returns:

Name	Type	Description
SRBenchmark		An initialized SRBenchmark instance containing the Nguyen datasets.

Source code in SRToolkit/dataset/srbenchmark.py

@staticmethod
def nguyen(dataset_directory: str):
    """
    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.

    Args:
        dataset_directory (str): The directory where the benchmark datasets will be stored and accessed.

    Returns:
        SRBenchmark: An initialized SRBenchmark instance containing the Nguyen datasets.
    """
    url = "https://raw.githubusercontent.com/smeznar/SymbolicRegressionToolkit/master/data/nguyen.zip"
    SRBenchmark.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()
    sl_1v.add_symbol("+", symbol_type="op", precedence=0, np_fn="{} = {} + {}")
    sl_1v.add_symbol("-", symbol_type="op", precedence=0, np_fn="{} = {} - {}")
    sl_1v.add_symbol("*", symbol_type="op", precedence=1, np_fn="{} = {} * {}")
    sl_1v.add_symbol("/", symbol_type="op", precedence=1, np_fn="{} = {} / {}")
    sl_1v.add_symbol("sin", symbol_type="fn", precedence=5, np_fn="{} = np.sin({})")
    sl_1v.add_symbol("cos", symbol_type="fn", precedence=5, np_fn="{} = np.cos({})")
    sl_1v.add_symbol("exp", symbol_type="fn", precedence=5, np_fn="{} = np.exp({})")
    sl_1v.add_symbol("log", symbol_type="fn", precedence=5, np_fn="{} = np.log10({})")
    sl_1v.add_symbol("sqrt", symbol_type="fn", precedence=5, np_fn="{} = np.sqrt({})")
    sl_1v.add_symbol("^2", symbol_type="fn", precedence=5, np_fn="{} = np.power({}, 2)")
    sl_1v.add_symbol("^3", symbol_type="fn", precedence=5, np_fn="{} = np.power({}, 3)")
    sl_1v.add_symbol("X_0", "var", 5, "X[:, 0]")

    sl_2v = copy.copy(sl_1v)
    sl_2v.add_symbol("X_1", "var", 5, "X[:, 1]")

    # Add datasets to the benchmark
    benchmark = SRBenchmark("Nguyen", dataset_directory)
    benchmark.add_dataset("NG-1", ["X_0", "+", "X_0", "^2", "+", "X_0", "^3"], sl_1v,
                          original_equation="x+x^2+x^3", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=1,
                          dataset_metadata=benchmark.metadata)
    benchmark.add_dataset("NG-2", ["X_0", "+", "X_0", "^2", "+", "X_0", "^3", "+", "X_0","*", "X_0", "^3"], sl_1v,
                          original_equation="x+x^2+x^3+x^4", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=1,
                          dataset_metadata=benchmark.metadata)
    benchmark.add_dataset("NG-3", ["X_0", "+", "X_0", "^2", "+", "X_0", "^3", "+", "X_0","*", "X_0", "^3", "+", "X_0","^2", "*", "X_0", "^3"], sl_1v,
                          original_equation="x+x^2+x^3+x^4+x^5", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=1,
                          dataset_metadata=benchmark.metadata)
    benchmark.add_dataset("NG-4", ["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"], sl_1v,
                          original_equation="x+x^2+x^3+x^4+x^5+x^6", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=1,
                          dataset_metadata=benchmark.metadata)
    benchmark.add_dataset("NG-5", ["sin", "(", "X_0", "^2", ")", "*", "cos", "(", "X_0", ")", "-", "1"], sl_1v,
                          original_equation="sin(x^2)*cos(x)-1", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=1,
                          dataset_metadata=benchmark.metadata)
    benchmark.add_dataset("NG-6", ["sin", "(", "X_0", ")", "+", "sin", "(", "X_0", "+", "X_0", "^2", ")"], sl_1v,
                          original_equation="sin(x)+sin(x+x^2)", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=1,
                          dataset_metadata=benchmark.metadata)
    benchmark.add_dataset("NG-7", ["log", "(", "1", "+", "X_0", ")", "+", "log", "(", "1", "+", "X_0", "^2", ")"], sl_1v,
                          original_equation="log(1+x)+log(1+x^2)", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=1,
                          dataset_metadata=benchmark.metadata)
    benchmark.add_dataset("NG-8", ["sqrt", "(", "X_0", ")"], sl_1v,
                          original_equation="sqrt(x)", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=1,
                          dataset_metadata=benchmark.metadata)
    benchmark.add_dataset("NG-9", ["sin", "(", "X_0", ")", "+", "sin", "(", "X_1", "^2", ")"], sl_2v,
                          original_equation="sin(x)+sin(y^2)", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=2,
                          dataset_metadata=benchmark.metadata)
    benchmark.add_dataset("NG-10", ["2", "*", "sin", "(", "X_0", ")", "*", "cos", "(", "X_1", ")"], sl_2v,
                          original_equation="2*sin(x)*cos(y)", max_evaluations=100000,
                          max_expression_length=50, success_threshold=1e-7, num_variables=2,
                          dataset_metadata=benchmark.metadata)

    return benchmark