Paired comparison

Sixty exercises under the same conditions

The comparison covers 60 exercises answered by both models: 33 from Mathematical Analysis III and 27 from General Physics II. Every pair uses the same problem statement and prompt, thinking enabled with high reasoning effort, the same maximum-output limit, and identical approved and frozen rubrics.

This is therefore a paired design. For each exercise, the Flash answer is compared directly with the Pro answer rather than with an unrelated aggregate.

60

Common exercises

33 + 27

Analysis III and Physics II

1:1

Directly paired answers

Accuracy

No detectable accuracy advantage in this panel

IndicatorV4 FlashV4 Pro
Exercises6060
Mean score97.2496.71
Median score100100
100/100 responses4236
Standard deviation9.177.12
Minimum score42.5064.75
Responses with no atomic errors4236
Major or fatal errors78

Flash scores 0.52 percentage points higher in the observed panel, but this difference is too small relative to the observed variability to conclude that Flash is intrinsically more accurate.

16Exercises won by FlashDirect pairwise comparison
35TiesMore than half the sample
9Exercises won by ProDirect pairwise comparison

After excluding ties, the two-sided sign test gives p = 0.230. The approximate 95% bootstrap confidence interval for the mean paired difference runs from −0.76 to +1.78 points and includes zero.

This benchmark reveals no statistically distinguishable accuracy advantage for DeepSeek V4 Pro over V4 Flash.

The result is stable across disciplines.

SubjectV4 FlashV4 ProDifference
Mathematical Analysis III97.1096.57+0.53
General Physics II97.4196.89+0.52

Data & methodDownload the comparison summary CSV ↗ and the exercise-score CSV ↗. Tests use the 60 within-exercise pairs described in the method ↗.

The near identity of the two subject-level differences matters: the overall tie is not produced by one model winning in mathematics while the other compensates in physics.

Generation profile

Flash reasons longer but answers more briefly

Equivalent scores do not imply identical generation behavior.

Mean tokens per exerciseV4 FlashV4 ProFlash difference
Reasoning20,10614,345+40.2%
Visible answer2,4052,755−12.7%
Total output22,51117,100+31.6%

Data & methodDownload the table summary CSV ↗ and the token-and-cost CSV ↗.

Flash uses about 5,761 additional reported reasoning tokens yet returns a final answer roughly 350 tokens shorter. The observed token allocation differs between the configurations; it does not by itself identify the underlying computational cause.

DeepSeek reports 13 billion active parameters for V4 Flash and 49 billion for V4 Pro, with 284 billion and 1.6 trillion total parameters respectively. The provider explicitly presents Flash as its smaller, lower-cost variant with reasoning capability close to Pro. See the DeepSeek V4 release note ↗.

Measurement limit. Token counts do not directly measure FLOPs, energy use or actual computation, especially across different Mixture-of-Experts architectures. They describe output allocation, not the full physical cost of inference.

The result is nevertheless consistent with work on test-time compute: in some regimes, an effective inference-time allocation can recover part of the gap associated with model scale. See Scaling LLM Test-Time Compute Optimally ↗.

Price efficiency

The real separation is economic

The run metadata preserves the pricing snapshot used for these estimates, captured on 10 Aug 2026.

Price per million tokensV4 FlashV4 Pro
Uncached input$0.14$0.435
Output$0.28$0.87

The provider's current Models & Pricing page ↗ may differ from that historical snapshot. Applying the recorded rates to observed consumption produces:

Estimated costV4 FlashV4 Pro
Mean per exercise$0.00641$0.01517
Total across 60 runs$0.3845$0.9102

Data & methodDownload the historical rate and comparison CSV ↗ and the run-derived token-and-cost CSV ↗.

57.8%lower estimated cost for V4 Flash

Despite producing 31.6% more total output tokens.

Flash scores 0.52 percentage points higher in the observed panel while using only 42.2% of Pro's estimated cost.

Mean latency is also slightly lower—227 seconds versus 244—but the timing result is much less stable. Flash is faster in 33 pairs and slower in 27, so the evidence does not support a latency advantage as clear as the economic one.

Risk profile

Equal means, different distributions

The average tie hides a difference in the shape of errors. Flash produces more perfect solutions—42 against 36—and fewer atomic errors overall—29 against 40.

Pro, however, has a more controlled lower tail: its minimum is 64.75 rather than 42.50, its standard deviation is 7.12 rather than 9.17, and it produces no fatal errors compared with one from Flash.

FlashMore perfect answersBut a small probability of severe failure
ProMore regular lower tailWithout a higher mean score

This distinction matters operationally. If every severe error triggers human review, mean accuracy alone is insufficient: the loss distribution and the cost of the negative tail must also enter the decision.

Conclusion

A commercial tier is not a utility metric

On this sample, DeepSeek V4 Pro provides no detectable accuracy improvement over V4 Flash. Flash uses more reasoning tokens and is slightly more variable, but reaches the same mean correctness, produces more perfect solutions, returns shorter final answers and costs about 58% less.

The result does not prove that Flash is universally superior. It establishes a more useful principle:

For university-level mathematical reasoning, capacity, test-time compute, reliability and cost must be evaluated separately.

References

Sources and further reading

Pricing note. Cost figures are historical estimates based on the rates recorded with the benchmark runs. Provider prices, peak/off-peak rules, exchange rates and subscription limits can change; current commercial pages may therefore differ from the archived snapshot.