Equations are specified as binary trees with the Node type, defined as follows:


Node defines a symbolic expression stored in a binary tree. A single Node instance is one "node" of this tree, and has references to its children. By tracing through the children nodes, you can evaluate or print a given expression.


  • degree::UInt8: Degree of the node. 0 for constants, 1 for unary operators, 2 for binary operators.
  • constant::Bool: Whether the node is a constant.
  • val::T: Value of the node. If degree==0, and constant==true, this is the value of the constant. It has a type specified by the overall type of the Node (e.g., Float64).
  • feature::UInt16: Index of the feature to use in the case of a feature node. Only used if degree==0 and constant==false. Only defined if degree == 0 && constant == false.
  • op::UInt8: If degree==1, this is the index of the operator in operators.unaops. If degree==2, this is the index of the operator in operators.binops. In other words, this is an enum of the operators, and is dependent on the specific OperatorEnum object. Only defined if degree >= 1
  • l::Node{T}: Left child of the node. Only defined if degree >= 1. Same type as the parent node.
  • r::Node{T}: Right child of the node. Only defined if degree == 2. Same type as the parent node. This is to be passed as the right argument to the binary operator.

There are a variety of constructors for Node objects, including:

Node([::Type{T}]; val=nothing, feature::Union{Integer,Nothing}=nothing) where {T}

Create a leaf node: either a constant, or a variable.


  • ::Type{T}, optionally specify the type of the node, if not already given by the type of val.
  • val, if you are specifying a constant, pass the value of the constant here.
  • feature::Integer, if you are specifying a variable, pass the index of the variable here.

When you create an Options object, the operators passed are also re-defined for Node types. This allows you use, e.g., t=Node(; feature=1) * 3f0 to create a tree, so long as * was specified as a binary operator. This works automatically for operators defined in Base, although you can also get this to work for user-defined operators by using @extend_operators:

@extend_operators options

Extends all operators defined in this options object to work on the Node type. While by default this is already done for operators defined in Base when you create an options and pass define_helper_functions=true, this does not apply to the user-defined operators. Thus, to do so, you must apply this macro to the operator enum in the same module you have the operators defined.


When using these node constructors, types will automatically be promoted. You can convert the type of a node using convert:

convert(::Type{Node{T1}}, n::Node{T2}) where {T1,T2}

Convert a Node{T2} to a Node{T1}. This will recursively convert all children nodes to Node{T1}, using convert(T1, tree.val) at constant nodes.


  • ::Type{Node{T1}}: Type to convert to.
  • tree::Node{T2}: Node to convert.

You can set a tree (in-place) with set_node!:

You can create a copy of a node with copy_node:

copy_node(tree::Node; preserve_sharing::Bool=false)

Copy a node, recursively copying all children nodes. This is more efficient than the built-in copy. With preserve_sharing=true, this will also preserve linkage between a node and multiple parents, whereas without, this would create duplicate child node copies.

id_map is a map from objectid(tree) to copy(tree). We check against the map before making a new copy; otherwise we can simply reference the existing copy. Thanks to Ted Hopp.

Note that this will not preserve loops in graphs.


Groups of equations are given as a population, which is an array of trees tagged with score, loss, and birthdate–-these values are given in the PopMember.

Population(pop::Array{PopMember{T,L}, 1})

Create population from list of PopMembers.

           population_size, nlength::Int=3, options::Options,

Create random population and score them on the dataset.

Population(X::AbstractMatrix{T}, y::AbstractVector{T};
           population_size, nlength::Int=3,
           options::Options, nfeatures::Int,

Create random population and score them on the dataset.


Population members

PopMember(t::Node{T}, score::L, loss::L)

Create a population member with a birth date at the current time. The type of the Node may be different from the type of the score and loss.


  • t::Node{T}: The tree for the population member.
  • score::L: The score (normalized to a baseline, and offset by a complexity penalty)
  • loss::L: The raw loss to assign.
          t::Node{T}, options::Options)

Create a population member with a birth date at the current time. Automatically compute the score for this tree.


  • dataset::Dataset{T,L}: The dataset to evaluate the tree on.
  • t::Node{T}: The tree for the population member.
  • options::Options: What options to use.

Hall of Fame


List of the best members seen all time in .members, with .members[c] being the best member seen at complexity c. Including only the members which actually have been set, you can run .members[exists].


  • members::Array{PopMember{T,L},1}: List of the best members seen all time. These are ordered by complexity, with .members[1] the member with complexity 1.
  • exists::Array{Bool,1}: Whether the member at the given complexity has been set.
HallOfFame(options::Options, ::Type{T}, ::Type{L}) where {T<:DATA_TYPE,L<:LOSS_TYPE}

Create empty HallOfFame. The HallOfFame stores a list of PopMember objects in .members, which is enumerated by size (i.e., .members[1] is the constant solution). .exists is used to determine whether the particular member has been instantiated or not.


  • options: Options containing specification about deterministic.
  • T: Type of Nodes to use in the population. e.g., Float64.
  • L: Type of loss to use in the population. e.g., Float64.




  • X::AbstractMatrix{T}: The input features, with shape (nfeatures, n).
  • y::AbstractVector{T}: The desired output values, with shape (n,).
  • n::Int: The number of samples.
  • nfeatures::Int: The number of features.
  • weighted::Bool: Whether the dataset is non-uniformly weighted.
  • weights::Union{AbstractVector{T},Nothing}: If the dataset is weighted, these specify the per-sample weight (with shape (n,)).
  • extra::NamedTuple: Extra information to pass to a custom evaluation function. Since this is an arbitrary named tuple, you could pass any sort of dataset you wish to here.
  • avg_y: The average value of y (weighted, if weights are passed).
  • use_baseline: Whether to use a baseline loss. This will be set to false if the baseline loss is calculated to be Inf.
  • baseline_loss: The loss of a constant function which predicts the average value of y. This is loss-dependent and should be updated with update_baseline_loss!.
  • variable_names::Array{String,1}: The names of the features, with shape (nfeatures,).
  • display_variable_names::Array{String,1}: A version of variable_names but for printing to the terminal (e.g., with unicode versions).
  • y_variable_name::String: The name of the output variable.
  • X_units: Unit information of X. When used, this is a vector of DynamicQuantities.Quantity{<:Any,<:Dimensions} with shape (nfeatures,).
  • y_units: Unit information of y. When used, this is a single DynamicQuantities.Quantity{<:Any,<:Dimensions}.
  • X_sym_units: Unit information of X. When used, this is a vector of DynamicQuantities.Quantity{<:Any,<:SymbolicDimensions} with shape (nfeatures,).
  • y_sym_units: Unit information of y. When used, this is a single DynamicQuantities.Quantity{<:Any,<:SymbolicDimensions}.
Dataset(X::AbstractMatrix{T}, y::Union{AbstractVector{T},Nothing}=nothing;
        weights::Union{AbstractVector{T}, Nothing}=nothing,
        variable_names::Union{Array{String, 1}, Nothing}=nothing,
        X_units::Union{AbstractVector, Nothing}=nothing,
) where {T<:DATA_TYPE}

Construct a dataset to pass between internal functions.