unary
Identity function · x
Even the identity function f(x) = x takes non-trivial nesting in pure EML: ln(exp(x)) = x.
depth 4
Domain: x ∈ ℝ⁺Definition
Formula
eml(1, eml(eml(1, eml(x, 1)), 1))Evaluate
2.5at x = 2.5
Reference: 2.5 ≈ 2.5
EML tree
Click a node to highlight it. Each node shows its computed value below the label.
Step-through evaluation
- 1.depth 1const 1
- 2.depth 3const 1
- 3.depth 4x = 2.5
- 4.depth 4const 1
- 5.depth 3exp(2.5) − ln(1) = 12.182494
- 6.depth 2exp(1) − ln(12.182494) = 0.218282
- 7.depth 2const 1
- 8.depth 1exp(0.218282) − ln(1) = 1.243938
- 9.depth 0exp(1) − ln(1.243938) = 2.5
Derivation
- 1.Substitute z = exp(x) = eml(x, 1) into the ln(z) tree.
- 2.ln(exp(x)) = x by the fundamental log–exp identity.
- 3.Result: a depth-4 tree whose value equals x for any x.