Microsoft Paper: Haiku’s 6.8x Cost Edge Narrows to 3.2x

A cheaper AI model’s cost advantage over an expensive one shrank from 6.8 times to 3.2 times per task on longer agent sessions, according to a Microsoft research paper posted to arXiv on 13 October 2026. The authors write that “cost depends on execution dynamics rather than token prices alone.”

The cheap model was Claude Haiku 4.5, priced at one fifth of GPT-5.6 Sol per input token. On the longer sessions it cost $0.37 a task against $1.18 for Sol, because it made more calls and read more tokens, the paper says.

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What the Paper Tested

The paper, “Whose turn is it? Context-guided model routing for stateful agents,” is by Anikesh Parashar, Avik Dutta, Vashu Chauhan, Sumit Gulwani, Priyanshu Gupta, Hosein Hasanbeig, Vu Le, Ashish Tiwari and Jack Williams, all listed under Microsoft. It is marked as a preprint.

The authors study routing for agents that work over many turns: before each user turn, a router decides whether a cheap or an expensive model handles it. They test this on multi-turn versions of two spreadsheet benchmarks, SheetCopilot and SpreadsheetBench 2.

They test three pairs: GPT-5.6 Sol against GPT-5.6 Luna, GPT-5.6 Sol against Claude Haiku 4.5, and Claude Opus 4.8 at high against low reasoning effort. GPT-5.6 Luna serves as the router in every condition, the paper says.

The tasks are hard for current models. Frontier models that lead software-engineering benchmarks pass at most 31.2% of the multi-turn SheetCopilot tasks, the authors write.

What Was Posted on X

DAIR.AI, which curates AI research papers, posted a summary of the Microsoft paper on 16 October 2026. It highlights the router that reads the session history, the cost of switching models under prompt caching, and the cheap model’s cost advantage shrinking from 6.8x to 3.2x on longer sessions. This piece reads the paper itself for every figure.

Cheap per Token, Not per Task

On the longer SpreadsheetBench 2 sessions, Haiku 4.5 takes about 41 model calls and 1.6 million input tokens per conversation, against about 25 calls and 0.9 million tokens for the other models, according to the paper.

That is why it costs only 3.2 times less than Sol per task, $0.37 against $1.18, while passing 16.4% of tasks rather than 27.1%, the authors write.

On SheetCopilot’s shorter sessions, 2.9 turns on average, Haiku uses about as many calls as Sol, 13.6 against 14.1, and is 6.8 times cheaper per task, above the 5 times list-price ratio. On SpreadsheetBench 2’s 4.8-turn sessions its discount falls to 3.2 times, the paper says.

The reason is that every call re-reads the session so far. The mean context per call roughly doubles, from about 18,000 tokens on SheetCopilot to about 38,000 on SpreadsheetBench 2, so extra calls cost more the longer the session runs, according to the paper.

Not every pair behaves that way. GPT-5.6 Luna’s discount against Sol holds at 5.6 to 6.1 times, and the gap between Opus 4.8 at high and low effort widens from 1.4 times to 1.9 times, the authors write.

On SpreadsheetBench 2, Luna keeps Sol’s call budget of 26 calls and costs about half as much as Haiku, $0.19, with a pass rate 6.3 points higher. The authors write: “The cheap candidate should therefore be chosen by its realized cost per task on the target workload, not by its list price.”

Session History Changes Which Turns Go Cheap

The paper’s second result is about quality. Two routers sent nearly the same share of turns to the cheap model, 23.3% without the session history and 22.7% with it. The one that read the history passed 28.3% of tasks against 25.0%, the authors write.

The 3.3-point gain held in every pair: 5.4 points for Sol and Haiku, 2.7 for Sol and Luna, and 1.7 for Opus at high and low effort. Because the share sent to the cheap model was matched, the gain comes from which turns are sent there, the paper says.

On SheetCopilot, always using the expensive model passed 27.7% of tasks and always using the cheap one 26.8%. The history-aware router passed 28.3% while sending 21.1% to 24.2% of turns to the cheap model, according to the paper.

On SpreadsheetBench 2, the same router used the cheap model on only 0.4% to 1.7% of turns and passed 29.3%, the same as always using the expensive model, the authors write.

What Routing Saved, and What It Did Not

The paper reports exact routed costs for one pair only, Opus 4.8 at high and low effort. There, the router cost $0.369 per task against $0.365 for always using the expensive setting on SheetCopilot, and $2.080 against $2.009 on SpreadsheetBench 2.

In some pairs, the cheap model alone is the better choice, the paper says. Luna alone passed 28.6% of SheetCopilot tasks at $0.061 per task run, against 26.8% for the router with history, according to the paper.

The authors write that choosing the pair “matters as much as routing within it.”

The Cache Cost of Switching

Switching models mid-session gives up the prompt cache the previous model built. The paper’s cache analysis finds that “downward switches (expensive to cheap) recover their cache cost within two LLM calls, whereas upward switches do not break even under the evaluated conditions.”

At the prices used in the paper, a switch from Sol to Luna or to Haiku pays for itself after 1.25 calls on the new model, the authors write.

Where This Sits

The paper is research and does not set a price. As we read it, it lands as the cost of using AI models becomes a question for buyers: Microsoft is building its own 2.8T-parameter model, and Accenture caps Claude funding at $29 a month per employee, as we reported.

The Structural Read

As we read it, list price is an input, not the bill: the paper finds the per-task gap depends on how many calls a model makes and how much context each call carries, which roughly doubles from about 18,000 to about 38,000 tokens between the two benchmarks.

As we read it, the router’s value in this paper is quality at a matched share of cheap turns rather than a lower bill: with the history it passed 28.3% of tasks against 25.0% without, while in the one pair with exact routed costs the router cost slightly more than the expensive setting.

As we read it, choosing the pair is the larger decision: the authors write that it “matters as much as routing within it,” and GPT-5.6 Luna alone passed 28.6% of SheetCopilot tasks at $0.061 per task run.

Three Implications

TEAMS BUYING MODELS The authors write that the cheap candidate should be chosen by its realized cost per task on the target workload, not by its list price.

AGENT BUILDERS Switching from the expensive model to the cheap one recovered its cache cost within two calls in the paper’s analysis, while switching up did not break even under the conditions tested.

ROUTER DESIGNERS Giving the router the session history raised the pass rate in every pair tested, by 5.4, 2.7 and 1.7 points, at a matched share of turns sent to the cheap model, the paper says.

The Business Engineer Lens

This story maps onto the Business Engineer framework The CFO’s Guide to the Token Economy.

The framework’s core claim is that “The cost of intelligence is collapsing while the cost of deploying intelligence is exploding.”

As we read it, the Microsoft paper measures one way that happens inside a single agent: a model one fifth the price per token cost only 3.2 times less per task on longer sessions. The framework predates the paper and does not discuss it or model routing.

What Is Not Established

The paper is a preprint and tests spreadsheet agents only. The 6.8 times and 3.2 times figures come from two benchmarks that also differ in workbook size and domain, so the authors call that comparison “descriptive.”

In what we read, the paper does not tie the method to a Microsoft product. In the only pair with exact routed costs, the router cost slightly more per task than always using the expensive setting.

The Bottom Line

A Microsoft paper finds that Claude Haiku 4.5’s per-task cost advantage over GPT-5.6 Sol narrowed from 6.8 times to 3.2 times on longer spreadsheet-agent sessions, because it made more calls that each re-read a growing context.

The same paper finds that a router given the session history passed 28.3% of tasks against 25.0% without it, at nearly the same share of turns sent to the cheap model.