EML: The NAND of Mathematics

Function Gallery

Each card is an elementary function rebuilt in pure EML. Click one to see the full tree and walk through the derivation. Depth is the height of the EML tree, lower is simpler.

exp(x)
depth 1
Exponential
eml(x, 1)
Transcendental
Open
e
depth 1
Euler's constant e
eml(1, 1)
Constant
Open
0
depth 3
Constant 0
eml(1, eml(eml(1, 1), 1))
Constant
Open
ln(x)
depth 3
Natural logarithm
eml(1, eml(eml(1, x), 1))
Transcendental
Open
x
depth 4
Identity function
eml(1, eml(eml(1, eml(x, 1)), 1))
Unary
Open

Coming in v2

Paper Table 4, verified trees pending

These functions exist in the paper but their concrete EML trees are not yet shipped in this library. They depend on multi-step constructions that the v1 release intentionally defers.

  • negate

    Paper Table 4 K = 15 (8 leaves), verified tree pending v2.

    K = 15

  • reciprocal

    Paper Table 4 K = 15, exp(−ln(x)) composed via shifted SUB; pending v2.

    K = 15

  • subtract

    Paper Table 4 K = 11 (6 leaves), pending v2.

    K = 11

  • add

    Paper Table 4 K = 19 (10 leaves), builds on subtract; pending v2.

    K = 19

  • divide

    Paper Table 4 K = 17, multiply ∘ reciprocal; pending v2.

    K = 17

  • multiply

    Paper Table 4 K = 17. Paper §3 also notes the displayed tree reaches depth 8.

    K = 17