~/playground

eml playground

A scientific calculator whose every operation is a pure EML tree, plus a REPL for hand-rolled expressions. Switch with the tabs below, each answer comes with the underlying eml(x, y) expansion you can inspect.

EML Calculator

Every operation routes through a pure-EML tree. Inputs are substituted into $x$ , $y$ leaves of the operator's tree; the value you see is what $\operatorname{eml}(x,\, y) = \exp(x) - \ln(y)$ nestings actually compute. Domain limit: $|\text{input}| < e^{e} \approx 15.15$ for shifted ops (+, −x, ±). Multiplicative ops require positive inputs.

Templates

One-click calculations that load straight into the display and the EML graph.

EML graph

Press a calculator button to render the EML tree behind the result.

Under the hood

Press a calculator button to see the EML composition behind the answer.

How the trees are built

The bedrock primitive is $\operatorname{SUB}(a,\, b) = \operatorname{eml}\bigl(\operatorname{LN}(a),\, \operatorname{EXP}(b)\bigr) = a - b$ (needs $a > 0$ ). Every other op composes from this:

$-x \;=\; (K - x) - K,\ \ K = e^{e}$
$x + y \;=\; \bigl((K - (-x)) - (-y)\bigr) - K$
$x \cdot y \;=\; \exp\bigl(\ln x + \ln y\bigr)$
$\dfrac{1}{x} \;=\; \exp(-\ln x)$
$x \div y \;=\; x \cdot \dfrac{1}{y}$
$\sqrt{x} \;=\; \exp\!\left(\dfrac{\ln x + K}{2} - \dfrac{K}{2}\right)$

Depths balloon, multiply alone is a tree with hundreds of nodes, but every leaf is either $1$ or one of your inputs. There are no other primitives.