rederive newton's law of universal gravitation with pysr

symbolic_regression.py

import numpy as np
num_samples=1000
noise = np.random.normal(1,
                         0.01, #0.001
                         size=num_samples)

input_vars = np.random.randn(num_samples, 3)
F = noise*(input_vars[:,0]*input_vars[:,1])/(input_vars[:,2]**2)

from pysr import PySRRegressor

model = PySRRegressor(
    procs=4,
    niterations=100,
    binary_operators=["*", "+", "-", "/"],
    unary_operators=["square", "cube", "exp"],

    nested_constraints={
        "square": {"square": 1, "cube": 1, "exp": 0},
        "cube": {"square": 1, "cube": 1, "exp": 0},
        "exp": {"square": 1, "cube": 1, "exp": 0},
    },
    # ^ Nesting constraints on operators. For example,
    # "square(exp(x))" is not allowed, since "square": {"exp": 0}.
    complexity_of_operators={"/": 2, "exp": 3},
    # ^ Custom complexity of particular operators.
    precision=64,
    # ^ Higher precision calculations.
    loss="loss(prediction, target) = sum((target .- prediction).^2) / length(target)",
)
model.fit(input_vars, F)
print(model)