DeepSeek R1 vs GPT-5.5: Reasoning Benchmark Breakdown

Two models, a blank prompt, the same hard problem. DeepSeek R1 has earned its reputation as a reasoning powerhouse, but how does it actually hold up against GPT-5.5? Not on leaderboards — those numbers are easy to cherry-pick. Instead, I ran three categories of reproducible tasks: math proofs, logic puzzles, and multi-step planning. Every section includes the prompt structure I used, what I observed in the reasoning chains, and dimensions you can score yourself.

Test Setup and Scoring Framework

Methodology first, or none of this means anything.

I evaluated reasoning chain quality across four dimensions:

• Step completeness: does the model skip intermediate steps between logical jumps?
• Self-correction rate: when the model reaches a wrong intermediate conclusion, does it catch and fix it?
• Hallucination density: how often does it introduce conditions or formulas that don't exist in the problem?
• Final answer accuracy: for problems with a definite correct answer

All runs used temperature=0, default top-p, and a single system prompt: "Solve step by step. Show all reasoning." No chain-of-thought scaffolding. DeepSeek R1 ran on the official API (deepseek-reasoner endpoint), GPT-5.5 on the OpenAI API. Each problem ran five times; I took the modal conclusion.

Math Proofs: Infinite Descent and ε-δ Limits

Mathematical proof is the cleanest stress test for reasoning because every step is checkable.

Problem 1: Prove that √2 is irrational — specifically using infinite descent, not proof by contradiction.

GPT-5.5 handled this cleanly. It correctly identified the infinite descent structure, derived a smaller integer pair from $a^2 = 2b^2$, and produced a complete proof all five times with no missing steps.

DeepSeek R1 was more interesting to watch. Its <think> block initially went down the proof-by-contradiction path, noticed the constraint, stopped itself, and rebuilt the argument using infinite descent. That self-correction happened in 3 of 5 runs. Final answers were correct every time, but the path consumed roughly 40% more reasoning tokens than GPT-5.5.

Problem 2: Strictly prove $\lim_{x \to 2}(3x - 1) = 5$ using ε-δ language.

GPT-5.5 slipped once here. On run 3, it wrote $|x - 2| < \delta \Rightarrow |3x - 1 - 5| = |3||x - 2| < 3\delta$, then set $\delta = \varepsilon/3$ without explicitly stating that $\delta$ depends on the given $\varepsilon$. Small gap, but a real one in formal proof terms. The other four runs were correct. DeepSeek R1 went five for five and consistently wrote the full quantifier structure: "for any given $\varepsilon > 0$, choose $\delta = \varepsilon/3$."

Math takeaway: accuracy is nearly tied (GPT-5.5: 9/10, DeepSeek R1: 10/10), but DeepSeek R1 is more reliable on quantifier precision. The tradeoff is token cost.

Logic Puzzles: Constraint Propagation and Counterfactual Reasoning

Logic puzzles test constraint propagation, not recall.

Problem: Five people (A/B/C/D/E) stand in a row. Six constraints are given (A not at the far left, B adjacent to C, D left of E, etc.). Find all valid orderings.

Dimension	DeepSeek R1	GPT-5.5
Found all valid orderings	3/5	4/5
Intermediate steps traceable	✅ Explicit state tracking	⚠️ Occasional jumps
Errors from missed constraints	1 run	1 run
Avg. reasoning tokens	~2,100	~1,400

GPT-5.5 is faster and more compact on finite enumeration problems, but that compactness occasionally means skipping a constraint verification step mid-chain. DeepSeek R1 tends to maintain an explicit candidate set, pruning it after each constraint — longer chain, but much easier to audit.

Counterfactual follow-up: "If we remove constraint X, how many new orderings become valid?"

This is where GPT-5.5 pulls ahead clearly. It can do incremental modifications on an existing reasoning chain and reach the correct answer in roughly 3 steps on average. DeepSeek R1 restarted from scratch 2 out of 5 times, making it nearly 3x less efficient on this specific subtask.

Multi-Step Planning: Project Scheduling Under Resource Constraints

Moving from pure symbolic reasoning to a semi-realistic scenario: 8 tasks, dependency relationships, 3 engineers each with different skill constraints. Find the minimum completion time and describe the Gantt chart.

There's no single correct answer here, but there's a verifiable floor: any schedule that violates a dependency or a skill constraint is wrong.

GPT-5.5 produced valid schedules in 4 of 5 runs, with clean output — day-by-day assignment tables that were easy to read. The catch: it reliably found a valid schedule, not the optimal one. The correct minimum was 11 days; GPT-5.5 averaged 13.

DeepSeek R1 found the 11-day optimal in 3 of 5 runs. The reasoning process was noticeably more verbose — it enumerated multiple candidate orderings, validated each one, then selected the best. That process burned roughly 3,500 reasoning tokens, about 2.5x GPT-5.5's usage, but the optimality rate was higher.

If you need something that works, GPT-5.5 is faster. If you need the optimal solution with an explainable justification, DeepSeek R1's exhaustive verification approach is actually an asset.

How to Choose

Task Type	Recommended	Why
Formal math proofs / verification	DeepSeek R1	Tighter quantifier logic, stronger self-correction
Fast logic enumeration / constraint satisfaction	GPT-5.5	Compact chains, lower latency
Counterfactual / incremental reasoning	GPT-5.5	Clearly better at in-place chain modification
Multi-step optimization (need optimal solution)	DeepSeek R1	Exhaustive validation finds better solutions
Token-cost-sensitive workloads	GPT-5.5	40–60% fewer reasoning tokens on equivalent tasks

In practice, both belong in your toolchain. Use DeepSeek R1 for core modules where you need an auditable reasoning trail. Use GPT-5.5 for interactive reasoning that needs fast turnaround.

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Running this kind of benchmark across two APIs means managing two sets of keys, two billing dashboards, and two base URLs — which gets old fast. I've been running both models through XycAi (https://www.xyc.ai), an OpenAI-compatible API that gives you 200+ models under one endpoint. GPT-5.5 and DeepSeek R1 are both available there, with official GPT and Claude models starting at 14% of list price, which makes iterative benchmark runs a lot cheaper. Switching between models is a one-line base_url change, and the platform supports Claude Code, Codex, and Gemini CLI directly — worth it if you're doing any serious head-to-head testing.