How to use the deap.gp function in deap

def get_toolbox(self, predictors, response, pset, variable_type_indices, variable_names):
        subset_size = int(math.floor(predictors.shape[0] * self.subset_proportion))
        creator.create("Error", base.Fitness, weights=(-1.0,))
        creator.create("Individual", sp.SimpleParametrizedPrimitiveTree, fitness=creator.Error, age=int)
        toolbox = base.Toolbox()
        toolbox.register("expr", sp.generate_parametrized_expression,
                         partial(gp.genHalfAndHalf, pset=pset, min_=self.min_depth_init, max_=self.max_depth_init),
                         variable_type_indices, variable_names)
        toolbox.register("individual", tools.initIterate, creator.Individual, toolbox.expr)
        toolbox.register("population", tools.initRepeat, list, toolbox.individual)
        toolbox.register("compile", gp.compile, pset=pset)
        toolbox.register("grow", sp.generate_parametrized_expression,
                         partial(gp.genGrow, pset=pset, min_=self.min_gen_grow, max_=self.max_gen_grow),
                         variable_type_indices, variable_names)
        toolbox.register("mutate", operators.mutation_biased, expr=toolbox.grow,
                         node_selector=operators.uniform_depth_node_selector)
        toolbox.decorate("mutate", operators.static_limit(key=operator.attrgetter("height"), max_value=self.max_height))
        toolbox.decorate("mutate", operators.static_limit(key=len, max_value=self.max_size))
        # self.history = tools.History()
        # toolbox.decorate("mutate", self.history.decorator)
        toolbox.register("error_func", self.error_function)
        expression_dict = cachetools.LRUCache(maxsize=1000)
        subset_selection_archive = subset_selection.RandomSubsetSelectionArchive(frequency=self.subset_change_frequency,

toolbox.register("expr", gp.genHalfAndHalf, pset=pset, min_=1, max_=2)
toolbox.register("individual", tools.initIterate, creator.Individual, toolbox.expr)
toolbox.register("population", tools.initRepeat, list, toolbox.individual)
toolbox.register("compile", gp.compile, pset=pset)

def evalSymbReg(individual, points):
    # Transform the tree expression in a callable function
    func = toolbox.compile(expr=individual)
    # Evaluate the mean squared error between the expression
    # and the real function : x**4 + x**3 + x**2 + x
    sqerrors = ((func(x) - x**4 - x**3 - x**2 - x)**2 for x in points)
    return math.fsum(sqerrors) / len(points),

toolbox.register("evaluate", evalSymbReg, points=[x/10. for x in range(-10,10)])
toolbox.register("select", tools.selTournament, tournsize=3)
toolbox.register("mate", gp.cxOnePoint)
toolbox.register("expr_mut", gp.genFull, min_=0, max_=2)
toolbox.register("mutate", gp.mutUniform, expr=toolbox.expr_mut, pset=pset)

toolbox.decorate("mate", gp.staticLimit(key=operator.attrgetter("height"), max_value=17))
toolbox.decorate("mutate", gp.staticLimit(key=operator.attrgetter("height"), max_value=17))

def main():
    random.seed(318)

    pop = toolbox.population(n=300)
    hof = tools.HallOfFame(1)
    
    stats_fit = tools.Statistics(lambda ind: ind.fitness.values)
    stats_size = tools.Statistics(len)
    mstats = tools.MultiStatistics(fitness=stats_fit, size=stats_size)
    mstats.register("avg", numpy.mean)

def evalSymbReg(individual, points):
    # Transform the tree expression in a callable function
    func = toolbox.compile(expr=individual)
    # Evaluate the mean squared error between the expression
    # and the real function : x**4 + x**3 + x**2 + x
    sqerrors = ((func(x) - x**4 - x**3 - x**2 - x)**2 for x in points)
    return math.fsum(sqerrors) / len(points),

toolbox.register("evaluate", evalSymbReg, points=[x/10. for x in range(-10,10)])
toolbox.register("select", tools.selTournament, tournsize=3)
toolbox.register("mate", gp.cxOnePoint)
toolbox.register("expr_mut", gp.genFull, min_=0, max_=2)
toolbox.register("mutate", gp.mutUniform, expr=toolbox.expr_mut, pset=pset)

toolbox.decorate("mate", gp.staticLimit(key=operator.attrgetter("height"), max_value=17))
toolbox.decorate("mutate", gp.staticLimit(key=operator.attrgetter("height"), max_value=17))

def main(verbose=True):
    random.seed(318)

    NGEN = 40
    CXPB = 0.5
    MUTPB = 0.1
    ALPHA = 0.05
    BETA = 10
    GAMMA = 0.25
    RHO = 0.9

    pop = toolbox.population(n=300)
    hof = tools.HallOfFame(1)

creator.create("FitnessMax", base.Fitness, weights=(1.0,))
    creator.create("Individual", gp.PrimitiveTree, fitness=creator.FitnessMax)

    toolbox = base.Toolbox()

    # Attribute generator
    toolbox.register("expr_init", gp.genFull, pset=pset, min_=1, max_=2)

    # Structure initializers
    toolbox.register("individual", tools.initIterate, creator.Individual, toolbox.expr_init)
    toolbox.register("population", tools.initRepeat, list, toolbox.individual)

    toolbox.register("evaluate", eval_func)
    toolbox.register("select", tools.selTournament, tournsize=7)
    toolbox.register("mate", gp.cxOnePoint)
    toolbox.register("expr_mut", gp.genFull, min_=0, max_=2)
    toolbox.register("mutate", gp.mutUniform, expr=toolbox.expr_mut, pset=pset)

    return toolbox

def main():
    pop_size = 100

    mate = deap.gp.cxOnePoint
    expr_mut = partial(deap.gp.genFull, min_=0, max_=2)
    mutate = partial(deap.gp.mutUniform, expr=expr_mut, pset=Individual.pset)
    simplify = gp.individual.simplify_constant

    algorithm = gp.algorithms.AgeFitness(mate, mutate, deap.tools.selNSGA2, Individual.create_population)

    pop = update_fitness(Individual.create_population(pop_size))

    for gen in range(20):
        pop = algorithm.evolve(pop)
        pop = [Individual(simplify(ind)) for ind in pop]

        pop = update_fitness(pop)
        best = deap.tools.selBest(pop, 1)[0]
        print(gp.individual.simplify_this(best), best.fitness.values)

import numpy

from deap import algorithms
from deap import base
from deap import creator
from deap import tools
from deap import gp

# Define new functions
def protectedDiv(left, right):
    try:
        return left / right
    except ZeroDivisionError:
        return 1

pset = gp.PrimitiveSet("MAIN", 1)
pset.addPrimitive(operator.add, 2)
pset.addPrimitive(operator.sub, 2)
pset.addPrimitive(operator.mul, 2)
pset.addPrimitive(protectedDiv, 2)
pset.addPrimitive(operator.neg, 1)
pset.addPrimitive(math.cos, 1)
pset.addPrimitive(math.sin, 1)
pset.addEphemeralConstant("rand101", lambda: random.randint(-1,1))
pset.renameArguments(ARG0='x')

creator.create("FitnessMin", base.Fitness, weights=(-1.0,))
creator.create("Individual", gp.PrimitiveTree, fitness=creator.FitnessMin)

toolbox = base.Toolbox()
toolbox.register("expr", gp.genHalfAndHalf, pset=pset, min_=1, max_=2)
toolbox.register("individual", tools.initIterate, creator.Individual, toolbox.expr)

def find_unmatched_terminal(individual):
    """ Finds the location of the first terminal that can not be matched with a primitive.

    Raises a `ValueError` if no terminals are found.
    """
    unmatched_args = []
    for i, el in enumerate(individual):
        if len(unmatched_args) > 0 and el.ret == unmatched_args[0]:
            unmatched_args.pop(0)
        elif issubclass(type(el), gp.Terminal):
            return i
        if issubclass(type(el), gp.Primitive):
            # Replace with list-inserts if performance is bad.
            unmatched_args = el.args + unmatched_args

    return False

def main():
    pop_size = 20

    observer = ProgressObserver()
    mate = deap.gp.cxOnePoint
    expr_mut = partial(deap.gp.genFull, min_=0, max_=2)
    mutate = partial(deap.gp.mutUniform, expr=expr_mut, pset=Individual.pset)

    algorithm = gp.algorithms.AgeFitness(mate, mutate, deap.tools.selNSGA2, Individual.create_population)
    stats = create_stats(2)
    logbook = deap.tools.Logbook()
    pop = update_fitness(Individual.create_population(pop_size))

    for gen in range(20):
        pop = algorithm.evolve(pop)
        pop = update_fitness(pop)

        records = stats.compile(pop)
        logbook.record(gen=gen, **records)
        front = deap.tools.ParetoFront()
        front.update(pop)

compiled by DEAP into a callable function

        allow_shrink: bool (True)
            If True the `mutShrink` operator, which randomly shrinks the pipeline,
            is allowed to be chosen as one of the random mutation operators.
            If False, `mutShrink`  will never be chosen as a mutation operator.

        Returns
        -------
        mut_ind: DEAP individual
            Returns the individual with one of the mutations applied to it

        """
        if self.tree_structure:
            mutation_techniques = [
                partial(gp.mutInsert, pset=self._pset),
                partial(mutNodeReplacement, pset=self._pset)
            ]
            # We can't shrink pipelines with only one primitive, so we only add it if we find more primitives.
            number_of_primitives = sum([isinstance(node, deap.gp.Primitive) for node in individual])
            if number_of_primitives > 1 and allow_shrink:
                mutation_techniques.append(partial(gp.mutShrink))
        else:
            mutation_techniques = [partial(mutNodeReplacement, pset=self._pset)]

        mutator = np.random.choice(mutation_techniques)

        unsuccesful_mutations = 0
        for _ in range(self._max_mut_loops):
            # We have to clone the individual because mutator operators work in-place.
            ind = self._toolbox.clone(individual)
            offspring, = mutator(ind)

def main1():
    """Komplett ohne modul application."""
    import deap

    mate = deap.gp.cxOnePoint
    expr_mut = partial(deap.gp.genFull, min_=0, max_=2)
    mutate = partial(deap.gp.mutUniform, expr=expr_mut, pset=Individual.pset)
    algorithm = gp.NSGA2(mate, mutate)

    population = Individual.create_population(pop_size)
    update_fitness(population)
    for gen in range(10):
        population = algorithm.evolve(population)
        update_fitness(population)
        print('generation:', gen)
    print('Solutions:', population)