- new solutions are inserted into the e-graph followed by one step of equality saturation to find and store some of the  equivalent expressions of the new offspring.
- the current population is replaced by the set of individuals formed by: the Pareto front, the next front after excluding the first Pareto-front, and a selection of the last offspring at random until it reaches the desired population size.
- the subtree crossover and mutation are modified to try to generate an unvisited exp

eggp - E-graph Genetic Programming for Symbolic Regression.

Usage: eggp (-d|--dataset INPUT-FILE) [-t|--test ARG] [-g|--generations GENS]
            (-s|--maxSize ARG) [-k|--split ARG] [--print-pareto] [--trace] 
            [--loss ARG] [--opt-iter ARG] [--opt-retries ARG] 
            [--number-params ARG] [--nPop ARG] [--tournament-size ARG] 
            [--pc ARG] [--pm ARG] [--non-terminals ARG] [--dump-to ARG] 
            [--load-from ARG] [--moo]

  An implementation of GP with modified crossover and mutation operators
  designed to exploit equality saturation and e-graphs.
  https://arxiv.org/abs/2501.17848

Available options:
  -d,--dataset INPUT-FILE  CSV dataset.
  -t,--test ARG            test data (default: "")
  -g,--generations GENS    Number of generations. (default: 100)
  -s,--maxSize ARG         max-size.
  -k,--split ARG           k-split ratio training-validation (default: 1)
  --print-pareto           print Pareto front instead of best found expression
  --trace                  print all evaluated expressions.
  --loss ARG               loss function: MSE, Gaussian, Poisson, Bernoulli.
                           (default: MSE)
  --opt-iter ARG           number of iterations in parameter optimization.
                           (default: 30)
  --opt-retries ARG        number of retries of parameter fitting. (default: 1)
  --number-params ARG      maximum number of parameters in the model. If this
                           argument is absent, the number is bounded by the
                           maximum size of the expression and there will be no
                           repeated parameter. (default: -1)
  --nPop ARG               population size (Default: 100). (default: 100)
  --tournament-size ARG    tournament size. (default: 2)
  --pc ARG                 probability of crossover. (default: 1.0)
  --pm ARG                 probability of mutation. (default: 0.3)
  --non-terminals ARG      set of non-terminals to use in the search.
                           (default: "Add,Sub,Mul,Div,PowerAbs,Recip")
  --dump-to ARG            dump final e-graph to a file. (default: "")
  --load-from ARG          load initial e-graph from a file. (default: "")
  --moo                    replace the current population with the pareto front
                           instead of replacing it with the generated children.
  -h,--help                Show this help text

eggp --dataset "dataset1.csv dataset2.csv dataset3.csv" ...

curl --proto '=https' --tlsv1.2 -sSf https://get-ghcup.haskell.org | sh

Set-ExecutionPolicy Bypass -Scope Process -Force;[System.Net.ServicePointManager]::SecurityProtocol = [System.Net.ServicePointManager]::SecurityProtocol -bor 3072; try { & ([ScriptBlock]::Create((Invoke-WebRequest https://www.haskell.org/ghcup/sh/bootstrap-haskell.ps1 -UseBasicParsing))) -Interactive -DisableCurl } catch { Write-Error $_ }

from eggp import EGGP
import numpy as np

# Create sample data
X = np.linspace(-10, 10, 100).reshape(-1, 1)
y = 2 * X.ravel() + 3 * np.sin(X.ravel()) + np.random.normal(0, 1, 100)

# Create and fit the model
model = EGGP(gen=100, nonterminals="add,sub,mul,div,sin,cos")
model.fit(X, y)

# Make predictions
y_pred = model.predict(X)

# Examine the results
print(model.results)

from eggp import EGGP
import numpy as np

# Create multiple views of data
X1 = np.linspace(-5, 5, 50).reshape(-1, 1)
y1 = np.sin(X1.ravel()) + np.random.normal(0, 0.1, 50)

X2 = np.linspace(0, 10, 100).reshape(-1, 1)
y2 = np.sin(X2.ravel()) + np.random.normal(0, 0.2, 100)

# Create and fit multi-view model
model = EGGP(gen=150, nPop=200)
model.fit_mvsr([X1, X2], [y1, y2])

# Make predictions for each view
y_pred1 = model.predict_mvsr(X1, view=0)
y_pred2 = model.predict_mvsr(X2, view=1)

from sklearn.model_selection import train_test_split
from sklearn.metrics import mean_squared_error
from eggp import EGGP

# Split data
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)

# Create and fit model
model = EGGP(gen=150, nPop=150, optIter=100)
model.fit(X_train, y_train)

# Evaluate on test set
y_pred = model.predict(X_test)
mse = mean_squared_error(y_test, y_pred)
print(f"Test MSE: {mse}")

@inproceedings{eggp,
author = {de Franca, Fabricio Olivetti and Kronberger, Gabriel},
title = {Improving Genetic Programming for Symbolic Regression with Equality Graphs},
year = {2025},
isbn = {9798400714658},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
url = {https://doi.org/10.1145/3712256.3726383},
doi = {10.1145/3712256.3726383},
booktitle = {Proceedings of the Genetic and Evolutionary Computation Conference},
pages = {},
numpages = {9},
keywords = {Symbolic regression, Genetic programming, Equality saturation, Equality graphs},
location = {Malaga, Spain},
series = {GECCO '25},
archivePrefix = {arXiv},
       eprint = {2501.17848},
 primaryClass = {cs.LG}, 
}