README.md

# [PySR](https://github.com/MilesCranmer/PySR)

(pronounced like *py* as in python, and then *sur* as in surface)

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**Parallelized symbolic regression built on Julia, and interfaced by Python.
Uses regularized evolution, simulated annealing, and gradient-free optimization.**

[Cite this software](https://github.com/MilesCranmer/PySR/blob/master/CITATION.md)

[Documentation](https://pysr.readthedocs.io/en/latest)

Check out [SymbolicRegression.jl](https://github.com/MilesCranmer/SymbolicRegression.jl) for
the pure-Julia version of this package.

Symbolic regression is a very interpretable machine learning algorithm
for low-dimensional problems: these tools search equation space
to find algebraic relations that approximate a dataset.

One can also
extend these approaches to higher-dimensional
spaces by using a neural network as proxy, as explained in 
[2006.11287](https://arxiv.org/abs/2006.11287), where we apply
it to N-body problems. Here, one essentially uses
symbolic regression to convert a neural net
to an analytic equation. Thus, these tools simultaneously present
an explicit and powerful way to interpret deep models.


*Backstory:*

Previously, we have used
[eureqa](https://www.creativemachineslab.com/eureqa.html),
which is a very efficient and user-friendly tool. However,
eureqa is GUI-only, doesn't allow for user-defined
operators, has no distributed capabilities,
and has become proprietary (and recently been merged into an online
service). Thus, the goal
of this package is to have an open-source symbolic regression tool
as efficient as eureqa, while also exposing a configurable
python interface.


# Installation
PySR uses both Julia and Python, so you need to have both installed.

Install Julia - see [downloads](https://julialang.org/downloads/), and
then instructions for [mac](https://julialang.org/downloads/platform/#macos)
and [linux](https://julialang.org/downloads/platform/#linux_and_freebsd).
(Don't use the `conda-forge` version; it doesn't seem to work properly.)
Then, at the command line, install and precompile the backend
and Python frontend with:

```bash
julia -e 'using Pkg; Pkg.add("SymbolicRegression"); using SymbolicRegression'
pip install pysr
```

# Quickstart

Here is some demo code (also found in `example.py`)
```python
import numpy as np
from pysr import pysr, best

# Dataset
X = 2*np.random.randn(100, 5)
y = 2*np.cos(X[:, 3]) + X[:, 0]**2 - 2

# Learn equations
equations = pysr(X, y, niterations=5,
    binary_operators=["plus", "mult"],
    unary_operators=[
      "cos", "exp", "sin", #Pre-defined library of operators (see https://pysr.readthedocs.io/en/latest/docs/operators/)
      "inv(x) = 1/x"]) # Define your own operator! (Julia syntax)

...# (you can use ctl-c to exit early)

print(best(equations))
```

which gives:

```python
x0**2 + 2.000016*cos(x3) - 1.9999845
```

One can also use `best_tex` to get the LaTeX form,
or `best_callable` to get a function you can call.
This uses a score which balances complexity and error;
however, one can see the full list of equations with:
```python
print(equations)
```
This is a pandas table, with additional columns:

- `MSE` - the mean square error of the formula
- `score` - a metric akin to Occam's razor; you should use this to help select the "true" equation.
- `sympy_format` - sympy equation.
- `lambda_format` - a lambda function for that equation, that you can pass values through.