Solution graph eq03
\[(x^3 + x + b)^3 + x^3 + 2b = 0\]
mo873.pdf: example 9, form (38) with \(f(x) = x^3,\ a = 1\)
Fully solved
Families found: 1 / 1
Judge: Completeness proven
Solution process: strong
Lean: 11 / 14
Fully solved. All reference solution families were found (1 of 1). It is proven that there are no other solutions; this conclusion matches the reference.
How to read the graph
The graph shows how the agent solved the problem, left to right. The answer is in the ★ solution nodes; everything to their left is how it was obtained.
- Problem
- the original equation, the root of the graph.
- Idea N
- a solution plan the agent formulated before trying.
- Variant N
- an attempt along idea N: “✓ gave a solution” or “dead end” (no solution; the whole branch is hidden by the filter).
- ★ Solution N
- the final solution of variant N — a finished answer. “matches reference” — the judge matched it to a solution family of the handbook; “Lean ✓” — its formal part compiles.
- Completeness → Step N
- the argument that there are no other solutions: steps and their solutions; ∎ Completeness conclusion — the result of this branch, if the agent stated one.
- Subtasks, fragments
- (toggle) how a variant was carried out: subtasks and their solutions; green fragments made it into the final solution.
- Judge
- (toggle) LLM-judge nodes: checks of solutions, comparison with the reference, the verdict.
Click a node to see its text, Lean code and check result; “Where it leads” in the panel is the node’s subtree.
Loading graph…
Prompts and raw model outputs are not shown; reference solutions and the judge's retelling of them are hidden.