For physical AI — modeling and simulation work where the model has to get the underlying physics right, not just produce code that runs — Claude Fable 5 currently scores highest on accuracy, while OpenAI's GPT-5.6 Sol and Terra get close for a fraction of the cost and in less time. Which one is "best" depends on whether you're optimizing for correctness or for throughput.
Short answer: On a controlled physical AI benchmark, Claude Fable 5 scored 0.889 on accuracy versus GPT-5.6 Sol's 0.814 and Terra's 0.786 — but Fable 5 cost $9.60 per trial against Sol's $1.74 and Terra's $1.25, and ran slower. Fable 5 wins on correctness; Sol and Terra win on value and speed.
"Physical AI" gets used loosely, so here's the specific bar this piece holds both models to: can the model derive equations of motion, thermodynamic behavior, or trajectory physics that are actually correct, not just code that compiles and runs. In my testing of this piece, I pulled the numbers below directly from a controlled study published by JuliaHub's modeling and simulation team on July 30, 2026, and cross-checked every price against OpenAI's and Anthropic's own current numbers rather than trusting aggregator sites, which tend to lag or round launch-week figures. Here's what the data actually shows, and how to decide which model fits your use case.
What you'll need
To reproduce this comparison yourself, or just to run your own physical AI task through either model, you need an OpenAI API account for GPT-5.6 (available in three tiers — Luna, Terra, and Sol — since the July 9, 2026 launch) and an Anthropic Claude API account for Fable 5, which has been generally available since June 9, 2026 under the model ID claude-fable-5. You'll also want a way to grade output against ground truth rather than just "did it run" — the study this article draws from used the Dyad AI agent harness, purpose-built for modeling and simulation workflows, with a fixed 1M-token context window and 128k-token budget held constant across every model so the comparison measured model skill, not harness generosity.
Step-by-step: figuring out which model actually wins for your task
1. Decide what "correct" means for your problem
A simulated aircraft, distillation column, or charged-particle model can compile and run cleanly while the physics it encodes is flat-out wrong. If your use case needs to catch that — engineering, research, anything with real-world consequences — accuracy against sealed ground truth is the metric that matters, not "did the code execute."
2. Match the benchmark to the task, not just the model
The JuliaHub study's most striking finding wasn't about GPT-5.6 or Fable 5 specifically — it was that the same frontier model scored 0.899 inside the Dyad harness and only 0.533 on a stock coding agent given the identical problem. Harness and tooling moved the score more than model choice did. Don't take a general coding leaderboard number and assume it predicts physical AI performance.
3. Compare accuracy at a fixed reasoning effort and token budget
With context window, reasoning effort, and token budget held constant, Fable 5 posted a difficulty-weighted accuracy of 0.889 across five sealed problems (three trials each on the first four, one long-horizon trial on a NASA HL-20-style flight-vehicle problem), the only model to sweep the core problem set cleanly. GPT-5.6 Sol came in at 0.814, Terra at 0.786, and the budget Luna tier at 0.727.
4. Compare cost per completed task, not sticker price per token
Fable 5's per-token price is the highest of the group, and that shows up directly in cost per trial: $9.60, roughly 3–8x what the GPT-5.6 variants cost to run the same problem. Sol came in at $1.74 per trial and Terra at $1.25 — the cheapest of the four.
5. Factor in speed if you're running many trials
Terra finished in 12.6 minutes on average, Sol in 13.4, Fable 5 in 16.1, and Luna trailed at 25.0 minutes. If you're iterating on a design and running dozens of trials a day, that gap compounds fast.
6. Pick based on your actual constraint
If a wrong answer is expensive — flight hardware, safety-critical simulation, published research — Fable 5's accuracy edge is worth the extra cost. If you're doing exploratory modeling, early-stage design iteration, or running high trial volumes on a budget, Sol or Terra get within a few points of Fable 5's accuracy for a fifth of the price.
Example prompts you can copy
These follow the shape of the sealed problems in the JuliaHub study — physics-heavy modeling tasks where a wrong derivation looks identical to a right one until you check it against ground truth:
- "Derive the equations of motion for a rigid-body aircraft undergoing a coordinated turn, then simulate a 60-second trajectory and flag any step where energy isn't conserved within 1%."
- "Model a binary distillation column with feed composition [X], reflux ratio [Y], and N theoretical trays. Report vapor and liquid compositions at each stage, and state your assumptions explicitly."
- "Simulate the trajectory of a charged particle entering a non-uniform magnetic field at [velocity/angle]. Show the governing equations before the code, not just the code."
- "Here's a reentry vehicle's mass, drag coefficient, and initial reentry angle [paste]. Model deceleration and peak heating, and tell me which of your assumptions would break first under real atmospheric variation."
- "Run the same physical model twice at different reasoning effort settings and diff the two outputs — tell me if the cheaper run changed the physics or just the write-up."
Common mistakes to avoid
The mistake I'd flag first: treating "the code ran without an error" as evidence the model got the physics right. Runnable and correct are different bars, and only the second one matters for physical AI. Second, comparing models on sticker price per million tokens instead of cost per completed, graded task — Fable 5's higher per-token rate doesn't tell you it costs 5–8x more per trial until you actually measure trial cost, which the JuliaHub numbers above do. Third, letting context window or reasoning effort vary between the models you're comparing; if one model gets more budget than the other, you're benchmarking the harness, not the model. Fourth, assuming a general coding or agentic benchmark score predicts physical AI performance — the harness-vs-stock-agent gap in this study (0.899 vs 0.533 on the same model) shows how much that assumption can mislead you. Fifth, picking Luna by default because it's cheapest per token — in this study it was both the least accurate and the slowest of the four, so it lost on every axis except sticker price.
GPT-5.6 vs. Claude Fable 5 for physical AI at a glance
| Model | Accuracy (Dyad harness, weighted) | Cost per trial | Speed per trial | API price ($/M tokens, in/out) |
|---|---|---|---|---|
| Claude Fable 5 | 0.889 (highest) | $9.60 | 16.1 min | $10 / $50 |
| GPT-5.6 Sol | 0.814 | $1.74 | 13.4 min | $5 / $30 |
| GPT-5.6 Terra | 0.786 | $1.25 (cheapest) | 12.6 min (fastest) | $2.50 / $15 |
| GPT-5.6 Luna | 0.727 (lowest) | $3.26 | 25.0 min (slowest) | $1 / $6 |
Prices confirmed against Anthropic’s own models overview and OpenAI's launch-week pricing as reported by TechCrunch on July 9, 2026. Accuracy, cost-per-trial, and speed figures come from JuliaHub’s Dyad harness study, published July 30, 2026.
This same physical AI question shows up in general coding rankings too, though the numbers there tell a different story: on OpenAI's own coding benchmark citation, Sol scores 2.8 points above Fable 5 while using under half the output tokens — a reminder that "best model" swings hard depending on whether you're grading code-that-runs or physics-that's-correct. If you want the general-purpose picture rather than the physical AI one, Claude Opus 5 covers how Anthropic's mid-tier model stacks up against Fable 5 on price and coding benchmarks specifically.
Tools that make this easier
If you're deciding which frontier model to standardize on beyond just physical AI work, Claude vs ChatGPT covers the everyday writing-and-coding comparison between Anthropic and OpenAI's consumer tools, and Grok 4.5: pricing, benchmarks, and setup guide adds a third vendor if you're comparing across the whole field rather than just these two. For coding specifically — where GPT-5.6 Sol and Claude Fable 5 also go head to head — see best AI tool for code and ChatGPT alternatives for coding. My starter kit for AI is the place to start if you haven't set up API accounts with either vendor yet, and how we rate AI tools explains the scoring approach behind comparisons like this one.
Where this leaves you
Neither model "wins" outright — they win at different jobs. Claude Fable 5 is the model to reach for when a wrong physics derivation is expensive to be wrong about: it was the only model in this study to sweep the core problem set, and that accuracy gap is real even after accounting for its higher per-token price. GPT-5.6 Sol is the better default for everyday physical AI work where you're iterating fast and a few accuracy points aren't worth 5x the cost — Terra is worth trying first if budget and speed matter more than squeezing out the last bit of accuracy. Luna, in this specific study, didn't win on any axis; it's better suited to lighter, non-physics agentic tasks than modeling and simulation work.
Last updated: July 31, 2026 · By Vishal Swami, Founder & Lead AI Reviewer, AISagely
Frequently Asked Questions
Is GPT-5.6 or Claude Fable 5 free to test?
Neither has a free tier for API access — both are pay-per-token. Claude Fable 5 runs $10/$50 per million input/output tokens; GPT-5.6 Sol is $5/$30, Terra is $2.50/$15, and the budget Luna tier is $1/$6. You can try Fable 5 through a Claude.ai subscription and GPT-5.6 through a ChatGPT Plus subscription without touching the API directly.
Which model actually performs best for physical AI?
On a controlled benchmark with context window and token budget held equal, Claude Fable 5 scored highest on accuracy (0.889) and was the only model to cleanly sweep the core problem set. GPT-5.6 Sol and Terra scored close behind (0.814 and 0.786) at roughly a fifth of the cost per trial, so "best" depends on whether accuracy or cost efficiency is your priority.
How much does it cost to run a physical AI evaluation with each model?
In the JuliaHub study, per-trial cost was $9.60 for Fable 5, $3.26 for Luna, $1.74 for Sol, and $1.25 for Terra. Cost per trial doesn't track cleanly with per-token price alone, since token usage and reasoning depth also vary by model.
Does GPT-5.6 Sol beat Claude Fable 5 outside of physical AI, like coding?
On OpenAI's own coding benchmark citation, Sol scored 2.8 points above Fable 5 using under half the output tokens and about a third of the cost. That's a different task category than the physics-derivation problems in the physical AI study above, so the two results aren't directly comparable.
Which one should I use for a robotics or simulation product?
If a wrong physics answer could cost real money or safety margin, start with Claude Fable 5 despite the higher price — its accuracy lead held up on the hardest long-horizon problem in the study. For early-stage design iteration where you're running high trial volumes and reviewing results yourself, GPT-5.6 Terra or Sol get close enough to Fable 5's accuracy at a fraction of the cost to be the more practical daily driver.