Enter an expression with + − × ÷ ^ (also *, /, **), parentheses, and implicit multiplication. Explicit parentheses are kept as fixed subtrees; every remaining order of operations is enumerated as a parse tree and evaluated.
Badges: PEMDAS marks the conventional parse (^ before × ÷ before + −, left-to-right within a level, ^ right-associative, implicit × treated like ×). PEMDAS · juxtaposition first marks the variant where implicit multiplication binds tighter than ÷ and × — shown only when it differs. In trees, teal · is implicit multiplication.
Associahedron view: vertices are all bracketings of the flattened operand sequence — the associahedron Km−1 in Loday's realization, PCA-projected to 3D (for five operands this is the genuine 3-dimensional associahedron; beyond that, a 3D shadow of the higher-dimensional polytope). Edges are single associativity flips. Colored vertices are parses reachable given your explicit parentheses; pale dashed vertices are blocked by them. Drag to rotate, scroll to zoom, click a vertex to inspect it, and click an edge to animate the tree rotation it represents.