← Session 5 — Phase 0: paper deep-read + Bombieri–Lagarias literature
thinking (2053 chars)
Exit code 143 = killed by timeout (600s default I set — I passed timeout 600000 = 10 min). The O(n²) mpmath loops at dps 1000 are too slow: lambda sums 2e6 iterations with mp.binomial at dps 1000 — binomial(2000,1000) is a 600-digit integer; mpmath binomial computes via factorials each time — expensive. Let me optimize:
1. Precompute binomials row by row? Each λ_n needs row n of Pascal — iterative update: C(n,j) from C(n,j−1)·(n−j+1)/j — exact integer via Python ints (arbitrary precision) — fast. Use plain Python ints for binomials (not mp.binomial).
2. The eta-sum and zeta-sum can share the binomial recurrence.
3. η/ζ terms as mpf; multiply int×mpf.
4. Reduce self-consistency recompute: it currently re-does stieltjes+eta at 1.4× dps for ALL k — that's the expensive part. Only need eta2/ζ2 for j ≤ sample n values... but sample includes n_max — full recompute anyway. Alternative: self-consistency via a SECOND run at n_max with different dps only for the final sums — reuse? simpler: keep but it's ~2× cost. Reduce sample to {1, 2, n_max//10, n_max//2} — drop n_max? No — n_max is the important one. Keep but optimize.
Estimated costs: the recursion E[k] O(n²) mpf muls at 1000 dps: 2e6 muls — mpmath mpf mul ~ 5µs → 10s ✔. The lambda sums: 2e6 iterations with Python-int binomial recurrence + int×mpf mul: ~10-20s ✔. stieltjes: measured fast. So the main cost was probably mp.binomial (factorial of huge ints per call: C(2000,j) via factorial(2000) — 2000 calls × ... actually per (n,j) pair! factorial(n) recomputed per pair — 2e6 factorials of up to 2000! — that's the killer. Fix with recurrence.
Also the self-consistency block doubles everything AND recomputes stieltjes at 1.4 dps — the stieltjes caching should make the second pass cheaper.
Let me rewrite the lambda computation with int binomial recurrence, and restructure for speed. Also consider computing λ_n incrementally... just do per-n loops with recurrence.
Also, exit 143 killed at 600s — output showed nothing? The output file should have the early prints. Check it.
Timed out at 10 min — `mp.binomial` per (n,j) pair (2e6 huge factorials) is the bottleneck. Checking partial output, then optimizing with integer Pascal recurrence.
tool: Bash
input
{
"command": "cat \"C:/Users/lucky/AppData/Local/Temp/nguyen/0a6cf0fe-113a-4054-8ead-c619b4a0182a/tasks/bfv9yy7id.output\"",
"description": "Read E-011 partial output"
}
raw content_json (database row)
[{"type":"thinking","thinking":"Exit code 143 = killed by timeout (600s default I set — I passed timeout 600000 = 10 min). The O(n²) mpmath loops at dps 1000 are too slow: lambda sums 2e6 iterations with mp.binomial at dps 1000 — binomial(2000,1000) is a 600-digit integer; mpmath binomial computes via factorials each time — expensive. Let me optimize:\n\n1. Precompute binomials row by row? Each λ_n needs row n of Pascal — iterative update: C(n,j) from C(n,j−1)·(n−j+1)/j — exact integer via Python ints (arbitrary precision) — fast. Use plain Python ints for binomials (not mp.binomial).\n2. The eta-sum and zeta-sum can share the binomial recurrence.\n3. η/ζ terms as mpf; multiply int×mpf.\n4. Reduce self-consistency recompute: it currently re-does stieltjes+eta at 1.4× dps for ALL k — that's the expensive part. Only need eta2/ζ2 for j ≤ sample n values... but sample includes n_max — full recompute anyway. Alternative: self-consistency via a SECOND run at n_max with different dps only for the final sums — reuse? simpler: keep but it's ~2× cost. Reduce sample to {1, 2, n_max//10, n_max//2} — drop n_max? No — n_max is the important one. Keep but optimize.\n\nEstimated costs: the recursion E[k] O(n²) mpf muls at 1000 dps: 2e6 muls — mpmath mpf mul ~ 5µs → 10s ✔. The lambda sums: 2e6 iterations with Python-int binomial recurrence + int×mpf mul: ~10-20s ✔. stieltjes: measured fast. So the main cost was probably mp.binomial (factorial of huge ints per call: C(2000,j) via factorial(2000) — 2000 calls × ... actually per (n,j) pair! factorial(n) recomputed per pair — 2e6 factorials of up to 2000! — that's the killer. Fix with recurrence.\n\nAlso the self-consistency block doubles everything AND recomputes stieltjes at 1.4 dps — the stieltjes caching should make the second pass cheaper.\n\nLet me rewrite the lambda computation with int binomial recurrence, and restructure for speed. Also consider computing λ_n incrementally... just do per-n loops with recurrence.\n\nAlso, exit 143 killed at 600s — output showed nothing? The output file should have the early prints. Check it.","signature":""},{"type":"text","text":"Timed out at 10 min — `mp.binomial` per (n,j) pair (2e6 huge factorials) is the bottleneck. Checking partial output, then optimizing with integer Pascal recurrence."},{"type":"tool_use","id":"Bash_187","name":"Bash","input":{"command":"cat \"C:/Users/lucky/AppData/Local/Temp/nguyen/0a6cf0fe-113a-4054-8ead-c619b4a0182a/tasks/bfv9yy7id.output\"","description":"Read E-011 partial output"},"extra_content":null}]