Crate phop_core 

phop-core — differentiable symbolic discovery on the EML operator

phop discovers closed-form expressions from data by learning both the topology and the numeric parameters of homogeneous binary trees built from a single primitive, the EML operator

eml(x, y) = exp(x) - ln(y)

together with the constant 1. The grammar is the trivial production S -> 1 | eml(S, S), which (Odrzywołek 2026) is functionally complete for the elementary functions. Homogeneity lets an entire population of candidate trees be evaluated inside a single automatic-differentiation graph and optimized end-to-end.

This crate is layered:

• Layer A (forest) — tensorized EML forest forward evaluation.
• Layer B (topology), C (loss/Pareto), D (distillation) build on top (see the crate TODO).

The AST, canonicalization, and LaTeX rendering are delegated to the oxieml crate; automatic differentiation and optimization to scirs2-autograd.

Re-exports

pub use accel::gpu_backend;

pub use accel::GpuBackend;

pub use affine::discover_affine;

pub use affine::discover_affine_pareto;

pub use affine::AffineSolution;

pub use analyze::analyze;

pub use analyze::certified_range;

pub use analyze::certified_root;

pub use analyze::Analysis;

pub use any_solution::merge_pareto;

pub use any_solution::AnySolution;

pub use config::Backend;

pub use config::Config;

pub use config::TempSchedule;

pub use dataset::DataSet;

pub use dataset::Standardizer;

pub use dimension::pi_groups;

pub use dimension::Dimension;

pub use discoverer::discover_auto;

pub use discoverer::discover_auto_all;

pub use discoverer::Discoverer;

pub use distill::distill;

pub use distill::Distilled;

pub use error::PhopError;

pub use error::Result;

pub use fit::fit_constants;

pub use fit::mse;

pub use fit::n_constants;

pub use forest::eml_guarded;

pub use forest::eval_tree;

pub use gated::discover_gated;

pub use gated::discover_gated_warm;

pub use gumbel::discover_gumbel;

pub use loss::RobustLoss;

pub use ode::discover_ode;

pub use optimize::polish_constants_scirs;

pub use optimize::ScirsPolish;

pub use pareto::ParetoFront;

pub use polish::polish_constants;

pub use polish::polish_constants_robust;

pub use polish::snap_constants;

pub use solution::Solution;

Modules

accel

Accelerator selection for the tensorized EML forward pass.

affine

Affine- and log-affine-leaf EML discovery (M6 root-cause fix, steps 1 + 2).

analyze

Layer D⁺ — post-discovery analysis of a recovered law via the oxieml computer-algebra system.

any_solution

A heterogeneous discovered law — either an EML-tree law from the differentiable core engine or a rich-leaf affine/log-linear law from crate::affine.

codegen

Code generation for discovered EML expressions (Rust, Python/NumPy).

config

Discovery configuration.

dataset

Dataset ingestion: (X, y) pairs from arrays or CSV.

dimension

Buckingham-π dimensional reduction (a discovery prior for phop).

discoverer

The top-level discovery engine.

distill

Layer D — symbolic distillation of a discovered EML tree.

error

Error types for the phop engine.

fit

M1 — gradient-based fitting of the real-valued constants of an EML tree.

forest

Layer A — tensorized EML forest forward evaluation.

gated

Differentiable tree shape via per-node expand/terminate gates (the depth-learning step).

gumbel

Layer B (M2) — differentiable topology via Gumbel-Softmax leaf selection.

loss

Robust regression losses for constant fitting under outliers.

ode

Governing-equation discovery: recover the right-hand side of an autonomous ODE dx/dt = f(x) from a sampled trajectory, using phop as the function learner.

optimize

Library-backed constant refinement via scirs2-optimize.

pareto

Pareto front over (complexity, MSE).

polish

Post-fit refinement of an expression’s constants.

silence

Scoped suppression of process stdout at the file-descriptor level.

solution

A discovered candidate expression and its quality metrics.

Structs

EmlTree

EML tree with metadata.

RootCertificate

Certificate for a verified root-finding result.

Enums

EmlNode

EML tree node. All nodes share the same type — uniform binary tree. Arc enables O(1) subtree sharing during symbolic regression.

RootStatus

Status of the root certificate.