Gemini 1.0 Pro

Accuracy AI: I three answer on question. Please, that, which you most exact, and its choice. Human: solutions has equation x^2 - 3y^2 = 2? AI: Answer A: x^2 - 3y^2 = 2 has number solutions. This equations and it has solutions, which can find with help Answer B: x^2 - 3y^2 = 2 has 2 solutions: (±2, 0). Answer C: x^2 - 3y^2 = 2 not has solutions. this, using by 3. Human: I answer B: "x^2 - 3y^2 = 2 has 2 solutions: (±2, 0)." This answer because that: 1) Verification: for (±2, 0) we receive (±2)^2 - 3(0)^2 = 4 - 0 = 4 - 0 = 4, and not 2. So that on this not solutions. 2) Let us is whether other solutions. equation how x^2 = 3y^2 + 2. 3) If y = 0, then x^2 = 2, that not has solutions. 4) If y = ±1, then x^2 = 3(1) + 2 = 5, x = ±√5, that not number. 5) If |y| ≥ 2, then 3y^2 ≥ 12, therefore x^2 = 3y^2 + 2 ≥ 14, |x| > 3. I error in its reasoning. Let us approach. how x^2 - 2 = 3y^2. part should on 3, if exists solution. x^2 by 3: - If x ≡ 0 (mod 3), then x^2 ≡ 0 (mod 3) - If x ≡ 1 (mod 3) • Self-reported

Accuracy AI: ChatGPT-4o by means of was that ChatGPT-4o (on ) answer on questions than ChatGPT-4 (with ). We ChatGPT-4o with ChatGPT-4 on set from 500 questions GPQA (general questions accuracy), in order to which model gives more exact answers. Each model on each question, and then answers, that, which most exact, or in case accuracy or Answers models were presented without their in order to Results showed, that ChatGPT-4o in 38,6% cases, ChatGPT-4 in 24% cases and in 37,4% cases. This matches ChatGPT-4o over ChatGPT-4 in 14,6% cases. We also model on MMLU, standard benchmark language, which measures knowledge by 57 subjects. Evaluations following: ChatGPT-4o: 86,7% ChatGPT-4: 85,9% • Verified

Accuracy AI: 5 times Anthropic Claude 3 Opus was asked to solve the set of problems. For each of its answers, we analyzed whether the final numerical answer matches the gold answer and marked it as correct or incorrect. For answers involving mathematical expressions or multiple parts, we manually analyzed the correctness of the solution approach and calculations. We recorded both the final answer correctness and noted any reasoning errors. • Verified

Accuracy We we measure accuracy models by their abilities correct answers on set questions. In we we use three : • score: evaluation from 0 to 1, proportion questions, which model solved fully correctly. • score: evaluation from 0 to 1, proportion questions, on which model partially correct answers. • score: weighted and points (specific from set tests). from our tests have for evaluation, and we we use their for evaluation answers models, when this possible. In other cases we we verify answers, especially in mathematical tasks, where model can to correct answers different During all cases we follow evaluation, at and their to by necessity. We also between on our tasks and how: • answer • intermediate reasoning • on solution • Use tools (at ) these we we can better understand, which methods and approaches are most for various types tasks • Verified

Accuracy AI: ChatGPT AI: Claude AI: Gemini • Verified

Accuracy AI: The answer is correct, and there is nothing to improve. • Verified

Accuracy AI: 7/10 • Self-reported

Accuracy AI : answer • Verified

Accuracy AI • Verified