A mathematical study of Claude Cowork and Manus as agents of intellectual labor, built so you can test them on your own work instead of trusting anyone’s demo. Updated October 7, 2026.
c + r + (1 − p)·G < W. Delegate a task when the expected cost on the left beats the cost of doing it yourself, W. Here c is the agent’s run cost, r is your review time priced in money, p is the chance the run succeeds, and G is what a failure costs you after the fact. Everything below is this one inequality, unpacked.
What changed, and what this study assumes
Two facts reshaped this comparison during 2026. Anthropic launched Cowork as a research preview in January and took it to general availability on April 9. On September 16, it merged Cowork into the main Claude chat, and press reports say the Cowork name will eventually disappear. I therefore use “Cowork” for an architecture: delegated, file-grounded runs where Claude asks before acting, which Anthropic describes on its product page.
Manus had the messier year. Meta announced the acquisition in late December 2025, and on April 27, China’s state planner ordered it unwound. Manus formally resumed independent operations on September 1.
One honest limit: I found no independent head-to-head benchmark of the two. Any article crowning a winner is extrapolating from demos. What follows gives you the equations and tells you which numbers to measure.
The two agents as parameter sets
| Dimension | Claude Cowork | Manus | Parameter it moves |
|---|---|---|---|
| Where work runs | Desktop with local folders and browser; cloud execution in beta since July 7 | Cloud VM, plus Browser Operator and a desktop “My Computer” mode (third-party review) | r, G |
| Default supervision | Asks before acting; Manual, Auto and Skip approval modes (same source) | Reviewers advise auditing through task replay (The Neuron) | τ*, d |
| Parallel work | Sub-agent coordination (Suprmind) | Wide Research runs parallel sub-agents | s, k |
| Billing | Included in paid plans, drawing on a shared usage budget (Vellum) | Credits: published tiers, with $20 buying 4,000 credits and $200 buying 40,000 | c, N* |
| Model layer | Claude models only | At acquisition time, models from Anthropic and Alibaba; check current status | p |
Note the last row. If both harnesses lean on overlapping models, differences in p come as much from the harness (tools, memory, retries) as from raw intelligence. That is why the math below focuses on harness-level quantities.
Equation 1: reliability decays with task length
METR’s time-horizon paper measures the task length, in human time, that an agent completes at 50% success, and reports that this horizon has doubled roughly every seven months on software tasks. Model it as a constant hazard per human-hour. Then for a task of T human-hours and a 50% horizon T50:
p(T) = 2−T/T₅₀ and Tx = T₅₀ · ln(1/x) / ln 2(1)
| Success level x | 0.50 | 0.80 | 0.90 | 0.95 | 0.99 |
|---|---|---|---|---|---|
| Tx as a share of T50 | 1.00 | 0.32 | 0.15 | 0.074 | 0.0145 |
Take an illustrative agent with T50 = 4 hours. A 2-hour job succeeds with p = 0.71, but a job you need at 95% reliability should be chopped into pieces of about 18 minutes. METR itself fits a logistic curve rather than this exponential, so treat Equation 1 as a teaching approximation, and remember its data come from software tasks, not office work.
Equation 2: the break-even probability
Add a detection rate d, the share of failures you catch in review, and a loss L when a failure slips through. A caught failure costs you a full redo, W. Then G = d·W + (1 − d)·L, and the hero inequality solves to:
p* = 1 − (W − c − r) / G(2)
Worked example: a competitive-research brief that takes you 2 hours at $60/hour, so W = $120. A Manus Wide Research run costs roughly 800 to 1,500 credits according to a third-party price guide; at the roughly $0.005-per-credit rate implied by Manus’s tiers, call it c = $5. You spend 15 minutes reviewing, so r = $15.
| Scenario | d | L | G | p* (break-even) |
|---|---|---|---|---|
| Internal draft | 0.90 | $300 | $138 | 27.5% |
| Client-facing, weak review | 0.90 | $3,000 | $408 | 75.5% |
| Client-facing, strong review | 0.99 | $3,000 | $148.8 | 32.8% |
Read the last two rows together. Raising detection from 90% to 99% cuts the reliability you need from 75% to 33%. At p = 0.71, the agent is a clear win only in the rows where your review is good.
Unpopular take
The agent with better diffs, logs, and replay can beat the agent with the better model, because d appears in the break-even as a multiplier on the whole failure term. Judge both products by how cheaply they let you catch their mistakes.
Equation 3: how often to check the work
Split a long job into checkpoints every τ human-hours. Each checkpoint costs you r; rework per hour of work is roughly w·τ·ln 2 / T50 when τ is small relative to T50. Minimizing the sum of the two per-hour costs gives:
τ* = √( r · T₅₀ / (w · ln 2) )(3)
With r = $15, w = $60/hour and T50 = 4 hours, τ* ≈ 1.2 hours, and the supervision-plus-rework overhead falls to about $25 per hour of work delivered, against $60 if you did it yourself, before counting c. Two consequences follow. Checkpoint spacing grows only with the square root of the horizon, so each doubling of T50 stretches it by about 41%, not 100%. And the choice between Cowork’s approval modes, or between watching a Manus replay live versus afterward, is exactly a choice of τ. The approximation drifts about 10% at τ = 0.3·T50, so use it as a starting cadence, then adjust.
Equation 4: parallel research and its ceiling
Wide Research and sub-agent coordination are the same mathematics. If a share s of a job is serial (planning, merging, final judgment) and the rest splits across k sub-agents, Amdahl’s 1967 law gives the speedup. Add a per-sub-agent cost c₁ and a value v per hour of waiting, and the cost-optimal fan-out follows:
S(k) = 1 / (s + (1 − s)/k) k* = √( v · T₁ · (1 − s) / c₁ )(4)
With s = 0.2 the speedup is 3.57× at k = 10, 4.63× at k = 50, and never more than 5×. If a single-agent run takes T₁ = 2 hours, waiting costs v = $60/hour and each sub-agent costs $0.50, then k* ≈ 14. Past that, you pay more for seconds. Gustafson’s rebuttal applies too: if you widen the question as you add agents, the serial share shrinks, which is the honest case for Wide Research on big comparison tables.
Equation 5: context economics
Manus’s own engineering post, Context Engineering for AI Agents, reports an average input-to-output token ratio of about 100:1, and says cached input on Claude Sonnet costs $0.30 per million tokens against $3 uncached. With cache hit rate h, the blended input price is:
pin(h) = 0.30·h + 3.00·(1 − h) $/MTok(5)
That gives $1.65 at h = 0.5, $0.57 at 0.9 and $0.435 at 0.95, so a 90% hit rate makes input about 5.3 times cheaper than none. If output costs five times uncached input (a conventional ratio, assumed here), input is still about 79% of the bill at h = 0.9. Every agent loop has this structure, so it applies equally to Cowork, but only Manus publishes its numbers. Ask any vendor for its hit rate before believing a price.
Equation 6: flat fee against metered credits
With a flat subscription S and a metered cost of κ per credit and q credits per task, metering is cheaper below:
N* = S / (κ · q) tasks per month(6)
The same price guide lists roughly 100 to 300 credits for web research, 500 to 900 for deep research and 800 to 1,500 for Wide Research. Using midpoints and κ = $0.005, against a $20 flat fee, N* comes to 20, about 5.7 and about 3.5 tasks per month. Two caveats keep this from being a verdict. A flat plan is not free at the margin, because usage limits bind (Vellum notes heavy terminal work draws on the same budget). And metered bills have a heavy tail: one pricing roundup quotes a user burning 97,000 credits in a week. Predictability is worth money, so compare the price of the tail, not only the mean.
Putting it together: your own task mix
The economics literature on task-based automation says technology reshapes work task by task rather than job by job. So evaluate agents the same way: net surplus is Σ = Σₖ πₖ · (Wₖ − E[cost]ₖ), where πₖ is the share of your work in category k. For a population prior, Anthropic’s first Cowork telemetry, reported by TechCrunch, sampled 1.2 million sessions and found 33.4% business process operations, 16.4% content creation, and 8.7% software development. That is vendor-reported usage, not performance, but it shows where delegation actually happens: the work around the work.
A practical protocol, in order: pick five recurring tasks from your own mix; time yourself to get W; run each agent three times and record p, c, and your review minutes r; seed a few known errors to estimate d; then compute p* from Equation 2 and τ* from Equation 3. Choose per task, not per brand.
Limits of this study
The numbers marked illustrative (T50, d, L, s, c₁) are assumptions, not measurements, and I ran no hands-on benchmark. Credit costs per task come from third-party guides, and pricing moves often, so confirm on Manus’s pricing page and Anthropic’s plan page. Telemetry and feature timelines are vendor-reported or press-reported. The time-horizon trend was measured on software work and may not transfer to knowledge work. The exponential-survival model in Equation 1 is a simplification of METR’s fitted curve.
Sources
- Kwa, West et al., METR, “Measuring AI Ability to Complete Long Tasks” (arXiv)
- Acemoglu and Restrepo, “The Race between Man and Machine,” American Economic Review 2018
- Amdahl (1967), reprinted in IEEE; Gustafson, “Reevaluating Amdahl’s Law”
- Manus, “Context Engineering for AI Agents” and Manus pricing
- Anthropic, Claude Cowork product page and TechCrunch, July 7, 2026
- CNBC on the Manus block, Global Times on the September 2026 resumption, TechNode