emltree

Compile elementary functions into pure EML form — binary trees built from the single Sheffer-like operator

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

plus the constant 1. Odrzywołek (arXiv:2603.21852) showed this one operator generates every function on a scientific calculator — the NAND gate of continuous mathematics.

Zero dependencies. JS port of the Python emltree package (same identities, same tree shapes).

Install

npm install emltree

Usage

import { compile, evaluate, toNested, toRpn, asciiTree } from 'emltree';

const tree = compile('sin(x)^2 + cos(x)^2');
evaluate(tree, { x: 1.37 });   // { re: 1.0000000…, im: ~0 }

toNested(compile('exp(x)'));   // 'eml(x, 1)'
toRpn(compile('log(x)'));      // '1 1 x E 1 E E'   (paper eq. 5)

Builders are exported too, if you'd rather skip the parser:

import { variable, sin, pow, add, integer, evaluate } from 'emltree';

const x = variable('x');
const tree = add(pow(sin(x), integer(2)), integer(1));

Evaluation is complex throughout ({ re, im }) — trig and the constants pi / I flow through complex intermediates even for real inputs, exactly as in the paper.

CLI

npx emltree "sin(x)" -f rpn
npx emltree "exp(x) - log(y)" --stats --eval x=0.3,y=2.5
npx emltree "pi" -f tree

Supported syntax: + - * / ^ **, sqrt exp log ln sin cos tan asin acos atan sinh cosh tanh asinh acosh atanh sigmoid, two-arg log(x, base), constants pi E I.

Caveats

• Branch cuts: outside their real domains (asin(2), acosh(-2), log of negatives, …) results flow through complex branch cuts and may land on a non-principal branch — or, where float fuzz compounds, off-sheet entirely (paper §4.1). On the usual real domains everything matches to ~1e-7.
• Addition overflow: add's expansion applies exp() to its second operand, so adding values past ~709 overflows float64. Integer/decimal constants avoid this internally (binary decomposition, multiplicative odd step), but x + y with huge y is an inherent ceiling of the encoding.

Canonical identities

exp(x) = eml(x, 1)
ln(x)  = eml(1, eml(eml(1, x), 1))      # paper eq. (5)
x - y  = eml(ln(x), exp(y))

Everything else is built compositionally on top of these three. The resulting trees are not optimised for size — the paper's direct search finds much shorter forms; this package prioritises correctness and coverage.

License

MIT