UniAIBenchresearch benchmark
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University benchmark · Mathematics and physics

AI models put to the teston advanced mathematics and physics.

Source codeUniAIBench

UniAIBench compares 21 model–mode configurations on the same 60 advanced university problems in Mathematical Analysis III and General Physics II, measuring accuracy, response time, cost, and token usage.

21 AI configurations, tested on the same 60 university problems in Mathematical Analysis III and General Physics II. Compare accuracy, time, cost and token use.

Build your ranking ↓Explore the paper PDF ↗
Why does the paper cover 14 configurations?

The paper remains a frozen 14 August 2026 snapshot. The live benchmark later added Mistral Medium 3.5, Mistral Small 4, and DeepSeek V4.1 Flash; GPT-6.1 Sol, GPT-6 Luna, Claude Opus 5.5, and Claude Sonnet 5.5 joined on 15 October 2026. The current site tables and Atlas cover all 21 configurations.

21model-mode configurationsconfigurations60advanced university exercisesexercises2subjects: mathematics + physicssubjects4decision metricsmetrics
Artistic representation of the AI models evaluated by UniAIBench, including the Sol sun, DeepSeek whale, Fable storybook, Mistral logo and provider symbols
UniAIBenchResearch benchmark
Explore results ↓
01

Parameters

Set priorities

Weights always sum to 100%. Changing one automatically redistributes the remainder across the other metrics.

Evaluation scopeAll subjects
Presets
Accuracy

Weight assigned to benchmark correctness.

How does this affect the ranking?
Medium priority. Accuracy matters, but cost or latency can offset small score gaps.
Latency

Weight assigned to response time.

How does this affect the ranking?
Low priority. Latency has limited influence.
Cost

Weight assigned to cost per response.

How does this affect the ranking?
Low priority. Cost has limited influence.
Total tokens

Weight assigned to total token use across the selected exercise scope.

How does this affect the ranking?
Low priority. Token use has limited influence.
Scoring weightsAccuracy 50%Latency 25%Cost 25%Tokens 0%Total: 100%
How is the score calculated?Open the four-metric method

Composite score

Four measurements become one scenario-specific ranking.

The score combines benchmark accuracy with lower latency, cost and token use. It changes when your priorities change; the underlying measurements do not.

01Measure

Use the selected subject’s accuracy, median latency, mean cost per response and total token use.

02Normalize

Convert each metric to a 0–1 scale among the included models. One always means the best observed value.

03Weight and combine

Apply the displayed percentages in a weighted geometric mean, so a weak highly weighted metric cannot be fully hidden.

Current calculationS = 100 × Q0.50 × L0.25 × C0.25 × R0.00Q accuracy · L latency · C cost · R tokens

Relative, not absolute. A score of 80 is not 80% correctness; it is a composite result within this model set.

Lower is better for resources. Latency, cost and tokens are inverted during normalization. Values are floored at 0.01 so the geometric mean remains defined.

02

Weighted result · All subjects

Scenario ranking

Highest composite score for the current scenario
A

Claude Sonnet 5.5

Anthropic

Selection basis

Highest composite score for the current weights.
Score95.3/ 100

The ranking changes with the selected weights and does not establish statistical superiority.

Composite index

Overall ranking

21 configurations
Selected for comparison · 3/4GPT-5.6 Sol · Gemini 3.5 Flash · DeepSeek V4 Flash (no thinking)
Open in Playground →

Base criterion

Accuracy ranking

Mean · higher is better
01Claude Opus 5.5
99.1%
02GPT-6.1 Sol
99.1%
03GPT-5.6 Sol
98.7%
04Claude Sonnet 5.5
98.7%
05GPT-6 Luna
98.5%
06Claude Fable 5
98.0%
07DeepSeek V4 Flash
97.2%
08DeepSeek V4.1 Flash
97.2%
09Gemini 3.1 Pro Preview
97.0%
10Gemini 3.5 Flash
96.9%
11DeepSeek V4 Pro
96.7%
12Grok 4.5
94.6%
13OpenAI o3
92.8%
14Mistral Medium 3.5
87.1%
15DeepSeek V4 Flash (no thinking)
86.3%
16Gemma 4 31B IT
85.6%
17Mistral Small 4
85.6%
18Grok 4.3
85.2%
19OpenAI GPT-4.1
71.6%
20Claude Sonnet 4.5
70.9%
21Claude Haiku 4.5
64.8%

Base criterion

Cost ranking

Mean USD · lower is better
01Gemma 4 31B IT
$0.0000
02DeepSeek V4 Flash (no thinking)
$0.0020
03GPT-6 Luna
$0.0058
04DeepSeek V4 Flash
$0.0064
05Mistral Small 4
$0.011
06DeepSeek V4 Pro
$0.015
07Claude Haiku 4.5
$0.020
08DeepSeek V4.1 Flash
$0.026
09Grok 4.3
$0.026
10OpenAI GPT-4.1
$0.038
11Claude Sonnet 4.5
$0.041
12Grok 4.5
$0.054
13Claude Sonnet 5.5
$0.056
14OpenAI o3
$0.082
15GPT-6.1 Sol
$0.091
16Gemini 3.1 Pro Preview
$0.131
17Gemini 3.5 Flash
$0.142
18Claude Opus 5.5
$0.146
19Mistral Medium 3.5
$0.147
20Claude Fable 5
$0.382
21GPT-5.6 Sol
$0.463

Base criterion

Latency ranking

Median · lower is better
01Claude Haiku 4.5
24.6s
02Claude Sonnet 5.5
34.8s
03DeepSeek V4 Flash (no thinking)
36.6s
04Claude Sonnet 4.5
37.4s
05OpenAI GPT-4.1
39.1s
06Claude Opus 5.5
61.0s
07Gemini 3.5 Flash
61.2s
08OpenAI o3
70.2s
09Grok 4.3
73.7s
10Gemma 4 31B IT
74.8s
11Mistral Small 4
77.6s
12Claude Fable 5
83.5s
13Mistral Medium 3.5
91.1s
14DeepSeek V4.1 Flash
92.2s
15GPT-6 Luna
95.0s
16Grok 4.5
113.8s
17Gemini 3.1 Pro Preview
114.7s
18GPT-6.1 Sol
172.9s
19DeepSeek V4 Flash
188.0s
20DeepSeek V4 Pro
202.4s
21GPT-5.6 Sol
307.0s

Base criterion

Tokens ranking

Selected-scope total · lower is better
01Claude Sonnet 4.5
202.0k
02Gemma 4 31B IT
209.2k
03Claude Haiku 4.5
278.9k
04OpenAI GPT-4.1
311.4k
05Claude Sonnet 5.5
386.6k
06DeepSeek V4 Flash (no thinking)
443.5k
07Claude Opus 5.5
486.6k
08Claude Fable 5
507.4k
09Grok 4.5
576.2k
10GPT-6.1 Sol
576.8k
11OpenAI o3
644.1k
12Grok 4.3
656.1k
13Gemini 3.1 Pro Preview
689.6k
14GPT-6 Luna
732.0k
15GPT-5.6 Sol
958.9k
16Gemini 3.5 Flash
976.2k
17DeepSeek V4 Pro
1066.4k
18Mistral Small 4
1089.5k
19Mistral Medium 3.5
1208.3k
20DeepSeek V4.1 Flash
1331.3k
21DeepSeek V4 Flash
1395.8k
03

Certified common panel

Benchmark evidence

Eight views covering correctness, cost, tokens and response time. All use the same 21-configuration × 60-exercise matched panel.

Correctness

Mean accuracy and uncertainty

Dot = mean · line = 95% bootstrap CI

Overall macro-mean; every exercise has equal weight. The focused 50–100% scale preserves differences among high-performing models.

Correctness profile

Performance across T1–T8

Cell = mean score (%)

ModelT1T2T3T4T5T6T7T8
Claude Opus 5.599.099.299.797.899.699.299.5100.0
GPT-6.1 Sol98.699.799.898.299.198.699.5100.0
GPT-5.6 Sol98.198.899.198.698.898.699.4100.0
Claude Sonnet 5.598.898.399.697.898.697.799.5100.0
GPT-6 Luna98.299.299.495.998.698.699.9100.0
Claude Fable 598.098.197.698.098.498.198.198.6
DeepSeek V4 Flash97.097.497.596.996.397.897.797.9
DeepSeek V4.1 Flash97.998.698.396.298.697.199.099.3
Gemini 3.1 Pro Preview97.097.297.396.696.897.297.397.3
Gemini 3.5 Flash97.497.496.696.196.897.696.898.2
DeepSeek V4 Pro96.597.197.196.196.297.296.1100.0
Grok 4.594.795.594.893.094.294.495.696.8
OpenAI o392.893.994.091.390.993.493.577.0
Mistral Medium 3.588.286.887.587.084.488.687.167.5
DeepSeek V4 Flash (no thinking)88.587.887.581.983.685.088.078.6
Gemma 4 31B IT87.389.185.580.783.386.487.470.7
Mistral Small 486.887.184.983.485.085.188.061.6
Grok 4.387.887.883.679.587.583.988.575.0
OpenAI GPT-4.176.876.470.663.273.067.873.232.7
Claude Sonnet 4.576.675.068.163.573.767.373.827.9
Claude Haiku 4.570.268.561.956.967.361.169.828.0
What do T1–T8 mean? +

T1Understanding / modelling

T2Method selection

T3Development

T4Final results

T5Domains / assumptions

T6Consistency

T7Rigor

T8Independent verification

T1–T8 expose the structure hidden by a single aggregate accuracy value. Darker green indicates stronger performance.

Resource use

Mean cost and uncertainty

Mean per exercise and 60-exercise panel total

Estimated cost uses the benchmark pricing snapshot. Gemma’s configured zero rate is campaign-specific.

Token anatomy

Token composition by model

InputVisible outputReasoningUnseparated output

Totals cover the 60 common exercises. Claude Fable 5 reports output without a visible/reasoning split and is shown separately.

Response time

Typical response-time ranking

Dot = median · line = Q1–Q3 interval

End-to-end time excludes the local queue before dispatch and includes the API call, generation and retries. Total panel time ranges from 25.5m to 12.1h.

Exercise profile

Where response times differ

Cell = model time / exercise median

0.5× faster relative time1.0× exercise median2.0× slower relative timeOutlined cell = retry
Mathematical Analysis III33 exercises
A3 25 P1A3 25 P2A3 25 P3A3 25 P4A3 25 P5A3 26 P1AA3 26 P1BA3 26 P2AA3 26 P2BA3 26 P3A3 26 P4
ModelE1E2E3E1E2E3E1E2E3E1E2E3E1E2E3E1E2E3E1E2E3E1E2E3E1E2E3E1E2E3E1E2E3
01 · Claude Haiku 4.50.30.30.20.30.20.40.30.20.50.30.20.30.40.30.30.50.30.50.60.30.40.30.20.40.30.20.30.40.20.60.40.30.4
02 · Claude Sonnet 5.50.30.31.10.50.40.80.50.40.70.60.40.40.60.40.60.60.40.80.60.40.50.40.40.60.40.40.50.70.30.60.40.40.5
03 · DeepSeek V4 Flash (no thinking)0.40.50.30.51.00.40.62.40.60.60.90.30.40.40.90.60.70.90.60.70.80.51.40.50.60.50.40.70.80.40.40.50.5
04 · Claude Sonnet 4.50.40.30.30.50.20.60.60.40.60.50.40.30.70.40.50.80.50.60.80.90.60.40.20.70.40.30.70.50.30.70.60.50.8
05 · OpenAI GPT-4.10.40.30.20.50.40.41.40.40.50.70.50.50.60.50.50.81.00.81.00.50.70.40.40.60.40.30.50.60.31.90.70.31.0
06 · Claude Opus 5.50.60.52.10.70.71.10.90.70.90.90.80.80.90.70.91.10.80.91.00.71.00.90.61.20.80.61.10.90.61.20.80.70.9
07 · Gemini 3.5 Flash2.31.92.12.23.83.13.23.53.94.35.04.36.06.14.80.70.50.50.80.80.60.60.60.90.60.50.60.90.71.01.00.80.9
08 · OpenAI o30.91.30.50.91.40.62.51.00.60.61.00.81.50.80.50.71.61.71.11.31.81.328.21.30.81.01.00.81.50.60.91.20.8
09 · Grok 4.30.70.70.71.02.20.60.70.90.70.91.21.21.10.90.61.11.00.91.11.00.91.31.01.01.81.01.51.01.31.01.21.61.0
10 · Gemma 4 31B IT0.90.90.61.00.81.01.00.60.91.10.80.81.21.00.61.11.11.11.11.61.51.01.01.51.11.01.21.00.61.01.01.01.3
11 · Mistral Small 40.91.30.80.91.21.00.71.00.90.81.30.40.91.20.81.20.90.90.91.20.81.11.00.90.91.01.51.31.20.951.01.41.1
12 · Claude Fable 52.74.93.11.01.01.41.00.91.01.00.91.11.20.91.01.00.91.01.11.11.21.01.01.21.11.11.017.310.51.322.75.716.3
13 · Mistral Medium 3.51.11.81.00.91.31.01.11.12.11.01.31.31.01.11.30.91.11.11.01.01.00.91.61.01.01.40.90.91.40.80.60.90.6
14 · DeepSeek V4.1 Flash1.40.51.00.90.71.50.81.11.71.10.81.00.91.01.41.00.71.00.90.81.01.20.80.91.21.30.90.91.01.50.71.01.1
15 · GPT-6 Luna1.00.71.71.40.91.80.91.12.31.31.01.10.90.71.20.91.11.41.11.01.20.90.80.91.00.80.81.01.01.31.00.71.2
16 · Grok 4.51.31.10.61.31.91.21.22.91.01.32.61.21.61.21.41.41.41.71.41.41.71.33.24.93.02.21.91.31.80.91.22.41.3
17 · Gemini 3.1 Pro Preview4.42.61.31.01.00.91.11.01.10.90.80.81.01.010.20.90.80.90.91.00.90.90.81.126.320.50.93.50.61.70.82.16.5
18 · GPT-6.1 Sol1.81.02.21.61.72.91.71.53.02.31.52.22.92.01.81.41.92.31.42.92.71.91.51.72.31.61.32.31.62.81.41.32.9
19 · DeepSeek V4 Flash3.61.53.32.81.62.72.22.53.32.42.618.62.41.62.82.52.22.72.92.12.63.32.02.33.52.12.26.22.13.21.71.82.1
20 · DeepSeek V4 Pro2.42.31.51.94.12.02.22.22.41.53.61.02.42.62.53.03.02.63.32.33.12.52.83.54.02.82.13.56.03.22.61.80.9
21 · GPT-5.6 Sol8.85.44.62.32.44.62.82.83.925.12.63.04.12.24.03.42.93.53.83.33.43.72.22.13.32.11.813.76.36.820.121.247.7
General Physics II27 exercises
F2 25 P1F2 25 P2F2 25 P3F2 25 P4F2 25 P5F2 26 P1F2 26 P2F2 26 P3F2 26 P4
ModelE1E2E3E1E2E3E1E2E3E1E2E3E1E2E3E1E2E3E1E2E3E1E2E3E1E2E3
01 · Claude Haiku 4.50.20.30.30.30.20.30.50.30.20.40.50.40.30.20.30.30.40.30.30.30.20.40.20.50.30.30.2
02 · Claude Sonnet 5.50.40.40.50.30.40.50.50.40.30.50.40.50.40.30.40.50.40.40.50.30.50.50.30.40.50.40.4
03 · DeepSeek V4 Flash (no thinking)0.30.50.20.70.40.30.40.60.60.40.60.50.40.40.40.50.30.40.20.30.70.40.30.50.50.30.2
04 · Claude Sonnet 4.50.50.50.50.40.50.40.60.50.30.40.70.50.50.50.60.50.50.60.40.40.40.60.50.60.40.40.3
05 · OpenAI GPT-4.10.60.90.50.50.60.40.80.60.40.40.80.40.60.40.60.70.50.40.70.20.30.60.40.50.40.70.3
06 · Claude Opus 5.50.50.70.70.50.70.90.80.70.40.90.80.90.50.50.60.90.70.80.70.70.60.80.60.80.70.60.8
07 · Gemini 3.5 Flash0.50.80.70.90.90.60.80.60.50.80.80.80.50.50.70.91.08.20.80.50.61.10.51.00.80.80.7
08 · OpenAI o31.90.80.60.50.60.80.90.51.90.61.00.83.30.80.52.30.91.01.51.31.00.70.91.31.00.90.6
09 · Grok 4.30.70.90.71.00.90.91.11.01.00.80.81.40.81.01.21.01.81.20.71.00.51.01.01.11.31.31.7
10 · Gemma 4 31B IT0.80.90.90.91.01.01.20.80.61.11.30.80.91.30.91.11.00.90.80.70.61.00.81.10.91.40.6
11 · Mistral Small 41.11.01.51.01.01.01.21.00.91.21.60.61.11.01.20.91.00.81.01.61.30.81.51.12.21.31.2
12 · Claude Fable 541.831.643.721.540.450.51.00.70.51.00.91.00.70.60.70.90.914.90.90.60.80.80.80.90.70.60.9
13 · Mistral Medium 3.51.01.51.21.01.31.30.91.81.80.92.21.93.21.51.01.33.31.01.22.21.31.81.41.21.31.02.5
14 · DeepSeek V4.1 Flash1.01.31.11.21.21.71.01.11.21.21.11.91.00.81.81.52.60.71.31.01.21.11.11.01.21.11.2
15 · GPT-6 Luna1.01.51.81.02.01.81.61.21.41.40.74.21.11.01.51.31.01.71.21.11.41.01.01.30.91.01.0
16 · Grok 4.51.51.71.01.62.41.81.21.72.41.61.52.01.51.41.51.03.41.01.51.62.71.11.61.01.32.45.4
17 · Gemini 3.1 Pro Preview30.93.671.632.138.330.62.61.41.01.61.813.81.31.61.214.81.31.11.06.313.55.91.11.01.11.61.2
18 · GPT-6.1 Sol1.82.12.51.72.63.63.62.01.62.71.83.61.71.52.13.52.53.72.21.72.23.62.32.31.81.92.4
19 · DeepSeek V4 Flash1.62.01.53.12.41.42.92.61.52.52.02.81.91.41.42.53.72.11.72.72.32.51.71.31.82.32.5
20 · DeepSeek V4 Pro3.42.01.72.16.82.31.52.52.13.02.63.62.02.42.22.32.63.21.32.64.01.02.21.36.63.58.2
21 · GPT-5.6 Sol40.729.160.429.465.341.33.94.22.94.52.55.42.92.03.34.02.64.63.33.12.93.33.44.53.02.84.3

A value of 0.5 means half the exercise’s typical time; 2.0 means twice as long. Normalization controls for exercise difficulty. Outlined cells include retries.

Time drivers

How mean response time is formed

Mean tokens × effective seconds per 1K

Bubble size represents mean response time. Seconds per 1K is an operational ratio including latency, generation and retries—not pure provider throughput.

Accuracy relationship

Response time vs. accuracy

Median time on a logarithmic scale

Key resultLonger response time is associated with higher accuracy, but gains flatten near the accuracy ceiling.Pearson r(log time) = 0.65 · rank correlation ρ = 0.47 · bounded-curve R² = 0.53

Descriptive association across 21 configurations; it does not establish causality.

Overall relationship · better = up + left

20s ← median response time (log scale) → 320s60% ← accuracy → 100%

Accuracy gap from expected trend

Positive gaps indicate more accuracy than expected at the observed median time; negative gaps indicate less.

Specifics

Review methods and benchmark versioning.

Open specifics →