Zymbol

Symbolic Automatic Differentiation for Zig

const std = @import("std");
const zymbol = @import("zymbol");

var registry = zymbol.Registry.init(allocator);
defer registry.deinit();
try registry.registerBuiltins();

var expr = try zymbol.Expression.parse(allocator, &registry, "x^2 + sin(x)");
defer expr.deinit();

var inputs = std.StringHashMap(f32).init(allocator);
defer inputs.deinit();
try inputs.put("x", 1.5);

const value = try expr.evaluate(inputs);
std.debug.print("f(1.5) = {d}\n", .{value});

var grad_expr = try expr.symbolicGradient("x");
defer grad_expr.deinit();

const grad_value = try grad_expr.evaluate(inputs);
std.debug.print("df/dx(1.5) = {d}\n", .{grad_value});

Features:

• Symbolic differentiation - generates derivative expressions at compile time
• Composable - grad(grad(f)) for higher-order derivatives
• Extensible - register custom operations without modifying the library
• Inspectable - convert graphs back to human-readable strings
• Simplified output - algebraic pass folds constants, collapses duplicate terms, and removes trivial factors (e.g. d/dx x^3 -> 3 * (x ^ 2), x + x -> 2 * x)
• Zero runtime overhead - all parsing happens at compile time (when used with comptime)
• Robust gradients - gracefully handles edge cases like non-positive power bases to avoid NaNs

Expression Syntax

• Identifiers map to input variables (e.g. x, foo_bar).
• Literals support integers and floating-point values (2, 3.14).
• Binary operators: +, -, *, /, ^ with standard precedence.
• Unary prefixes + and - are supported (-x, -(x + 1)).
• Parentheses group sub-expressions.
• Function calls invoke registered operations (sin(x), max(x, y), etc.).

WebAssembly Playground

Build an interactive derivative playground that runs entirely in the browser:

zig build wasm-example
cd zig-out/wasm
python -m http.server 8080

Then browse to http://localhost:8080. The page lets you type an expression, choose the differentiation variable, toggle simplification, and calls the compiled WASM module to print either the raw or simplified symbolic derivative. The build enables rdynamic so every exported Zig function stays visible to JavaScript.

Changes pushed to master are deployed automatically to https://arrufat.github.io/zymbol via the GitHub Actions workflow in .github/workflows/pages.yml, which builds with the latest Zig master toolchain.