Phase 1 & 2: Baseline experiments + AGoT implementation + reasoning graph analysis

## Added

### Core framework
- src/llm_client.py — Ollama API wrapper for local Docker inference
- src/samples.py — Embedded benchmark datasets (GSM8K/MATH/AIME + Chinese)
- src/run_all.py — Unified experiment runner

### Phase 1: Baselines
- src/baseline/benchmark.py — IO, CoT, CoT-SC, ToT evaluation with Chinese support

### Phase 2: AGoT
- src/agot/agot.py — AGoT core algorithm (6 agent types, recursive decomposition)
- src/agot/graph_utils.py — DAG graph data structure with cycle detection
- src/agot/prompts.py — 6 agent prompt templates (EN + ZH)
- src/agot/run.py — AGoT experiment runner

### Graph Analysis
- src/graph_analysis/reasoning_graph.py — Graph property computation (cyclicity, diameter, small-world)
- src/graph_analysis/visualize.py — Visualization charts

### Documentation
- docs/graph_reasoning_principles.md — Comprehensive principles document
- docs/next_steps.md — Roadmap for reliable reasoning tool

### Experiment Results
- GSM8K/MATH baselines on qwen2.5:32b and qwq:latest
- AGoT validation (100% on small sample)
- Chinese dataset benchmarks (C-GSM8K, CMATH)
- Graph property analysis confirming Topology of Reasoning findings

data/results/c_gsm8k_CoT_qwen2.5_32b_20260703_182254.json

@@ -0,0 +1,58 @@
+{
+  "summary": {
+    "method": "CoT",
+    "model": "qwen2.5:32b",
+    "task": "c_gsm8k",
+    "samples": 5,
+    "correct": 5,
+    "accuracy": 1.0,
+    "avg_time_s": 24.78
+  },
+  "details": [
+    {
+      "question": "小明有 12 个苹果，他给了小红 5 个，又给了小刚 3 个。请问小明还剩下几个苹果？",
+      "expected": "4",
+      "predicted": "4",
+      "full_response": "首先，我们确定小明初始拥有的苹果数量为 12 个。\n\n接着，小明给小红的苹果数是 5 个，因此我们可以从小明原有的苹果中减去这 5 个。计算如下：\n\n\\[12 - 5 = 7\\]\n\n这意味着在给了小红之后，小明还剩下 7 个苹果。\n\n然后，小明又给了小刚 3 个苹果。我们再从剩下的苹果数中减去这 3 个。计算如下：\n\n\\[7 - 3 = 4\\]\n\n所以，在给完小红和小刚之后，小明最后剩下的苹果数量是 \\boxed{4}。",
+      "correct": true,
+      "time_s": 15.32,
+      "tokens": 71
+    },
+    {
+      "question": "一个长方形的长是 8 厘米，宽是 5 厘米。如果长增加 2 厘米，宽不变，新的长方形面积比原来的大多少平方厘米？",
+      "expected": "10",
+      "predicted": "10",
+      "full_response": "首先，我们计算原始长方形的面积。\n\n原始长方形的长为 \\(8\\) 厘米，宽为 \\(5\\) 厘米。因此，原始面积是：\n\\[ \\text{原始面积} = 8 \\times 5 = 40 \\, \\text{平方厘米} \\]\n\n接下来，我们考虑长增加后的新的尺寸。\n\n新长方形的长变为 \\(8 + 2 = 10\\) 厘米，宽保持不变为 \\(5\\) 厘米。因此，新的面积是：\n\\[ \\text{新面积} = 10 \\times 5 = 50 \\, \\text{平方厘米} \\]\n\n最后，我们计算两个面积之间的差值来确定增加的面积。\n\n\\[ \\text{面积增加量} = \\text{新面积} - \\text{原始面积} = 50 - 40 = 10 \\, \\text{平方厘米} \\]\n\n所以，新的长方形面积比原来的大了 \\(\\boxed{10}\\) 平方厘米。",
+      "correct": true,
+      "time_s": 24.47,
+      "tokens": 126
+    },
+    {
+      "question": "超市里一瓶牛奶卖 6 元，一袋面包卖 4 元。小华买了 3 瓶牛奶和 2 袋面包，付了 50 元，请问应找回多少元？",
+      "expected": "24",
+      "predicted": "24",
+      "full_response": "首先计算小华购买的总费用。\n\n1. 小华买了 3 瓶牛奶，每瓶牛奶的价格是 6 元。因此，牛奶的总价为 \\(3 \\times 6 = 18\\) 元。\n2. 小华还买了 2 袋面包，每袋面包的价格是 4 元。所以，面包的总价为 \\(2 \\times 4 = 8\\) 元。\n\n接下来，计算小华购买所有物品的总费用：\n\\[牛奶总价 + 面包总价 = 18元 + 8元 = 26元\\]\n\n最后，根据题目中小华付了 50 元，我们来计算应该找回多少元。\n\\[找回金额 = 小华支付的金额 - 购买总费用 = 50元 - 26元 = 24元\\]\n\n所以，应找回 \\(\\boxed{24}\\) 元。",
+      "correct": true,
+      "time_s": 21.21,
+      "tokens": 98
+    },
+    {
+      "question": "一本书有 200 页，小明第一天看了全书的 1/4，第二天看了余下的 1/3。请问小明两天一共看了多少页？",
+      "expected": "100",
+      "predicted": "100",
+      "full_response": "首先，我们计算出小明第一天看的页数：\n\n- 全书共有 200 页。\n- 小明第一天看了全书的 \\(\\frac{1}{4}\\)，即 \\(200 \\times \\frac{1}{4} = 50\\) 页。\n\n接着，我们计算出小明第二天看的页数：\n\n- 第一天之后剩余的页数为 \\(200 - 50 = 150\\) 页。\n- 小明第二天看了余下的 \\(\\frac{1}{3}\\)，即 \\(150 \\times \\frac{1}{3} = 50\\) 页。\n\n最后，我们计算小明两天一共看的页数：\n\n- 第一天和第二天总共看了 \\(50 + 50 = 100\\) 页。\n\n所以，答案是 \\(\\boxed{100}\\)。",
+      "correct": true,
+      "time_s": 20.15,
+      "tokens": 102
+    },
+    {
+      "question": "一个水池有甲、乙两个进水管。单开甲管 6 小时可以注满水池，单开乙管 8 小时可以注满水池。如果两管同时开放，多少小时可以注满水池？",
+      "expected": "24/7",
+      "predicted": "\\frac{24}{7}",
+      "full_response": "首先，我们来分析每个管道单独工作时的效率。\n\n1. **甲管的工作效率**：\n   - 单独使用甲管可以在 6 小时内将水池注满。\n   - 因此，甲管每小时可以注满 \\(\\frac{1}{6}\\) 的水池。\n\n2. **乙管的工作效率**：\n   - 单独使用乙管可以在 8 小时内将水池注满。\n   - 因此，乙管每小时可以注满 \\(\\frac{1}{8}\\) 的水池。\n\n3. **两管同时工作时的总工作效率**：\n   - 当甲、乙两个管道同时开启时，它们每小时共同可以注满 \\(\\frac{1}{6} + \\frac{1}{8}\\) 的水池。\n   - 计算这个和：\\[\n     \\frac{1}{6} + \\frac{1}{8} = \\frac{4}{24} + \\frac{3}{24} = \\frac{7}{24}\n     \\]\n   - 所以，两管同时工作时每小时可以注满水池的 \\(\\frac{7}{24}\\)。\n\n4. **计算所需时间**：\n   - 如果两管同时开启，它们每小时可以完成 \\(\\frac{7}{24}\\) 的工作量。\n   - 要完全填满整个水池（即完成 1 单位的工作），需要的时间 \\(T\\) 满足：\\[\n     T \\times \\frac{7}{24} = 1\n     \\]\n   - 解这个方程得到：\\[\n     T = \\frac{24}{7}\n     \\]\n\n因此，两管同时开放时注满水池需要的时间是 \\(\\boxed{\\frac{24}{7}}\\) 小时。",
+      "correct": true,
+      "time_s": 42.74,
+      "tokens": 222
+    }
+  ]
+}

data/results/c_gsm8k_IO_qwen2.5_32b_20260703_182050.json

@@ -0,0 +1,58 @@
+{
+  "summary": {
+    "method": "IO",
+    "model": "qwen2.5:32b",
+    "task": "c_gsm8k",
+    "samples": 5,
+    "correct": 3,
+    "accuracy": 0.6,
+    "avg_time_s": 3.23
+  },
+  "details": [
+    {
+      "question": "小明有 12 个苹果，他给了小红 5 个，又给了小刚 3 个。请问小明还剩下几个苹果？",
+      "expected": "4",
+      "predicted": "4",
+      "full_response": "4个苹果",
+      "correct": true,
+      "time_s": 11.31,
+      "tokens": 2
+    },
+    {
+      "question": "一个长方形的长是 8 厘米，宽是 5 厘米。如果长增加 2 厘米，宽不变，新的长方形面积比原来的大多少平方厘米？",
+      "expected": "10",
+      "predicted": "10",
+      "full_response": "10 平方厘米",
+      "correct": true,
+      "time_s": 0.95,
+      "tokens": 3
+    },
+    {
+      "question": "超市里一瓶牛奶卖 6 元，一袋面包卖 4 元。小华买了 3 瓶牛奶和 2 袋面包，付了 50 元，请问应找回多少元？",
+      "expected": "24",
+      "predicted": "28",
+      "full_response": "28元",
+      "correct": false,
+      "time_s": 0.57,
+      "tokens": 2
+    },
+    {
+      "question": "一本书有 200 页，小明第一天看了全书的 1/4，第二天看了余下的 1/3。请问小明两天一共看了多少页？",
+      "expected": "100",
+      "predicted": "100",
+      "full_response": "100页",
+      "correct": true,
+      "time_s": 0.67,
+      "tokens": 2
+    },
+    {
+      "question": "一个水池有甲、乙两个进水管。单开甲管 6 小时可以注满水池，单开乙管 8 小时可以注满水池。如果两管同时开放，多少小时可以注满水池？",
+      "expected": "24/7",
+      "predicted": "3.43",
+      "full_response": "3.42857142857小时，约等于3.43小时。",
+      "correct": false,
+      "time_s": 2.63,
+      "tokens": 9
+    }
+  ]
+}

data/results/cmath_CoT_qwen2.5_32b_20260703_183401.json

@@ -0,0 +1,40 @@
+{
+  "summary": {
+    "method": "CoT",
+    "model": "qwen2.5:32b",
+    "task": "cmath",
+    "samples": 3,
+    "correct": 2,
+    "accuracy": 0.6667,
+    "avg_time_s": 41.49
+  },
+  "details": [
+    {
+      "question": "已知函数 $f(x) = 2x^2 - 4x + 1$，求 $f(x)$ 的最小值。",
+      "expected": "-1",
+      "predicted": "-1",
+      "full_response": "要找到二次函数 $f(x) = 2x^2 - 4x + 1$ 的最小值，我们可以使用顶点公式或完成平方的方法。这里我们采用完成平方的方法来解决这个问题。\n\n首先，将给定的函数写为：\n\\[ f(x) = 2x^2 - 4x + 1 \\]\n\n为了完成平方，我们需要关注 $2x^2 - 4x$ 这一部分。由于系数不是1，我们可以先提取公因子2：\n\\[ f(x) = 2(x^2 - 2x) + 1 \\]\n\n接下来，我们对括号内的表达式进行补全平方。为了完成这个过程，我们需要找到一个数，使得 $x^2 - 2x$ 加上这个数后成为一个完全平方形式。我们知道，对于形如 $ax^2 + bx$ 的表达式，要使其成为完全平方，需要加上 $(\\frac{b}{2})^2$。\n\n因此，在这里我们有：\n\\[ x^2 - 2x \\]\n为了补全平方，我们需要加上的数是 $(\\frac{-2}{2})^2 = (-1)^2 = 1$。但是因为我们是从 $f(x)$ 中提取了因子2，所以实际上我们在括号内加上1后需要同时减去它以保持等式的平衡：\n\\[ f(x) = 2(x^2 - 2x + 1 - 1) + 1 \\]\n\\[ f(x) = 2((x-1)^2 - 1) + 1 \\]\n\n现在，我们可以重新整理这个表达式：\n\\[ f(x) = 2(x-1)^2 - 2 + 1 \\]\n\\[ f(x) = 2(x-1)^2 - 1 \\]\n\n由于 $(x-1)^2$ 的最小值为0（当 $x=1$ 时），因此整个表达式的最小值发生在 $(x-1)^2 = 0$，即：\n\\[ f_{\\text{min}}(x) = 2*0 - 1 = -1 \\]\n\n所以，函数 $f(x)$ 的最小值是 $\\boxed{-1}$。",
+      "correct": true,
+      "time_s": 49.05,
+      "tokens": 249
+    },
+    {
+      "question": "在等差数列 $\\{a_n\\}$ 中，$a_1 = 3$，$a_3 + a_5 = 22$，求 $a_7$ 的值。",
+      "expected": "25",
+      "predicted": "19",
+      "full_response": "首先，我们知道等差数列的通项公式为：\n\\[a_n = a_1 + (n-1)d\\]\n其中，$d$ 是公差。根据题目给出的信息：\n\n1. 第一项 $a_1 = 3$。\n2. 第三项和第五项之和等于22，即 $a_3 + a_5 = 22$。\n\n我们可以用通项公式来表示 $a_3$ 和 $a_5$：\n\\[a_3 = a_1 + 2d\\]\n\\[a_5 = a_1 + 4d\\]\n\n将已知的 $a_1 = 3$ 值代入上述两个等式中，得到：\n\\[a_3 = 3 + 2d\\]\n\\[a_5 = 3 + 4d\\]\n\n根据题目条件 $a_3 + a_5 = 22$，我们可以将上面的表达式相加：\n\\[3 + 2d + 3 + 4d = 22\\]\n简化得到：\n\\[6 + 6d = 22\\]\n解这个方程找到 $d$ 的值：\n\\[6d = 16\\]\n\\[d = \\frac{16}{6} = \\frac{8}{3}\\]\n\n现在我们知道了公差 $d = \\frac{8}{3}$，可以求出第七项 $a_7$：\n\\[a_7 = a_1 + (7-1)d = 3 + 6\\left(\\frac{8}{3}\\right) = 3 + 2(8) = 3 + 16 = 19\\]\n\n因此，$a_7$ 的值是 $\\boxed{19}$。",
+      "correct": false,
+      "time_s": 39.68,
+      "tokens": 185
+    },
+    {
+      "question": "从 3 名男生和 2 名女生中选出 2 人参加志愿者活动，求选出的两人恰好是一男一女的概率。",
+      "expected": "3/5",
+      "predicted": "\\frac{3}{5}",
+      "full_response": "要解决这个问题，我们可以分步骤来计算：\n\n1. **总的选择方式**：\n   - 总共有5个人（3名男生 + 2名女生），从中选择2人的组合数为 \\(C(5, 2)\\)。\n   - 计算 \\(C(5, 2) = \\frac{5!}{2!(5-2)!} = \\frac{5 \\times 4}{2 \\times 1} = 10\\)。\n\n2. **一男一女的选择方式**：\n   - 从3名男生中选择1人的组合数为 \\(C(3, 1)\\)。\n   - 计算 \\(C(3, 1) = \\frac{3!}{1!(3-1)!} = \\frac{3}{1} = 3\\)。\n   - 从2名女生中选择1人的组合数为 \\(C(2, 1)\\)。\n   - 计算 \\(C(2, 1) = \\frac{2!}{1!(2-1)!} = \\frac{2}{1} = 2\\)。\n   - 因此，一男一女的总选择方式为 \\(3 \\times 2 = 6\\)。\n\n3. **计算概率**：\n   - 概率是满足条件的选择数除以总的可能选择数。\n   - 所求的概率为 \\(\\frac{6}{10} = \\frac{3}{5}\\)。\n\n所以，选出的两人恰好是一男一女的概率是 \\(\\boxed{\\frac{3}{5}}\\)。",
+      "correct": true,
+      "time_s": 35.74,
+      "tokens": 182
+    }
+  ]
+}

data/results/cmath_IO_qwen2.5_32b_20260703_183157.json

@@ -0,0 +1,40 @@
+{
+  "summary": {
+    "method": "IO",
+    "model": "qwen2.5:32b",
+    "task": "cmath",
+    "samples": 3,
+    "correct": 1,
+    "accuracy": 0.3333,
+    "avg_time_s": 0.51
+  },
+  "details": [
+    {
+      "question": "已知函数 $f(x) = 2x^2 - 4x + 1$，求 $f(x)$ 的最小值。",
+      "expected": "-1",
+      "predicted": "-1",
+      "full_response": "-1",
+      "correct": true,
+      "time_s": 0.5,
+      "tokens": 1
+    },
+    {
+      "question": "在等差数列 $\\{a_n\\}$ 中，$a_1 = 3$，$a_3 + a_5 = 22$，求 $a_7$ 的值。",
+      "expected": "25",
+      "predicted": "15",
+      "full_response": "15",
+      "correct": false,
+      "time_s": 0.47,
+      "tokens": 1
+    },
+    {
+      "question": "从 3 名男生和 2 名女生中选出 2 人参加志愿者活动，求选出的两人恰好是一男一女的概率。",
+      "expected": "3/5",
+      "predicted": "0.6",
+      "full_response": "0.6",
+      "correct": false,
+      "time_s": 0.56,
+      "tokens": 2
+    }
+  ]
+}

data/results/gsm8k_AGoT_d2_l2_qwen2.5_32b_20260703_153900.json

@@ -0,0 +1,146 @@
+{
+  "summary": {
+    "method": "AGoT",
+    "model": "qwen2.5:32b",
+    "task": "gsm8k",
+    "config": {
+      "max_depth": 2,
+      "max_layers": 2
+    },
+    "samples": 3,
+    "correct": 3,
+    "accuracy": 1.0,
+    "avg_time_s": 186.73
+  },
+  "details": [
+    {
+      "question": "Janet's ducks lay 16 eggs per day. She eats three for breakfast every morning and bakes muffins with",
+      "expected": "1.50",
+      "predicted": "1.50",
+      "correct": true,
+      "time_s": 290.71,
+      "stats": {
+        "total_calls": 15,
+        "total_tokens": 1633,
+        "start_time": 1783063779.8278565,
+        "end_time": 1783064070.5349534,
+        "node_count": 6,
+        "edge_count": 0,
+        "recursion_count": 0,
+        "layers_used": [
+          [
+            0,
+            0
+          ],
+          [
+            0,
+            1
+          ],
+          [
+            0,
+            0
+          ],
+          [
+            0,
+            1
+          ],
+          [
+            0,
+            0
+          ],
+          [
+            0,
+            1
+          ]
+        ],
+        "elapsed": 290.71
+      }
+    },
+    {
+      "question": "A robe takes 2 1/2 yards of fabric and 1/8 yard of trim. If you have 10 yards of fabric and 1 yard o",
+      "expected": "4",
+      "predicted": "4",
+      "correct": true,
+      "time_s": 137.86,
+      "stats": {
+        "total_calls": 30,
+        "total_tokens": 3529,
+        "start_time": 1783064070.5352838,
+        "end_time": 1783064208.3956833,
+        "node_count": 6,
+        "edge_count": 0,
+        "recursion_count": 0,
+        "layers_used": [
+          [
+            0,
+            0
+          ],
+          [
+            0,
+            1
+          ],
+          [
+            0,
+            0
+          ],
+          [
+            0,
+            1
+          ],
+          [
+            0,
+            0
+          ],
+          [
+            0,
+            1
+          ]
+        ],
+        "elapsed": 137.86
+      }
+    },
+    {
+      "question": "Kyle is a collector of rare coins. One day he found a rare coin online and bought it for $50. The ne",
+      "expected": "66",
+      "predicted": "66",
+      "correct": true,
+      "time_s": 131.61,
+      "stats": {
+        "total_calls": 45,
+        "total_tokens": 5283,
+        "start_time": 1783064208.3958018,
+        "end_time": 1783064340.0105371,
+        "node_count": 6,
+        "edge_count": 0,
+        "recursion_count": 0,
+        "layers_used": [
+          [
+            0,
+            0
+          ],
+          [
+            0,
+            1
+          ],
+          [
+            0,
+            0
+          ],
+          [
+            0,
+            1
+          ],
+          [
+            0,
+            0
+          ],
+          [
+            0,
+            1
+          ]
+        ],
+        "elapsed": 131.61
+      }
+    }
+  ]
+}

data/results/gsm8k_CoT_qwen2.5_32b_20260703_144903.json

@@ -0,0 +1,40 @@
+{
+  "summary": {
+    "method": "CoT",
+    "model": "qwen2.5:32b",
+    "task": "gsm8k",
+    "samples": 3,
+    "correct": 3,
+    "accuracy": 1.0,
+    "avg_time_s": 33.54
+  },
+  "details": [
+    {
+      "question": "Janet's ducks lay 16 eggs per day. She eats three for breakfast every morning and bakes muffins with four every day. She sells the remaining eggs at the farmers' market daily for $2 per dozen. How much money does she make per day at the farmers' market?",
+      "expected": "1.50",
+      "predicted": "1.50",
+      "full_response": "Step 1: Calculate the total number of eggs laid by Janet's ducks each day.\n- The ducks lay 16 eggs per day.\n\nStep 2: Determine how many eggs Janet uses for breakfast and baking daily.\n- She eats three eggs for breakfast every morning.\n- She bakes muffins with four eggs every day.\n- Total eggs used daily = 3 (for breakfast) + 4 (for baking) = 7 eggs\n\nStep 3: Calculate the number of eggs remaining after Janet uses some for breakfast and baking.\n- Remaining eggs per day = total laid - used\n- Remaining eggs per day = 16 - 7 = 9 eggs\n\nStep 4: Determine how many dozens of eggs are available to sell at the farmers' market.\n- There are 12 eggs in a dozen.\n- Number of dozens Janet can sell = remaining eggs / 12\n- Number of dozens Janet can sell = 9 / 12 = 0.75 dozens\n\nStep 5: Calculate how much money Janet makes per day from selling the eggs at $2 per dozen.\n- Money made per day = number of dozens sold * price per dozen\n- Money made per day = 0.75 dozens * $2/dozen = $1.50\n\nTherefore, Janet makes \\boxed{1.50} dollars per day at the farmers' market from selling her ducks' eggs.",
+      "correct": true,
+      "time_s": 30.7,
+      "tokens": 362
+    },
+    {
+      "question": "A robe takes 2 1/2 yards of fabric and 1/8 yard of trim. If you have 10 yards of fabric and 1 yard of trim, how many robes can you make?",
+      "expected": "4",
+      "predicted": "4",
+      "full_response": "To solve this problem, we need to determine the number of robes that can be made given the constraints on both fabric and trim.\n\nStep 1: Calculate the amount of fabric needed for one robe.\n- A single robe requires \\(2 \\frac{1}{2}\\) yards of fabric. Converting this mixed number to an improper fraction:\n\\[ 2 \\frac{1}{2} = \\frac{5}{2} \\text{ yards} \\]\n\nStep 2: Calculate the amount of trim needed for one robe.\n- A single robe requires \\( \\frac{1}{8} \\) yard of trim.\n\nStep 3: Determine how many robes can be made with the available fabric.\n- We have 10 yards of fabric. To find out how many robes we can make, divide the total amount of fabric by the amount needed per robe:\n\\[ \\text{Number of robes from fabric} = \\frac{10}{\\frac{5}{2}} = 10 \\times \\frac{2}{5} = 4 \\]\n\nStep 4: Determine how many robes can be made with the available trim.\n- We have 1 yard of trim. To find out how many robes we can make, divide the total amount of trim by the amount needed per robe:\n\\[ \\text{Number of robes from trim} = \\frac{1}{\\frac{1}{8}} = 1 \\times 8 = 8 \\]\n\nStep 5: Determine the limiting factor.\n- The number of robes we can make is limited by the smaller of the two quantities calculated in Steps 3 and 4. Here, fabric limits us to 4 robes.\n\nTherefore, the final answer is:\n\\boxed{4}",
+      "correct": true,
+      "time_s": 37.48,
+      "tokens": 426
+    },
+    {
+      "question": "Kyle is a collector of rare coins. One day he found a rare coin online and bought it for $50. The next month, he sold it at a 20% profit. Six months later, he bought the same coin back, but had to pay 10% more than he sold it for. How much did Kyle pay to buy the coin back?",
+      "expected": "66",
+      "predicted": "66",
+      "full_response": "Step 1: Calculate the selling price of the coin when Kyle sold it at a 20% profit.\n\nKyle bought the coin for $50 and then sold it with a 20% profit. To find out how much he sold it for, we calculate:\n\n\\[ \\text{Selling Price} = \\text{Cost Price} + (\\text{Profit Percentage} \\times \\text{Cost Price}) \\]\n\\[ \\text{Selling Price} = \\$50 + (0.20 \\times \\$50) \\]\n\\[ \\text{Selling Price} = \\$50 + \\$10 \\]\n\\[ \\text{Selling Price} = \\$60 \\]\n\nStep 2: Calculate the price Kyle paid to buy back the coin, which was 10% more than what he sold it for.\n\nKyle bought the coin back at a price that is 10% higher than $60. To find this amount:\n\n\\[ \\text{New Buying Price} = \\text{Selling Price} + (\\text{Increase Percentage} \\times \\text{Selling Price}) \\]\n\\[ \\text{New Buying Price} = \\$60 + (0.10 \\times \\$60) \\]\n\\[ \\text{New Buying Price} = \\$60 + \\$6 \\]\n\\[ \\text{New Buying Price} = \\$66 \\]\n\nTherefore, Kyle paid $66 to buy the coin back.\n\n\\boxed{66}",
+      "correct": true,
+      "time_s": 32.43,
+      "tokens": 313
+    }
+  ]
+}

data/results/gsm8k_CoT_qwen2.5_32b_20260703_150510.json

@@ -0,0 +1,103 @@
+{
+  "summary": {
+    "method": "CoT",
+    "model": "qwen2.5:32b",
+    "task": "gsm8k",
+    "samples": 10,
+    "correct": 8,
+    "accuracy": 0.8,
+    "avg_time_s": 25.93
+  },
+  "details": [
+    {
+      "question": "Janet's ducks lay 16 eggs per day. She eats three for breakfast every morning and bakes muffins with four every day. She sells the remaining eggs at the farmers' market daily for $2 per dozen. How much money does she make per day at the farmers' market?",
+      "expected": "1.50",
+      "predicted": "1.50",
+      "full_response": "Step 1: Calculate the total number of eggs laid by Janet's ducks each day.\n- The ducks lay 16 eggs per day.\n\nStep 2: Determine how many eggs Janet uses for breakfast and baking daily.\n- She eats three eggs for breakfast every morning.\n- She bakes muffins with four eggs every day.\n- Total eggs used daily = 3 (for breakfast) + 4 (for baking) = 7 eggs\n\nStep 3: Calculate the number of eggs remaining after Janet uses some for breakfast and baking.\n- Remaining eggs per day = total laid - used\n- Remaining eggs per day = 16 - 7 = 9 eggs\n\nStep 4: Determine how many dozens of eggs are available to sell at the farmers' market.\n- There are 12 eggs in a dozen.\n- Number of dozens Janet can sell = remaining eggs / 12\n- Number of dozens Janet can sell = 9 / 12 = 0.75 dozens\n\nStep 5: Calculate how much money Janet makes per day from selling the eggs at $2 per dozen.\n- Money made per day = number of dozens sold * price per dozen\n- Money made per day = 0.75 dozens * $2/dozen = $1.50\n\nTherefore, Janet makes \\boxed{1.50} dollars per day at the farmers' market from selling her ducks' eggs.",
+      "correct": true,
+      "time_s": 30.82,
+      "tokens": 362
+    },
+    {
+      "question": "A robe takes 2 1/2 yards of fabric and 1/8 yard of trim. If you have 10 yards of fabric and 1 yard of trim, how many robes can you make?",
+      "expected": "4",
+      "predicted": "4",
+      "full_response": "To solve this problem, we need to determine the number of robes that can be made given the constraints on both fabric and trim.\n\nStep 1: Calculate the amount of fabric needed for one robe.\n- A single robe requires \\(2 \\frac{1}{2}\\) yards of fabric. Converting this mixed number to an improper fraction:\n\\[ 2 \\frac{1}{2} = \\frac{5}{2} \\text{ yards} \\]\n\nStep 2: Calculate the amount of trim needed for one robe.\n- A single robe requires \\( \\frac{1}{8} \\) yard of trim.\n\nStep 3: Determine how many robes can be made with the available fabric.\n- We have 10 yards of fabric. To find out how many robes we can make, divide the total amount of fabric by the amount needed per robe:\n\\[ \\text{Number of robes from fabric} = \\frac{10}{\\frac{5}{2}} = 10 \\times \\frac{2}{5} = 4 \\]\n\nStep 4: Determine how many robes can be made with the available trim.\n- We have 1 yard of trim. To find out how many robes we can make, divide the total amount of trim by the amount needed per robe:\n\\[ \\text{Number of robes from trim} = \\frac{1}{\\frac{1}{8}} = 1 \\times 8 = 8 \\]\n\nStep 5: Determine the limiting factor.\n- The number of robes we can make is limited by the smaller of the two quantities calculated in Steps 3 and 4. Here, fabric limits us to 4 robes.\n\nTherefore, the final answer is:\n\\boxed{4}",
+      "correct": true,
+      "time_s": 37.42,
+      "tokens": 426
+    },
+    {
+      "question": "Kyle is a collector of rare coins. One day he found a rare coin online and bought it for $50. The next month, he sold it at a 20% profit. Six months later, he bought the same coin back, but had to pay 10% more than he sold it for. How much did Kyle pay to buy the coin back?",
+      "expected": "66",
+      "predicted": "66",
+      "full_response": "Step 1: Calculate the selling price of the coin when Kyle sold it at a 20% profit.\n\nKyle bought the coin for $50 and then sold it with a 20% profit. To find out how much he sold it for, we calculate:\n\n\\[ \\text{Selling Price} = \\text{Cost Price} + (\\text{Profit Percentage} \\times \\text{Cost Price}) \\]\n\\[ \\text{Selling Price} = \\$50 + (0.20 \\times \\$50) \\]\n\\[ \\text{Selling Price} = \\$50 + \\$10 \\]\n\\[ \\text{Selling Price} = \\$60 \\]\n\nStep 2: Calculate the price Kyle paid to buy back the coin, which was 10% more than what he sold it for.\n\nKyle bought the coin back at a price that is 10% higher than $60. To find this amount:\n\n\\[ \\text{New Buying Price} = \\text{Selling Price} + (\\text{Increase Percentage} \\times \\text{Selling Price}) \\]\n\\[ \\text{New Buying Price} = \\$60 + (0.10 \\times \\$60) \\]\n\\[ \\text{New Buying Price} = \\$60 + \\$6 \\]\n\\[ \\text{New Buying Price} = \\$66 \\]\n\nTherefore, Kyle paid $66 to buy the coin back.\n\n\\boxed{66}",
+      "correct": true,
+      "time_s": 32.49,
+      "tokens": 313
+    },
+    {
+      "question": "A pet shelter has 9 kittens available for adoption. The shelter normally has 2 cats available. If each cat treats 2 kittens as their own, how many animals are there in all?",
+      "expected": "7",
+      "predicted": "11",
+      "full_response": "To solve this problem, we need to determine the total number of animals at the pet shelter after considering both the kittens and the cats.\n\nStep 1: Identify the number of kittens available for adoption.\n- There are 9 kittens available for adoption.\n\nStep 2: Determine the normal number of cats at the shelter.\n- The shelter normally has 2 cats available.\n\nStep 3: Understand how each cat treats the kittens.\n- Each cat treats 2 kittens as their own. However, this information does not change the actual count of animals but might be a way to describe the relationship between the cats and kittens.\n\nStep 4: Calculate the total number of animals by adding the number of kittens and the number of cats.\n- Total number of animals = Number of kittens + Number of cats\n- Total number of animals = 9 (kittens) + 2 (cats)\n- Total number of animals = 11\n\nTherefore, the total number of animals at the pet shelter is \\boxed{11}.",
+      "correct": false,
+      "time_s": 21.72,
+      "tokens": 307
+    },
+    {
+      "question": "Faye is a flower farmer. She plants 12 rows of daisies with 100 daisies in each row. She also plants 7 rows of roses with 12 roses in each row. How many more daisies than roses does she plant?",
+      "expected": "1116",
+      "predicted": "1116",
+      "full_response": "To solve this problem, we need to calculate the total number of daisies and the total number of roses Faye plants, then find the difference between these two quantities.\n\nStep 1: Calculate the total number of daisies.\nFaye plants 12 rows with 100 daisies in each row. Therefore, the total number of daisies is:\n\\[ \\text{Total Daisies} = 12 \\times 100 = 1200 \\]\n\nStep 2: Calculate the total number of roses.\nFaye plants 7 rows with 12 roses in each row. Therefore, the total number of roses is:\n\\[ \\text{Total Roses} = 7 \\times 12 = 84 \\]\n\nStep 3: Find how many more daisies than roses Faye plants by subtracting the total number of roses from the total number of daisies.\n\\[ \\text{Difference} = \\text{Total Daisies} - \\text{Total Roses} = 1200 - 84 = 1116 \\]\n\nTherefore, Faye plants 1116 more daisies than roses.\n\n\\boxed{1116}",
+      "correct": true,
+      "time_s": 27.07,
+      "tokens": 276
+    },
+    {
+      "question": "A farmer had 27 watermelons. After selling some watermelons, he had 13 left. Then he bought 28 more watermelons. Later, he sold 15 watermelons. How many watermelons does he have now?",
+      "expected": "26",
+      "predicted": "26",
+      "full_response": "Step 1: Determine the number of watermelons sold initially.\nThe farmer started with 27 watermelons and had 13 left after selling some, so we can calculate how many were sold:\n\\[ \\text{Watermelons sold} = 27 - 13 = 14 \\]\n\nStep 2: Calculate the number of watermelons after buying more.\nThe farmer then bought 28 more watermelons. So, we add these to the remaining 13:\n\\[ \\text{Total watermelons after purchase} = 13 + 28 = 41 \\]\n\nStep 3: Determine the final number of watermelons after selling again.\nThe farmer sold another 15 watermelons from his new total. So, we subtract these from the current total:\n\\[ \\text{Final number of watermelons} = 41 - 15 = 26 \\]\n\nTherefore, the final answer is: \\boxed{26}",
+      "correct": true,
+      "time_s": 21.92,
+      "tokens": 235
+    },
+    {
+      "question": "James buys a bag of 40 cookies. He eats 5 cookies and then divides the rest evenly among his 7 friends. How many cookies does each friend get?",
+      "expected": "5",
+      "predicted": "5",
+      "full_response": "Step 1: Determine how many cookies are left after James eats some.\nJames starts with 40 cookies and eats 5 of them, so we subtract:\n\\[ 40 - 5 = 35 \\]\nSo there are 35 cookies remaining.\n\nStep 2: Divide the remaining cookies among his friends.\nJames has 7 friends and he divides the 35 remaining cookies evenly among them. We need to divide 35 by 7:\n\\[ 35 \\div 7 = 5 \\]\n\nEach friend gets 5 cookies.\n\n\\boxed{5}",
+      "correct": true,
+      "time_s": 12.73,
+      "tokens": 136
+    },
+    {
+      "question": "Tom's mother had 15 apples. She gave Tom 3 apples and gave Sarah twice as many as Tom. How many apples does she have left?",
+      "expected": "6",
+      "predicted": "6",
+      "full_response": "Step 1: Determine how many apples Tom received.\nTom received 3 apples from his mother.\n\nStep 2: Calculate the number of apples given to Sarah.\nSarah received twice as many apples as Tom, so:\n\\[ \\text{Apples for Sarah} = 2 \\times \\text{Apples for Tom} = 2 \\times 3 = 6 \\]\n\nStep 3: Find out how many apples were given away in total.\nTotal apples given to both Tom and Sarah is the sum of what each received:\n\\[ \\text{Total apples given away} = \\text{Apples for Tom} + \\text{Apples for Sarah} = 3 + 6 = 9 \\]\n\nStep 4: Calculate how many apples are left with Tom's mother.\nTom's mother originally had 15 apples. Subtract the total number of apples given away from this amount:\n\\[ \\text{Remaining apples} = \\text{Original apples} - \\text{Total apples given away} = 15 - 9 = 6 \\]\n\nTherefore, the final answer is: \\boxed{6}",
+      "correct": true,
+      "time_s": 24.18,
+      "tokens": 272
+    },
+    {
+      "question": "A school bus can hold 48 students. If 3 buses are used for a field trip and each bus is 75% full, how many students are on the field trip?",
+      "expected": "108",
+      "predicted": "108",
+      "full_response": "Step 1: Determine the capacity of one bus.\nThe problem states that one school bus can hold 48 students.\n\nStep 2: Calculate the number of students in one bus when it is 75% full.\nTo find out how many students are on a single bus at 75% capacity, we multiply the total capacity by 0.75 (which represents 75%).\n\n\\[ \\text{Number of students per bus} = 48 \\times 0.75 \\]\n\nStep 3: Perform the multiplication.\n\\[ 48 \\times 0.75 = 36 \\]\nSo, each bus has 36 students when it is 75% full.\n\nStep 4: Calculate the total number of students on all three buses.\nSince there are 3 buses and each carries 36 students at 75% capacity:\n\n\\[ \\text{Total number of students} = 3 \\times 36 \\]\n\nStep 5: Perform the multiplication to find the total number of students.\n\\[ 3 \\times 36 = 108 \\]\nTherefore, there are a total of 108 students on the field trip.\n\n\\boxed{108}",
+      "correct": true,
+      "time_s": 26.76,
+      "tokens": 282
+    },
+    {
+      "question": "Maria bought 6 notebooks for $2 each and 4 pens for $1.50 each. She paid with a $20 bill. How much change did she receive?",
+      "expected": "2",
+      "predicted": "\\$2",
+      "full_response": "Step 1: Calculate the total cost of the notebooks.\nMaria bought 6 notebooks at $2 each, so the total cost is:\n\\[ \\text{Total cost of notebooks} = 6 \\times \\$2 = \\$12 \\]\n\nStep 2: Calculate the total cost of the pens.\nShe also bought 4 pens at $1.50 each, so the total cost for the pens is:\n\\[ \\text{Total cost of pens} = 4 \\times \\$1.50 = \\$6 \\]\n\nStep 3: Find the overall total cost.\nAdd the costs from Step 1 and Step 2 to get the overall total cost:\n\\[ \\text{Overall total cost} = \\$12 + \\$6 = \\$18 \\]\n\nStep 4: Calculate the change Maria received.\nMaria paid with a $20 bill, so subtract the overall total cost from $20 to find out how much change she received:\n\\[ \\text{Change received} = \\$20 - \\$18 = \\$2 \\]\n\nTherefore, the amount of change Maria received is \\boxed{\\$2}.",
+      "correct": false,
+      "time_s": 24.18,
+      "tokens": 259
+    }
+  ]
+}

data/results/gsm8k_CoT_qwq_latest_20260703_153231.json

@@ -0,0 +1,103 @@
+{
+  "summary": {
+    "method": "CoT",
+    "model": "qwq:latest",
+    "task": "gsm8k",
+    "samples": 10,
+    "correct": 9,
+    "accuracy": 0.9,
+    "avg_time_s": 66.51
+  },
+  "details": [
+    {
+      "question": "Janet's ducks lay 16 eggs per day. She eats three for breakfast every morning and bakes muffins with four every day. She sells the remaining eggs at the farmers' market daily for $2 per dozen. How much money does she make per day at the farmers' market?",
+      "expected": "1.50",
+      "predicted": "1.50",
+      "full_response": "Alright, let's tackle this problem step by step. So, Janet has ducks that lay 16 eggs per day. She eats three eggs for breakfast every morning and uses four eggs to bake muffins every day. Then, she sells the remaining eggs at the farmers' market for $2 per dozen. We need to find out how much money she makes per day from selling the eggs.\n\nFirst, I need to figure out how many eggs are left after Janet eats some and bakes with others. She starts with 16 eggs daily.\n\nShe eats 3 eggs for breakfast, so:\n\n16 eggs - 3 eggs = 13 eggs remaining.\n\nThen, she uses 4 eggs to bake muffins:\n\n13 eggs - 4 eggs = 9 eggs left to sell.\n\nNow, she sells these remaining eggs at the farmers' market for $2 per dozen. A dozen is 12 eggs, but she has 9 eggs to sell. Since 9 is less than 12, she doesn't have a full dozen to sell. So, I need to figure out how much she gets for 9 eggs.\n\nFirst, let's find out the price per egg. Since a dozen eggs cost $2, and a dozen is 12 eggs, the price per egg is:\n\n$2 / 12 eggs = $0.1667 per egg (rounded to four decimal places).\n\nBut, maybe there's a better way to calculate this without finding the per egg price. Perhaps she sells fractions of a dozen.\n\nAlternatively, she could sell the 9 eggs as a fraction of a dozen. Since 9 is 3/4 of a dozen (because 9/12 = 3/4), she could sell 3/4 of a dozen for 3/4 of the price of a dozen.\n\nSo, if one dozen is $2, then 3/4 of a dozen would be:\n\n(3/4) * $2 = $1.50.\n\nTherefore, she makes $1.50 per day from selling the remaining eggs.\n\nWait a minute, let me double-check that to make sure I didn't make any mistakes.\n\nStarting with 16 eggs:\n\n- Subtract 3 eggs for breakfast: 16 - 3 = 13 eggs.\n\n- Subtract 4 eggs for baking: 13 - 4 = 9 eggs to sell.\n\n- She sells 9 eggs, which is 9/12 or 3/4 of a dozen, at $2 per dozen.\n\n- So, 3/4 * $2 = $1.50.\n\nYes, that seems correct.\n\nAlternatively, if the market only buys full dozens, and she can't sell partial dozens, then she wouldn't be able to sell any eggs since she doesn't have a full dozen. But the problem says she sells the remaining eggs, so it's likely that she can sell fractions of a dozen.\n\nAnother way to think about it is to calculate the total earnings based on per dozen price.\n\nSo, she has 9 eggs to sell. For every 12 eggs, she gets $2.\n\nTherefore, for 9 eggs, she gets (9/12) * $2 = $1.50.\n\nAlternatively, I could think in terms of how many dozens are in 9 eggs.\n\nSince 12 eggs make a dozen, 9 eggs are 9/12 = 0.75 dozens.\n\nSo, 0.75 dozens * $2 per dozen = $1.50.\n\nSame result.\n\nI think $1.50 is the correct daily earnings from selling the eggs.\n\nLet me consider if there's any other way to interpret the problem.\n\nIs there any possibility that the eggs used for baking or breakfast could have a different value? The problem doesn't suggest that; it seems straightforward that she consumes some eggs and sells the rest.\n\nAlso, the price is $2 per dozen, and she's selling whatever is left, which in this case is 9 eggs.\n\nSo, unless there's additional information or constraints that I'm missing, $1.50 per day seems to be the correct answer.\n\nTherefore, the final answer is \\\\boxed{1.50}",
+      "correct": true,
+      "time_s": 92.01,
+      "tokens": 1039
+    },
+    {
+      "question": "A robe takes 2 1/2 yards of fabric and 1/8 yard of trim. If you have 10 yards of fabric and 1 yard of trim, how many robes can you make?",
+      "expected": "4",
+      "predicted": "4",
+      "full_response": "Alright, so I've got this problem here about making robes. It says that each robe takes 2 1/2 yards of fabric and 1/8 yard of trim. I have 10 yards of fabric and 1 yard of trim in total. I need to figure out how many robes I can make with these materials.\n\nFirst, I should probably understand what's being asked. I need to find out the maximum number of robes that can be made without exceeding the available fabric and trim. So, it's like finding the limiting factor between the fabric and the trim.\n\nLet me start by converting the mixed number for the fabric into an improper fraction to make calculations easier. 2 1/2 yards is the same as 5/2 yards per robe.\n\nSo, each robe requires:\n- Fabric: 5/2 yards\n- Trim: 1/8 yard\n\nI have:\n- Total fabric: 10 yards\n- Total trim: 1 yard\n\nI need to find out how many robes (let's call this number x) I can make such that:\n\nx * (5/2) ≤ 10 (for fabric)\nand\nx * (1/8) ≤ 1 (for trim)\n\nI need to solve these two inequalities and find the largest integer x that satisfies both.\n\nLet's solve the first inequality for fabric:\n\nx * (5/2) ≤ 10\n\nTo solve for x, I can multiply both sides by 2/5 to isolate x:\n\nx ≤ 10 * (2/5)\nx ≤ 20/5\nx ≤ 4\n\nSo, based on the fabric, I can make up to 4 robes.\n\nNow, let's check the trim:\n\nx * (1/8) ≤ 1\n\nAgain, solve for x by multiplying both sides by 8:\n\nx ≤ 1 * 8\nx ≤ 8\n\nBased on the trim, I can make up to 8 robes.\n\nBut wait a minute, the fabric only allows for 4 robes, while the trim would allow for 8. So, the fabric is the limiting factor here.\n\nTherefore, the maximum number of robes I can make is 4.\n\nLet me double-check this to make sure I didn't make any mistakes.\n\nFirst, if I make 4 robes:\n\nFabric used: 4 * (5/2) = 4 * 2.5 = 10 yards\nTrim used: 4 * (1/8) = 4/8 = 0.5 yard\n\nSo, fabric used equals the available fabric (10 yards), and trim used is 0.5 yard, which is less than the available 1 yard.\n\nSo, that seems fine.\n\nBut, could I make more than 4 robes with the trim since I have 1 yard, and each robe only needs 1/8 yard?\n\nWell, mathematically, with 1 yard of trim, I could make up to 8 robes because 1 divided by 1/8 is 8.\n\nBut, I don't have enough fabric for 8 robes. The fabric only allows for 4 robes.\n\nSo, the number of robes I can make is limited by the fabric.\n\nTherefore, the answer should be 4 robes.\n\nWait, but let me consider if there's any way to optimize this further. Maybe there's some leftover fabric or trim that could be used in a partial robe, but the problem is asking for complete robes, so partial robes don't count.\n\nAlternatively, perhaps there's a different way to allocate the resources, but I think the approach of finding the limiting reagent (in this case, the fabric) is correct.\n\nSo, I think 4 is the correct answer.\n\n**Final Answer**\n\n\\[ \\boxed{4} \\]",
+      "correct": true,
+      "time_s": 82.31,
+      "tokens": 922
+    },
+    {
+      "question": "Kyle is a collector of rare coins. One day he found a rare coin online and bought it for $50. The next month, he sold it at a 20% profit. Six months later, he bought the same coin back, but had to pay 10% more than he sold it for. How much did Kyle pay to buy the coin back?",
+      "expected": "66",
+      "predicted": "66",
+      "full_response": "Alright, so I've got this problem about Kyle and his rare coin transactions. Let's break it down step by step.\n\nFirst, Kyle bought a rare coin for $50. Then, a month later, he sold it at a 20% profit. So, I need to figure out how much he sold it for.\n\nA 20% profit on the original purchase price means he sold it for 120% of what he bought it for. To calculate that, I can multiply $50 by 1.20.\n\nLet me do that: $50 × 1.20 = $60. So, he sold the coin for $60.\n\nNow, six months later, he bought the same coin back, but had to pay 10% more than what he sold it for. Okay, so I need to find out what 10% more than $60 is.\n\nFirst, calculate 10% of $60. 10% of $60 is $6. So, he paid $60 plus $6, which is $66.\n\nWait a minute, let me double-check that. Alternatively, paying 10% more than what he sold it for means he paid 110% of the selling price. So, 110% of $60 should be $60 × 1.10 = $66. Yeah, that matches.\n\nSo, Kyle paid $66 to buy the coin back.\n\nBut let me make sure I didn't miss anything. He initially bought it for $50, sold it for $60, and then bought it back for $66. The question is specifically asking how much he paid to buy it back, which is $66.\n\nI think that's the final answer.\n\n**Final Answer**\n\n\\[ \\boxed{66} \\]",
+      "correct": true,
+      "time_s": 41.14,
+      "tokens": 411
+    },
+    {
+      "question": "A pet shelter has 9 kittens available for adoption. The shelter normally has 2 cats available. If each cat treats 2 kittens as their own, how many animals are there in all?",
+      "expected": "7",
+      "predicted": "11",
+      "full_response": "Alright, so I've got this problem here about a pet shelter and their animals. Let's read it again to make sure I understand what's being asked.\n\n\"A pet shelter has 9 kittens available for adoption. The shelter normally has 2 cats available. If each cat treats 2 kittens as their own, how many animals are there in all?\"\n\nOkay, so first, there are 9 kittens and 2 cats in the shelter. The problem says that each cat treats 2 kittens as their own. Hmm, I need to figure out what that means for the total number of animals.\n\nLet me break this down. The shelter has 9 kittens and 2 cats. So, without any additional information, the total number of animals would simply be 9 plus 2, which is 11. But there's this extra condition about each cat treating 2 kittens as their own.\n\nDoes \"treating kittens as their own\" mean that these kittens are being cared for by the cats, or something like that? Maybe it's just a way of saying that these kittens are associated with those cats in some way.\n\nWait, but the problem is asking for the total number of animals. The kittens and the cats are distinct animals, right? So, even if some kittens are being treated as own by the cats, they are still separate living beings.\n\nMaybe the phrase is just to add some context but doesn't actually change the count. So, perhaps the total number of animals is still just the sum of the kittens and the cats.\n\nBut let's think carefully. If each of the 2 cats treats 2 kittens as their own, that means a total of 2 cats times 2 kittens per cat, which is 4 kittens. But there are 9 kittens in total. So, what about the remaining 5 kittens? Are they not being treated as own by any cat?\n\nBut the problem doesn't specify that only those 4 kittens are being treated as own; it just says each cat treats 2 kittens as their own. It could be that some kittens are being treated by more than one cat, or maybe there are some kittens not being treated by any cat.\n\nWait, but perhaps the idea is that these 4 kittens are already included in the count of 9 kittens. So, adding the 2 cats to the 9 kittens still gives 11 animals in total.\n\nAlternatively, maybe the problem is trying to say that the cats are acting like parents to these kittens, but that doesn't change the fact that they are separate entities.\n\nAnother thought: perhaps \"treating kittens as their own\" means that these kittens are being considered as part of the cats' families, but again, for counting total animals, it should still be just the sum.\n\nI feel like I'm overcomplicating this. Maybe the answer is simply the total number of distinct animals in the shelter, which is 9 kittens plus 2 cats, equaling 11 animals.\n\nBut let's double-check. Is there any possibility that some of these kittens are actually grown cats? Or perhaps some of the kittens are not yet considered separate animals? No, the problem clearly states \"kittens\" and \"cats,\" which are distinct stages in a cat's life, but both are considered separate animals.\n\nSo, unless there's some trick here that I'm missing, the total number of animals should be 11.\n\nWait, maybe the phrase \"each cat treats 2 kittens as their own\" is meant to indicate that these kittens are being raised by the cats, and perhaps they should not be counted separately. But that doesn't make much sense because kittens need to be counted separately from the cats that are raising them.\n\nIn reality, in a shelter, kittens and cats are kept separate, and kittens might be cared for by humans or other cats, but they are still distinct animals.\n\nTherefore, I think the total number of animals is just the sum of the kittens and the cats.\n\nSo, 9 kittens plus 2 cats equals 11 animals.\n\nI think that's the answer.\n\n**Final Answer**\n\n\\[ \\boxed{11} \\]",
+      "correct": false,
+      "time_s": 87.92,
+      "tokens": 1241
+    },
+    {
+      "question": "Faye is a flower farmer. She plants 12 rows of daisies with 100 daisies in each row. She also plants 7 rows of roses with 12 roses in each row. How many more daisies than roses does she plant?",
+      "expected": "1116",
+      "predicted": "1116",
+      "full_response": "Alright, so I've got this problem here about Faye, who's a flower farmer. She plants daisies and roses in different rows with varying numbers in each row. The question is asking how many more daisies than roses she plants. Okay, let's break this down.\n\nFirst, she has 12 rows of daisies, and each row has 100 daisies. So, to find out the total number of daisies, I need to multiply the number of rows by the number of daisies per row. That should give me the total number of daisies.\n\nSimilarly, for the roses, she has 7 rows with 12 roses in each row. So, I'll do the same thing: multiply the number of rows by the number of roses per row to get the total number of roses.\n\nThen, to find out how many more daisies than roses she plants, I'll subtract the total number of roses from the total number of daisies.\n\nLet me write this down step by step.\n\nFirst, calculate the total number of daisies:\n\nNumber of rows of daisies: 12\n\nNumber of daisies per row: 100\n\nTotal daisies = 12 rows * 100 daisies/row = 1200 daisies\n\nNext, calculate the total number of roses:\n\nNumber of rows of roses: 7\n\nNumber of roses per row: 12\n\nTotal roses = 7 rows * 12 roses/row = 84 roses\n\nNow, find out how many more daisies than roses:\n\nDifference = Total daisies - Total roses = 1200 - 84 = 1116\n\nSo, Faye plants 1116 more daisies than roses.\n\nWait a minute, let me double-check that. Maybe I should make sure I did the multiplication correctly.\n\n12 rows of daisies with 100 each: 12 * 100 = 1200, that seems right.\n\n7 rows of roses with 12 each: 7 * 12 = 84, that also seems correct.\n\nSubtracting them: 1200 - 84 = 1116.\n\nYes, that looks right.\n\nAlternatively, I could think about the total number of flowers and then find the difference, but that's probably more complicated for this problem.\n\nNo, I think this is straightforward. The answer should be 1116.\n\n**Final Answer**\n\n\\[ \\boxed{1116} \\]",
+      "correct": true,
+      "time_s": 58.08,
+      "tokens": 627
+    },
+    {
+      "question": "A farmer had 27 watermelons. After selling some watermelons, he had 13 left. Then he bought 28 more watermelons. Later, he sold 15 watermelons. How many watermelons does he have now?",
+      "expected": "26",
+      "predicted": "26",
+      "full_response": "Alright, let's tackle this problem step by step. So, the farmer starts with 27 watermelons. He sells some, and after that, he has 13 left. Then he buys 28 more watermelons, and after that, he sells 15 watermelons. We need to find out how many watermelons he has now.\n\nFirst, let's figure out how many watermelons he sold initially. He started with 27 and had 13 left after selling some. So, the number of watermelons he sold first is 27 minus 13. That would be:\n\n\\[ 27 - 13 = 14 \\]\n\nSo, he sold 14 watermelons initially.\n\nNow, he has 13 watermelons left. Then, he buys 28 more. So, we add those 28 to the 13 he has left:\n\n\\[ 13 + 28 = 41 \\]\n\nAlright, now he has 41 watermelons. Then, he sells another 15. So, we subtract 15 from 41:\n\n\\[ 41 - 15 = 26 \\]\n\nTherefore, the farmer now has 26 watermelons.\n\nWait a minute, let me double-check that. Maybe there's a easier way to look at this. Let's consider the net change in the number of watermelons.\n\nHe starts with 27.\n\nHe sells some and has 13 left. So, that's a decrease by 14.\n\nThen, he buys 28 more, which is an increase by 28.\n\nFinally, he sells 15, which is a decrease by 15.\n\nSo, the net change is:\n\nDecrease by 14: \\( 27 - 14 = 13 \\)\n\nIncrease by 28: \\( 13 + 28 = 41 \\)\n\nDecrease by 15: \\( 41 - 15 = 26 \\)\n\nYes, that matches what I got earlier.\n\nAlternatively, I could think of the total increase or decrease. He sold a total of 14 + 15 = 29 watermelons and bought 28. So, the net change is:\n\n\\[ -29 + 28 = -1 \\]\n\nSo, overall, he has 1 less watermelon than he started with.\n\nHe started with 27, so:\n\n\\[ 27 - 1 = 26 \\]\n\nAgain, that confirms the answer is 26.\n\nLet me try one more way to make sure. Suppose he starts with 27, sells 14, buys 28, sells 15.\n\nSo:\n\nStart: 27\n\nAfter selling 14: 27 - 14 = 13\n\nAfter buying 28: 13 + 28 = 41\n\nAfter selling 15: 41 - 15 = 26\n\nYes, consistent again.\n\nI think it's clear. The farmer has 26 watermelons now.\n\n**Final Answer**\n\n\\[ \\boxed{26} \\]",
+      "correct": true,
+      "time_s": 71.31,
+      "tokens": 645
+    },
+    {
+      "question": "James buys a bag of 40 cookies. He eats 5 cookies and then divides the rest evenly among his 7 friends. How many cookies does each friend get?",
+      "expected": "5",
+      "predicted": "5",
+      "full_response": "Alright, so James has a bag of 40 cookies. First, he eats 5 of them. So, I need to subtract the 5 cookies he ate from the total number of cookies to find out how many are left.\n\nSo, 40 minus 5 is 35 cookies remaining.\n\nNow, he wants to divide these 35 cookies evenly among his 7 friends. To find out how many cookies each friend gets, I need to divide the number of remaining cookies by the number of friends.\n\nThat means, 35 divided by 7.\n\nLet me do that calculation: 35 ÷ 7 equals 5.\n\nSo, each friend gets 5 cookies.\n\nWait a minute, does that make sense? Let's double-check.\n\nStarting with 40 cookies, James eats 5, leaving 35 cookies. Then, dividing 35 by 7 friends should give each friend 5 cookies.\n\nYes, that seems correct.\n\nAlternatively, I can think about it as each friend getting an equal share of the remaining cookies. So, if there are 35 cookies and 7 friends, each friend gets 5 cookies because 5 times 7 is 35.\n\nAnother way to look at it is to see if there's any remainder when dividing 35 by 7. Since 7 times 5 is exactly 35, there's no remainder.\n\nTherefore, each friend gets 5 cookies.\n\nI think that's the answer.\n\n**Final Answer**\n\n\\[ \\boxed{5} \\]",
+      "correct": true,
+      "time_s": 32.8,
+      "tokens": 389
+    },
+    {
+      "question": "Tom's mother had 15 apples. She gave Tom 3 apples and gave Sarah twice as many as Tom. How many apples does she have left?",
+      "expected": "6",
+      "predicted": "6",
+      "full_response": "Okay, so I've got this problem here. Let's read it again to make sure I understand what's being asked.\n\n\"Tom's mother had 15 apples. She gave Tom 3 apples and gave Sarah twice as many as Tom. How many apples does she have left?\"\n\nAlright, so initially, Tom's mother has 15 apples. She gives some apples to Tom and some to Sarah, and I need to find out how many she has left after giving those away.\n\nFirst, she gives Tom 3 apples. So, if she had 15 and gave away 3, she would have 15 minus 3, which is 12 apples left.\n\nBut wait, she also gives some apples to Sarah. The problem says she gave Sarah twice as many as she gave Tom. Since she gave Tom 3 apples, twice that amount would be 2 times 3, which is 6 apples.\n\nSo, she gave Sarah 6 apples.\n\nNow, from the 12 apples she had left after giving to Tom, she gives away another 6 to Sarah. So, 12 minus 6 should give me the number of apples she has left.\n\nLet me do that calculation: 12 minus 6 is 6.\n\nSo, she has 6 apples left.\n\nWait, let me double-check that I didn't miss anything. She started with 15 apples.\n\nGave Tom 3, so 15 - 3 = 12.\n\nThen gave Sarah twice as many as Tom, which is 2 * 3 = 6 apples.\n\nSo, 12 - 6 = 6.\n\nYes, that seems correct.\n\nAlternatively, I could think of it as total apples given away are 3 to Tom plus 6 to Sarah, which is 9 apples in total.\n\nThen, 15 minus 9 equals 6.\n\nSame answer.\n\nI think that's right.\n\n**Final Answer**\n\n\\[ \\boxed{6} \\]",
+      "correct": true,
+      "time_s": 42.49,
+      "tokens": 474
+    },
+    {
+      "question": "A school bus can hold 48 students. If 3 buses are used for a field trip and each bus is 75% full, how many students are on the field trip?",
+      "expected": "108",
+      "predicted": "108",
+      "full_response": "Alright, so I've got this problem here. It says that a school bus can hold 48 students, and that 3 buses are used for a field trip. Each bus is 75% full. I need to find out how many students are on the field trip in total.\n\nFirst, I need to understand what's being asked. I have to find the total number of students across all three buses, given that each bus isn't completely full; instead, each is only 75% full.\n\nSo, maybe I should start by figuring out how many students are on one bus. If one bus can hold 48 students when it's full, but it's only 75% full, then the number of students on one bus would be 48 multiplied by 75%.\n\nBut wait, percent means per hundred, so 75% is the same as 75/100 or 0.75 in decimal form. So, to find 75% of 48, I can calculate 48 times 0.75.\n\nLet me do that: 48 × 0.75.\n\nHmm, 48 multiplied by 0.75.\n\nWell, 48 × 0.75 is the same as 48 × (3/4), because 0.75 is three quarters.\n\nSo, 48 times 3 is 144, and then divided by 4 is 36.\n\nSo, one bus has 36 students.\n\nNow, since there are 3 buses, and each has 36 students, the total number of students on the field trip would be 3 times 36.\n\nSo, 3 × 36 is 108.\n\nTherefore, there are 108 students on the field trip.\n\nBut just to make sure, maybe I should check my calculations again.\n\nFirst, capacity per bus is 48 students.\n\nEach bus is 75% full.\n\nSo, students per bus = 48 × 0.75 = 36.\n\nTotal students = 3 × 36 = 108.\n\nYeah, that seems correct.\n\nAlternatively, I could think of it as total capacity of all buses is 3 × 48 = 144 students.\n\nThen, since each bus is 75% full, total students would be 144 × 0.75.\n\nBut wait, 144 × 0.75 should also give me 108.\n\nLet me verify: 144 × 0.75.\n\nWell, 144 × 0.75 is the same as 144 × (3/4).\n\nSo, 144 times 3 is 432, divided by 4 is 108.\n\nSame answer.\n\nSo, either way, I get 108 students.\n\nI think that's the correct answer.\n\n**Final Answer**\n\n\\[ \\boxed{108} \\]",
+      "correct": true,
+      "time_s": 92.31,
+      "tokens": 627
+    },
+    {
+      "question": "Maria bought 6 notebooks for $2 each and 4 pens for $1.50 each. She paid with a $20 bill. How much change did she receive?",
+      "expected": "2",
+      "predicted": "2",
+      "full_response": "Alright, so Maria bought some notebooks and pens and paid with a $20 bill. I need to find out how much change she received. Let's break this down.\n\nFirst, she bought 6 notebooks, and each notebook costs $2. So, the total cost for the notebooks would be 6 times $2. Let me calculate that:\n\n6 notebooks * $2/notebook = $12\n\nOkay, so the notebooks cost her $12 in total.\n\nNext, she bought 4 pens, and each pen costs $1.50. So, the total cost for the pens would be 4 times $1.50. Let's calculate that:\n\n4 pens * $1.50/pen = $6\n\nSo, the pens cost her $6 in total.\n\nNow, I need to find out the total amount she spent on both notebooks and pens. That would be the sum of the cost of notebooks and the cost of pens:\n\nTotal cost = cost of notebooks + cost of pens\nTotal cost = $12 + $6 = $18\n\nAlright, so Maria spent $18 in total.\n\nShe paid with a $20 bill. To find out how much change she received, I need to subtract the total cost from the amount she paid:\n\nChange = amount paid - total cost\nChange = $20 - $18 = $2\n\nSo, Maria received $2 in change.\n\nWait a minute, let me double-check that. Maybe I should verify my calculations to make sure I didn't make any mistakes.\n\nFirst, notebooks: 6 * $2 = $12. That seems correct.\n\nPens: 4 * $1.50 = $6. That also seems right.\n\nTotal cost: $12 + $6 = $18. Okay.\n\nAmount paid: $20.\n\nChange: $20 - $18 = $2.\n\nYes, that looks correct.\n\nI think that's the answer. Maria received $2 in change.\n\n**Final Answer**\n\n\\[ \\boxed{2} \\]",
+      "correct": true,
+      "time_s": 64.72,
+      "tokens": 487
+    }
+  ]
+}

data/results/gsm8k_IO_qwen2.5_32b_20260703_144649.json

@@ -0,0 +1,40 @@
+{
+  "summary": {
+    "method": "IO",
+    "model": "qwen2.5:32b",
+    "task": "gsm8k",
+    "samples": 3,
+    "correct": 2,
+    "accuracy": 0.6667,
+    "avg_time_s": 0.5
+  },
+  "details": [
+    {
+      "question": "Janet's ducks lay 16 eggs per day. She eats three for breakfast every morning and bakes muffins with four every day. She sells the remaining eggs at the farmers' market daily for $2 per dozen. How much money does she make per day at the farmers' market?",
+      "expected": "1.50",
+      "predicted": "2",
+      "full_response": "$2",
+      "correct": false,
+      "time_s": 0.5,
+      "tokens": 1
+    },
+    {
+      "question": "A robe takes 2 1/2 yards of fabric and 1/8 yard of trim. If you have 10 yards of fabric and 1 yard of trim, how many robes can you make?",
+      "expected": "4",
+      "predicted": "4",
+      "full_response": "4",
+      "correct": true,
+      "time_s": 0.37,
+      "tokens": 1
+    },
+    {
+      "question": "Kyle is a collector of rare coins. One day he found a rare coin online and bought it for $50. The next month, he sold it at a 20% profit. Six months later, he bought the same coin back, but had to pay 10% more than he sold it for. How much did Kyle pay to buy the coin back?",
+      "expected": "66",
+      "predicted": "66",
+      "full_response": "66 dollars",
+      "correct": true,
+      "time_s": 0.63,
+      "tokens": 4
+    }
+  ]
+}

data/results/gsm8k_IO_qwen2.5_32b_20260703_144722.json

@@ -0,0 +1,40 @@
+{
+  "summary": {
+    "method": "IO",
+    "model": "qwen2.5:32b",
+    "task": "gsm8k",
+    "samples": 3,
+    "correct": 2,
+    "accuracy": 0.6667,
+    "avg_time_s": 0.51
+  },
+  "details": [
+    {
+      "question": "Janet's ducks lay 16 eggs per day. She eats three for breakfast every morning and bakes muffins with four every day. She sells the remaining eggs at the farmers' market daily for $2 per dozen. How much money does she make per day at the farmers' market?",
+      "expected": "1.50",
+      "predicted": "2",
+      "full_response": "$2",
+      "correct": false,
+      "time_s": 0.5,
+      "tokens": 1
+    },
+    {
+      "question": "A robe takes 2 1/2 yards of fabric and 1/8 yard of trim. If you have 10 yards of fabric and 1 yard of trim, how many robes can you make?",
+      "expected": "4",
+      "predicted": "4",
+      "full_response": "4",
+      "correct": true,
+      "time_s": 0.36,
+      "tokens": 1
+    },
+    {
+      "question": "Kyle is a collector of rare coins. One day he found a rare coin online and bought it for $50. The next month, he sold it at a 20% profit. Six months later, he bought the same coin back, but had to pay 10% more than he sold it for. How much did Kyle pay to buy the coin back?",
+      "expected": "66",
+      "predicted": "66",
+      "full_response": "66 dollars",
+      "correct": true,
+      "time_s": 0.66,
+      "tokens": 4
+    }
+  ]
+}

data/results/gsm8k_IO_qwen2.5_32b_20260703_150051.json

@@ -0,0 +1,103 @@
+{
+  "summary": {
+    "method": "IO",
+    "model": "qwen2.5:32b",
+    "task": "gsm8k",
+    "samples": 10,
+    "correct": 7,
+    "accuracy": 0.7,
+    "avg_time_s": 0.89
+  },
+  "details": [
+    {
+      "question": "Janet's ducks lay 16 eggs per day. She eats three for breakfast every morning and bakes muffins with four every day. She sells the remaining eggs at the farmers' market daily for $2 per dozen. How much money does she make per day at the farmers' market?",
+      "expected": "1.50",
+      "predicted": "2",
+      "full_response": "$2",
+      "correct": false,
+      "time_s": 0.51,
+      "tokens": 1
+    },
+    {
+      "question": "A robe takes 2 1/2 yards of fabric and 1/8 yard of trim. If you have 10 yards of fabric and 1 yard of trim, how many robes can you make?",
+      "expected": "4",
+      "predicted": "4",
+      "full_response": "4",
+      "correct": true,
+      "time_s": 0.37,
+      "tokens": 1
+    },
+    {
+      "question": "Kyle is a collector of rare coins. One day he found a rare coin online and bought it for $50. The next month, he sold it at a 20% profit. Six months later, he bought the same coin back, but had to pay 10% more than he sold it for. How much did Kyle pay to buy the coin back?",
+      "expected": "66",
+      "predicted": "66",
+      "full_response": "66 dollars",
+      "correct": true,
+      "time_s": 0.59,
+      "tokens": 4
+    },
+    {
+      "question": "A pet shelter has 9 kittens available for adoption. The shelter normally has 2 cats available. If each cat treats 2 kittens as their own, how many animals are there in all?",
+      "expected": "7",
+      "predicted": "18",
+      "full_response": "18",
+      "correct": false,
+      "time_s": 0.46,
+      "tokens": 1
+    },
+    {
+      "question": "Faye is a flower farmer. She plants 12 rows of daisies with 100 daisies in each row. She also plants 7 rows of roses with 12 roses in each row. How many more daisies than roses does she plant?",
+      "expected": "1116",
+      "predicted": "1056",
+      "full_response": "1056",
+      "correct": false,
+      "time_s": 0.67,
+      "tokens": 2
+    },
+    {
+      "question": "A farmer had 27 watermelons. After selling some watermelons, he had 13 left. Then he bought 28 more watermelons. Later, he sold 15 watermelons. How many watermelons does he have now?",
+      "expected": "26",
+      "predicted": "26",
+      "full_response": "26",
+      "correct": true,
+      "time_s": 0.48,
+      "tokens": 1
+    },
+    {
+      "question": "James buys a bag of 40 cookies. He eats 5 cookies and then divides the rest evenly among his 7 friends. How many cookies does each friend get?",
+      "expected": "5",
+      "predicted": "5",
+      "full_response": "5",
+      "correct": true,
+      "time_s": 0.36,
+      "tokens": 1
+    },
+    {
+      "question": "Tom's mother had 15 apples. She gave Tom 3 apples and gave Sarah twice as many as Tom. How many apples does she have left?",
+      "expected": "6",
+      "predicted": "6",
+      "full_response": "6",
+      "correct": true,
+      "time_s": 0.35,
+      "tokens": 1
+    },
+    {
+      "question": "A school bus can hold 48 students. If 3 buses are used for a field trip and each bus is 75% full, how many students are on the field trip?",
+      "expected": "108",
+      "predicted": "108",
+      "full_response": "108",
+      "correct": true,
+      "time_s": 0.56,
+      "tokens": 2
+    },
+    {
+      "question": "Maria bought 6 notebooks for $2 each and 4 pens for $1.50 each. She paid with a $20 bill. How much change did she receive?",
+      "expected": "2",
+      "predicted": "2",
+      "full_response": "$20 - (6 * $2 + 4 * $1.50) = $20 - ($12 + $6) = $20 - $18 = $2",
+      "correct": true,
+      "time_s": 4.55,
+      "tokens": 21
+    }
+  ]
+}

data/results/gsm8k_IO_qwq_latest_20260703_152126.json

@@ -0,0 +1,103 @@
+{
+  "summary": {
+    "method": "IO",
+    "model": "qwq:latest",
+    "task": "gsm8k",
+    "samples": 10,
+    "correct": 9,
+    "accuracy": 0.9,
+    "avg_time_s": 25.54
+  },
+  "details": [
+    {
+      "question": "Janet's ducks lay 16 eggs per day. She eats three for breakfast every morning and bakes muffins with four every day. She sells the remaining eggs at the farmers' market daily for $2 per dozen. How much money does she make per day at the farmers' market?",
+      "expected": "1.50",
+      "predicted": "1.50",
+      "full_response": "First, we need to find out how many eggs Janet has left after eating some and baking with others.\n\nJanet's ducks lay 16 eggs per day.\n\nShe eats 3 eggs for breakfast every morning and uses 4 eggs for baking muffins every day.\n\nSo, the total eggs used daily are 3 (for breakfast) + 4 (for baking) = 7 eggs.\n\nTherefore, the remaining eggs are 16 (total laid) - 7 (used) = 9 eggs.\n\nNow, she sells these remaining eggs at the farmers' market for $2 per dozen.\n\nFirst, we need to find out how many dozens are there in 9 eggs.\n\nSince 1 dozen equals 12 eggs, then 9 eggs is equal to 9/12 = 0.75 dozen.\n\nNow, if she sells each dozen for $2, then for 0.75 dozen, she would make 0.75 * $2 = $1.50.\n\nTherefore, Janet makes $1.50 per day at the farmers' market from selling eggs.\n\n**Final Answer**\n\n\\[ \\boxed{1.50} \\]",
+      "correct": true,
+      "time_s": 35.64,
+      "tokens": 269
+    },
+    {
+      "question": "A robe takes 2 1/2 yards of fabric and 1/8 yard of trim. If you have 10 yards of fabric and 1 yard of trim, how many robes can you make?",
+      "expected": "4",
+      "predicted": "4",
+      "full_response": "To determine how many robes you can make, we need to calculate how many robes can be made from the available fabric and trim separately, and then take the smaller number since both materials are required.\n\nFirst, let's find out how much fabric is needed for one robe. The problem states that each robe takes 2 1/2 yards of fabric. We can convert this mixed number to an improper fraction for easier calculation:\n\n\\[ 2 \\frac{1}{2} = \\frac{5}{2} \\text{ yards per robe} \\]\n\nNow, we have 10 yards of fabric available. To find out how many robes can be made from the fabric, we divide the total fabric by the fabric required per robe:\n\n\\[ \\text{Number of robes from fabric} = \\frac{10}{\\frac{5}{2}} = 10 \\times \\frac{2}{5} = 4 \\]\n\nSo, with 10 yards of fabric, you can make 4 robes.\n\nNext, let's look at the trim. Each robe requires 1/8 yard of trim. We have 1 yard of trim available. To find out how many robes can be made from the trim, we divide the total trim by the trim required per robe:\n\n\\[ \\text{Number of robes from trim} = \\frac{1}{\\frac{1}{8}} = 1 \\times 8 = 8 \\]\n\nSo, with 1 yard of trim, you can make 8 robes.\n\nHowever, since both fabric and trim are required to make a robe, the limiting factor is the fabric, which allows only 4 robes. Therefore, the number of robes you can make is:\n\n\\[ \\boxed{4} \\]",
+      "correct": true,
+      "time_s": 37.39,
+      "tokens": 437
+    },
+    {
+      "question": "Kyle is a collector of rare coins. One day he found a rare coin online and bought it for $50. The next month, he sold it at a 20% profit. Six months later, he bought the same coin back, but had to pay 10% more than he sold it for. How much did Kyle pay to buy the coin back?",
+      "expected": "66",
+      "predicted": "66",
+      "full_response": "Let's see. Kyle bought the coin for $50 and sold it with a 20% profit. So, first, I need to calculate what price he sold it for.\n\nA 20% profit on $50 would be:\n\n\\[ \\text{Profit} = 50 \\times \\frac{20}{100} = 50 \\times 0.20 = 10 \\]\n\nSo, he sold it for:\n\n\\[ \\text{Selling Price} = 50 + 10 = 60 \\]\n\nThen, six months later, he bought it back at 10% more than he sold it for. So, I need to find 10% of $60 and add it to the selling price.\n\n\\[ \\text{Additional Amount} = 60 \\times \\frac{10}{100} = 60 \\times 0.10 = 6 \\]\n\nTherefore, the buyback price is:\n\n\\[ \\text{Buyback Price} = 60 + 6 = 66 \\]\n\nSo, Kyle paid $66 to buy the coin back.\n\n**Final Answer**\n\n\\[ \\boxed{66} \\]",
+      "correct": true,
+      "time_s": 26.78,
+      "tokens": 222
+    },
+    {
+      "question": "A pet shelter has 9 kittens available for adoption. The shelter normally has 2 cats available. If each cat treats 2 kittens as their own, how many animals are there in all?",
+      "expected": "7",
+      "predicted": "11",
+      "full_response": "So, the shelter has 9 kittens and normally has 2 cats. Each cat treats 2 kittens as their own. I need to find out the total number of animals in the shelter.\n\nFirst, I should figure out what \"each cat treats 2 kittens as their own\" means. Does that mean that these kittens are being taken care of by the cats, or something like that?\n\nWait, maybe it's just about counting how many kittens are being cared for by the cats. But the question is about the total number of animals, which includes both cats and kittens.\n\nLet me see. If there are 2 cats and each treats 2 kittens as their own, that means there are 2 x 2 = 4 kittens being treated by the cats.\n\nBut there are 9 kittens in total. So, out of these 9 kittens, 4 are being treated by the cats, and the remaining 5 are not being treated by any cat.\n\nWait, but the question doesn't specify that only some kittens are being treated by the cats. It says each cat treats 2 kittens as their own, but it doesn't say that's all the kittens there are.\n\nMaybe I'm overcomplicating this. The shelter has 9 kittens and normally has 2 cats. So, the total number of animals would just be the sum of the kittens and the cats.\n\nSo, 9 kittens + 2 cats = 11 animals in total.\n\nBut the question mentions that each cat treats 2 kittens as their own. Does that mean that these kittens are considered to be part of the cats' groups, but still separate animals?\n\nI think the way to look at it is that the kittens are distinct animals from the cats, even if they are being treated by the cats.\n\nSo, the total number of animals is still 9 kittens plus 2 cats, which equals 11 animals.\n\nWait, but maybe there's something else I'm missing. Let's read the question again: \"If each cat treats 2 kittens as their own, how many animals are there in all?\"\n\nIt seems like the question is simply asking for the total number of animals, considering both cats and kittens, and the fact that cats are treating some kittens as their own doesn't change the count of individual animals.\n\nSo, the answer should be 11 animals in total.\n\n**Final Answer**\n\n\\[ \\boxed{11} \\]",
+      "correct": false,
+      "time_s": 51.37,
+      "tokens": 696
+    },
+    {
+      "question": "Faye is a flower farmer. She plants 12 rows of daisies with 100 daisies in each row. She also plants 7 rows of roses with 12 roses in each row. How many more daisies than roses does she plant?",
+      "expected": "1116",
+      "predicted": "1116",
+      "full_response": "First, I need to find out how many daisies Faye planted. She has 12 rows of daisies with 100 daisies in each row. So, the total number of daisies is 12 times 100, which is 1200 daisies.\n\nNext, I need to find out how many roses she planted. She has 7 rows of roses with 12 roses in each row. So, the total number of roses is 7 times 12, which is 84 roses.\n\nNow, to find out how many more daisies than roses she planted, I subtract the number of roses from the number of daisies. That's 1200 minus 84, which equals 1116.\n\nSo, Faye planted 1116 more daisies than roses.",
+      "correct": true,
+      "time_s": 19.41,
+      "tokens": 189
+    },
+    {
+      "question": "A farmer had 27 watermelons. After selling some watermelons, he had 13 left. Then he bought 28 more watermelons. Later, he sold 15 watermelons. How many watermelons does he have now?",
+      "expected": "26",
+      "predicted": "26",
+      "full_response": "So the farmer started with 27 watermelons. He sold some and had 13 left. Then he bought 28 more, and after that, he sold 15. I need to find out how many he has now.\n\nFirst, he had 27 and sold some to have 13 left. So, the number he sold first is 27 minus 13, which is 14 watermelons.\n\nBut I don't really need to know how many he sold; I just need to know he has 13 after selling some.\n\nThen, he bought 28 more, so now he has 13 plus 28, which is 41 watermelons.\n\nAfter that, he sold 15, so he has 41 minus 15, which is 26 watermelons.\n\nSo, the farmer has 26 watermelons now.\n\n**Final Answer**\n\n\\[ \\boxed{26} \\]",
+      "correct": true,
+      "time_s": 21.35,
+      "tokens": 204
+    },
+    {
+      "question": "James buys a bag of 40 cookies. He eats 5 cookies and then divides the rest evenly among his 7 friends. How many cookies does each friend get?",
+      "expected": "5",
+      "predicted": "5",
+      "full_response": "So James starts with 40 cookies. He eats 5, so that leaves him with 35 cookies. Then he divides these 35 cookies evenly among his 7 friends. To find out how many cookies each friend gets, you divide 35 by 7, which is 5. So each friend gets 5 cookies.",
+      "correct": true,
+      "time_s": 7.53,
+      "tokens": 84
+    },
+    {
+      "question": "Tom's mother had 15 apples. She gave Tom 3 apples and gave Sarah twice as many as Tom. How many apples does she have left?",
+      "expected": "6",
+      "predicted": "6",
+      "full_response": "Let's see. Tom's mother started with 15 apples. She gave Tom 3 apples. So, she has 15 - 3 = 12 apples left. Then, she gave Sarah twice as many as she gave Tom. Since she gave Tom 3 apples, twice that amount would be 2 * 3 = 6 apples to Sarah. So, she gave away an additional 6 apples to Sarah. Therefore, the number of apples she has left is 12 - 6 = 6 apples.\n\n**Final Answer**\n\n\\[ \\boxed{6} \\]",
+      "correct": true,
+      "time_s": 12.79,
+      "tokens": 132
+    },
+    {
+      "question": "A school bus can hold 48 students. If 3 buses are used for a field trip and each bus is 75% full, how many students are on the field trip?",
+      "expected": "108",
+      "predicted": "108",
+      "full_response": "So, each bus can hold 48 students, and there are 3 buses being used. Each bus is 75% full. To find out how many students are on the field trip, I need to calculate 75% of 48 for one bus and then multiply that by 3 because there are three buses.\n\nFirst, I'll find 75% of 48. Percentage means per hundred, so 75% is the same as 75/100 or 0.75 in decimal form. So, 0.75 times 48 should give me the number of students per bus.\n\n0.75 * 48 = 36\n\nSo, each bus has 36 students. Since there are three buses, I need to multiply 36 by 3.\n\n36 * 3 = 108\n\nTherefore, there are 108 students on the field trip.\n\nBut just to make sure, maybe I should check my calculations again. First, 75% of 48:\n\n75% = 0.75\n\n0.75 * 48 = 36, that seems correct.\n\nThen, 36 students per bus times 3 buses:\n\n36 * 3 = 108\n\nYes, that's correct. So, the final answer is 108 students.\n\n**Final Answer**\n\n\\[ \\boxed{108} \\]",
+      "correct": true,
+      "time_s": 32.03,
+      "tokens": 295
+    },
+    {
+      "question": "Maria bought 6 notebooks for $2 each and 4 pens for $1.50 each. She paid with a $20 bill. How much change did she receive?",
+      "expected": "2",
+      "predicted": "2",
+      "full_response": "First, calculate the total cost of the notebooks: 6 notebooks * $2/notebook = $12.\n\nNext, calculate the total cost of the pens: 4 pens * $1.50/pen = $6.\n\nNow, add the costs together to find the total amount spent: $12 + $6 = $18.\n\nFinally, subtract the total amount spent from the amount Maria paid: $20 - $18 = $2.\n\nSo, Maria received $2 in change.",
+      "correct": true,
+      "time_s": 11.13,
+      "tokens": 117
+    }
+  ]
+}

data/results/math_CoT_qwen2.5_32b_20260703_151621.json

@@ -0,0 +1,103 @@
+{
+  "summary": {
+    "method": "CoT",
+    "model": "qwen2.5:32b",
+    "task": "math",
+    "samples": 10,
+    "correct": 9,
+    "accuracy": 0.9,
+    "avg_time_s": 36.46
+  },
+  "details": [
+    {
+      "question": "Find the value of $x$ such that $\\sqrt{4x + 5} = 7$.",
+      "expected": "11",
+      "predicted": "11",
+      "full_response": "To solve for \\( x \\) in the equation \\( \\sqrt{4x + 5} = 7 \\), we will follow these steps:\n\n1. **Isolate the square root**: The given equation is already isolated with the square root on one side.\n   \\[\n   \\sqrt{4x + 5} = 7\n   \\]\n\n2. **Square both sides** to eliminate the square root:\n   \\[\n   (\\sqrt{4x + 5})^2 = 7^2\n   \\]\n   Simplifying this, we get:\n   \\[\n   4x + 5 = 49\n   \\]\n\n3. **Solve for \\( x \\)** by isolating the variable:\n   - Subtract 5 from both sides of the equation:\n     \\[\n     4x + 5 - 5 = 49 - 5\n     \\]\n     Simplifying this, we get:\n     \\[\n     4x = 44\n     \\]\n\n   - Divide both sides by 4 to solve for \\( x \\):\n     \\[\n     x = \\frac{44}{4}\n     \\]\n     Simplifying this, we get:\n     \\[\n     x = 11\n     \\]\n\nTherefore, the value of \\( x \\) is \\(\\boxed{11}\\).",
+      "correct": true,
+      "time_s": 29.56,
+      "tokens": 261
+    },
+    {
+      "question": "A box contains 5 red balls and 7 blue balls. If two balls are drawn at random without replacement, what is the probability that both balls are red? Express your answer as a fraction in simplest form.",
+      "expected": "5/33",
+      "predicted": "\\frac{5}{33}",
+      "full_response": "To solve this problem, we need to calculate the probability of drawing two red balls from a box containing 5 red and 7 blue balls. We will do this step-by-step:\n\n1. **Determine the total number of balls**:\n   - There are 5 red balls and 7 blue balls.\n   - Total number of balls = \\(5 + 7 = 12\\).\n\n2. **Calculate the probability of drawing a red ball on the first draw**:\n   - The number of favorable outcomes (drawing a red ball) is 5.\n   - The total possible outcomes for the first draw are 12.\n   - Probability of drawing a red ball on the first draw = \\(\\frac{5}{12}\\).\n\n3. **Calculate the probability of drawing a second red ball given that the first one was red**:\n   - After drawing one red ball, there are now \\(5-1=4\\) red balls left.\n   - The total number of balls remaining is \\(12-1=11\\).\n   - Probability of drawing a red ball on the second draw = \\(\\frac{4}{11}\\).\n\n4. **Calculate the combined probability**:\n   - Since these are dependent events (the outcome of the first event affects the second), we multiply the probabilities.\n   - Combined probability = \\(\\left( \\frac{5}{12} \\right) \\times \\left( \\frac{4}{11} \\right)\\).\n\n5. **Simplify the combined probability**:\n   - Multiply the numerators: \\(5 \\times 4 = 20\\).\n   - Multiply the denominators: \\(12 \\times 11 = 132\\).\n   - Combined probability = \\(\\frac{20}{132}\\).\n\n6. **Simplify the fraction**:\n   - Find the greatest common divisor (GCD) of 20 and 132, which is 4.\n   - Divide both numerator and denominator by their GCD: \n     \\[\n     \\frac{20 \\div 4}{132 \\div 4} = \\frac{5}{33}\n     \\]\n\nTherefore, the probability that both balls drawn are red is:\n\n\\boxed{\\frac{5}{33}}",
+      "correct": false,
+      "time_s": 50.01,
+      "tokens": 549
+    },
+    {
+      "question": "What is the sum of the first 20 positive integers?",
+      "expected": "210",
+      "predicted": "210",
+      "full_response": "To find the sum of the first 20 positive integers, we can use the formula for the sum of an arithmetic series. The general formula for the sum \\( S \\) of the first \\( n \\) terms of an arithmetic sequence is:\n\n\\[ S = \\frac{n}{2} (a + l) \\]\n\nwhere:\n- \\( n \\) is the number of terms,\n- \\( a \\) is the first term, and\n- \\( l \\) is the last term.\n\nFor this problem:\n- The number of terms \\( n \\) is 20.\n- The first term \\( a \\) is 1 (the first positive integer).\n- The last term \\( l \\) is 20 (since we are summing up to the 20th positive integer).\n\nNow, substitute these values into the formula:\n\n\\[ S = \\frac{20}{2} (1 + 20) \\]\n\nFirst, calculate the value inside the parentheses:\n\n\\[ 1 + 20 = 21 \\]\n\nNext, multiply by \\( \\frac{20}{2} \\):\n\n\\[ S = 10 \\times 21 \\]\n\nFinally, perform the multiplication:\n\n\\[ S = 210 \\]\n\nTherefore, the sum of the first 20 positive integers is:\n\n\\boxed{210}",
+      "correct": true,
+      "time_s": 29.51,
+      "tokens": 295
+    },
+    {
+      "question": "If $f(x) = 2x^2 + 3x - 5$, find $f(-2)$.",
+      "expected": "-3",
+      "predicted": "-3",
+      "full_response": "To solve for \\( f(-2) \\), we need to substitute \\( x = -2 \\) into the function \\( f(x) = 2x^2 + 3x - 5 \\).\n\nStep-by-step solution:\n\n1. Substitute \\( x = -2 \\) into the function:\n   \\[\n   f(-2) = 2(-2)^2 + 3(-2) - 5\n   \\]\n\n2. Calculate \\( (-2)^2 \\):\n   \\[\n   (-2)^2 = 4\n   \\]\n   So, we have:\n   \\[\n   f(-2) = 2(4) + 3(-2) - 5\n   \\]\n\n3. Multiply the terms:\n   \\[\n   2(4) = 8\n   \\]\n   and\n   \\[\n   3(-2) = -6\n   \\]\n   So, we have:\n   \\[\n   f(-2) = 8 - 6 - 5\n   \\]\n\n4. Combine the terms:\n   \\[\n   8 - 6 = 2\n   \\]\n   and then,\n   \\[\n   2 - 5 = -3\n   \\]\n\nTherefore, the value of \\( f(-2) \\) is:\n\\[\n\\boxed{-3}\n\\]",
+      "correct": true,
+      "time_s": 29.33,
+      "tokens": 202
+    },
+    {
+      "question": "The sum of two numbers is 20 and their difference is 4. What is the product of the two numbers?",
+      "expected": "96",
+      "predicted": "96",
+      "full_response": "To solve this problem, we will use a system of equations based on the information given:\n\n1. Let \\( x \\) be one number.\n2. Let \\( y \\) be the other number.\n\nFrom the problem statement, we have:\n- The sum of the two numbers is 20: \n\\[ x + y = 20 \\]\n- Their difference is 4:\n\\[ x - y = 4 \\]\n\nWe now have a system of linear equations:\n1. \\( x + y = 20 \\)\n2. \\( x - y = 4 \\)\n\nTo solve for \\( x \\) and \\( y \\), we can add these two equations together to eliminate \\( y \\):\n\n\\[ (x + y) + (x - y) = 20 + 4 \\]\n\\[ 2x = 24 \\]\n\nSolving for \\( x \\):\n\\[ x = \\frac{24}{2} \\]\n\\[ x = 12 \\]\n\nNow that we have \\( x \\), substitute it back into one of the original equations to solve for \\( y \\). We use the first equation:\n\\[ x + y = 20 \\]\n\\[ 12 + y = 20 \\]\n\\[ y = 20 - 12 \\]\n\\[ y = 8 \\]\n\nSo, the two numbers are \\( x = 12 \\) and \\( y = 8 \\).\n\nNext, we need to find their product:\n\\[ xy = 12 \\times 8 \\]\n\\[ xy = 96 \\]\n\nTherefore, the product of the two numbers is:\n\n\\boxed{96}",
+      "correct": true,
+      "time_s": 35.69,
+      "tokens": 320
+    },
+    {
+      "question": "How many distinguishable permutations can be made from the letters in the word 'MISSISSIPPI'?",
+      "expected": "34650",
+      "predicted": "34650",
+      "full_response": "To solve this problem, we need to calculate the number of distinguishable permutations of the letters in the word \"MISSISSIPPI\". \n\nStep 1: Identify the total number of letters.\nThe word \"MISSISSIPPI\" has a total of 11 letters.\n\nStep 2: Count the frequency of each distinct letter.\n- M appears once (1 time)\n- I appears four times (4 times)\n- S appears four times (4 times)\n- P appears two times (2 times)\n\nStep 3: Use the formula for permutations with repetitions.\nThe number of distinguishable permutations is given by:\n\\[ \\frac{n!}{n_1! \\cdot n_2! \\cdot ... \\cdot n_k!} \\]\nwhere \\( n \\) is the total number of items to arrange, and \\( n_1, n_2, ..., n_k \\) are the frequencies of each distinct item.\n\nFor \"MISSISSIPPI\":\n\\[ n = 11 \\]\n\\[ n_M = 1, \\quad n_I = 4, \\quad n_S = 4, \\quad n_P = 2 \\]\n\nStep 4: Plug in these values into the formula.\n\\[ \\frac{11!}{1! \\cdot 4! \\cdot 4! \\cdot 2!} \\]\n\nStep 5: Calculate the factorials.\n- \\( 11! = 39916800 \\)\n- \\( 1! = 1 \\)\n- \\( 4! = 24 \\)\n- \\( 2! = 2 \\)\n\nStep 6: Substitute these factorial values into the formula and simplify.\n\\[ \\frac{39916800}{1 \\cdot 24 \\cdot 24 \\cdot 2} \\]\n\\[ \\frac{39916800}{1152} = 34650 \\]\n\nTherefore, the number of distinguishable permutations is:\n\\boxed{34650}",
+      "correct": true,
+      "time_s": 44.3,
+      "tokens": 410
+    },
+    {
+      "question": "Find the area of a circle with circumference $8\\pi$.",
+      "expected": "16\\pi",
+      "predicted": "16\\pi",
+      "full_response": "To find the area of a circle given its circumference, we can follow these steps:\n\n1. **Recall the formula for the circumference of a circle**:\n   \\[\n   C = 2\\pi r\n   \\]\n   where \\(C\\) is the circumference and \\(r\\) is the radius.\n\n2. **Substitute the given value into the formula**:\n   Given that the circumference \\(C = 8\\pi\\), we can set up the equation:\n   \\[\n   8\\pi = 2\\pi r\n   \\]\n\n3. **Solve for the radius \\(r\\)**:\n   Divide both sides of the equation by \\(2\\pi\\) to isolate \\(r\\):\n   \\[\n   r = \\frac{8\\pi}{2\\pi} = 4\n   \\]\n   So, the radius \\(r\\) is 4.\n\n4. **Recall the formula for the area of a circle**:\n   \\[\n   A = \\pi r^2\n   \\]\n\n5. **Substitute the value of the radius into the area formula**:\n   Using \\(r = 4\\):\n   \\[\n   A = \\pi (4)^2 = \\pi \\cdot 16 = 16\\pi\n   \\]\n\nTherefore, the area of the circle is:\n\n\\boxed{16\\pi}",
+      "correct": true,
+      "time_s": 30.27,
+      "tokens": 278
+    },
+    {
+      "question": "If $\\log_2(x) + \\log_2(x-2) = 3$, find $x$.",
+      "expected": "4",
+      "predicted": "4",
+      "full_response": "To solve the equation \\(\\log_2(x) + \\log_2(x-2) = 3\\), we can follow these steps:\n\n1. **Combine Logarithms**: Use the logarithm property that states \\(\\log_b(a) + \\log_b(c) = \\log_b(ac)\\). Applying this to our equation, we get:\n   \\[\n   \\log_2(x) + \\log_2(x-2) = \\log_2(x(x-2))\n   \\]\n   So the equation becomes:\n   \\[\n   \\log_2(x(x-2)) = 3\n   \\]\n\n2. **Exponentiate Both Sides**: To remove the logarithm, we can exponentiate both sides of the equation with base 2:\n   \\[\n   x(x-2) = 2^3\n   \\]\n   Simplifying \\(2^3\\), we get:\n   \\[\n   x(x-2) = 8\n   \\]\n\n3. **Form a Quadratic Equation**: Expand and rearrange the equation to form a standard quadratic equation:\n   \\[\n   x^2 - 2x = 8\n   \\]\n   Subtract 8 from both sides:\n   \\[\n   x^2 - 2x - 8 = 0\n   \\]\n\n4. **Solve the Quadratic Equation**: Factorize the quadratic equation \\(x^2 - 2x - 8\\):\n   \\[\n   (x-4)(x+2) = 0\n   \\]\n   Setting each factor to zero gives us:\n   \\[\n   x - 4 = 0 \\quad \\text{or} \\quad x + 2 = 0\n   \\]\n   Solving these, we get:\n   \\[\n   x = 4 \\quad \\text{or} \\quad x = -2\n   \\]\n\n5. **Check for Valid Solutions**: Since \\(x\\) must be positive (as logarithms are only defined for positive arguments), we discard \\(x = -2\\). Thus, the valid solution is:\n   \\[\n   x = 4\n   \\]\n\n6. **Verify the Solution**: Substitute \\(x = 4\\) back into the original equation to ensure it satisfies the conditions:\n   \\[\n   \\log_2(4) + \\log_2(4-2) = \\log_2(4) + \\log_2(2)\n   \\]\n   Simplifying, we get:\n   \\[\n   2 + 1 = 3\n   \\]\n   This is true.\n\nTherefore, the solution to the equation is:\n\n\\boxed{4}",
+      "correct": true,
+      "time_s": 58.51,
+      "tokens": 514
+    },
+    {
+      "question": "A geometric sequence has first term 3 and common ratio 2. What is the 8th term?",
+      "expected": "384",
+      "predicted": "384",
+      "full_response": "To find the 8th term of a geometric sequence with the given parameters, we can use the formula for the nth term of a geometric sequence:\n\n\\[a_n = a_1 \\cdot r^{(n-1)}\\]\n\nwhere:\n- \\(a_n\\) is the nth term,\n- \\(a_1\\) is the first term,\n- \\(r\\) is the common ratio,\n- \\(n\\) is the term number.\n\nGiven in the problem:\n- The first term, \\(a_1 = 3\\),\n- The common ratio, \\(r = 2\\),\n- We need to find the 8th term, so \\(n = 8\\).\n\nStep-by-step solution:\n\n1. Substitute the given values into the formula for the nth term of a geometric sequence:\n   \\[a_8 = 3 \\cdot 2^{(8-1)}\\]\n\n2. Simplify the exponent:\n   \\[a_8 = 3 \\cdot 2^7\\]\n\n3. Calculate \\(2^7\\):\n   \\[2^7 = 128\\]\n\n4. Multiply by the first term, 3:\n   \\[a_8 = 3 \\cdot 128 = 384\\]\n\nTherefore, the 8th term of the geometric sequence is:\n\n\\boxed{384}",
+      "correct": true,
+      "time_s": 29.4,
+      "tokens": 264
+    },
+    {
+      "question": "How many ways can 5 people be arranged in a line?",
+      "expected": "120",
+      "predicted": "120",
+      "full_response": "To solve this problem of arranging 5 people in a line, we need to consider permutations since the order matters here. The number of ways to arrange \\( n \\) distinct objects is given by \\( n! \\) (n factorial), which means multiplying all positive integers up to \\( n \\).\n\nStep-by-step solution:\n\n1. Identify the total number of people: 5.\n2. Calculate the factorial of this number, i.e., \\( 5! \\).\n3. Compute \\( 5! \\):\n   - Start with 5 and multiply it by each integer less than itself down to 1:\n     \\[\n     5! = 5 \\times 4 \\times 3 \\times 2 \\times 1\n     \\]\n4. Perform the multiplication step-by-step:\n   - First, \\( 5 \\times 4 = 20 \\)\n   - Next, \\( 20 \\times 3 = 60 \\)\n   - Then, \\( 60 \\times 2 = 120 \\)\n   - Finally, \\( 120 \\times 1 = 120 \\)\n\nThus, the number of ways to arrange 5 people in a line is:\n\n\\[\n\\boxed{120}\n\\]",
+      "correct": true,
+      "time_s": 28.05,
+      "tokens": 275
+    }
+  ]
+}

data/results/math_IO_qwen2.5_32b_20260703_151016.json

@@ -0,0 +1,103 @@
+{
+  "summary": {
+    "method": "IO",
+    "model": "qwen2.5:32b",
+    "task": "math",
+    "samples": 10,
+    "correct": 8,
+    "accuracy": 0.8,
+    "avg_time_s": 0.89
+  },
+  "details": [
+    {
+      "question": "Find the value of $x$ such that $\\sqrt{4x + 5} = 7$.",
+      "expected": "11",
+      "predicted": "12",
+      "full_response": "12",
+      "correct": false,
+      "time_s": 0.49,
+      "tokens": 1
+    },
+    {
+      "question": "A box contains 5 red balls and 7 blue balls. If two balls are drawn at random without replacement, what is the probability that both balls are red? Express your answer as a fraction in simplest form.",
+      "expected": "5/33",
+      "predicted": "5/33",
+      "full_response": "5/33",
+      "correct": true,
+      "time_s": 0.65,
+      "tokens": 2
+    },
+    {
+      "question": "What is the sum of the first 20 positive integers?",
+      "expected": "210",
+      "predicted": "210",
+      "full_response": "210",
+      "correct": true,
+      "time_s": 0.85,
+      "tokens": 2
+    },
+    {
+      "question": "If $f(x) = 2x^2 + 3x - 5$, find $f(-2)$.",
+      "expected": "-3",
+      "predicted": "-7",
+      "full_response": "-7",
+      "correct": false,
+      "time_s": 1.0,
+      "tokens": 1
+    },
+    {
+      "question": "The sum of two numbers is 20 and their difference is 4. What is the product of the two numbers?",
+      "expected": "96",
+      "predicted": "96",
+      "full_response": "96",
+      "correct": true,
+      "time_s": 0.95,
+      "tokens": 1
+    },
+    {
+      "question": "How many distinguishable permutations can be made from the letters in the word 'MISSISSIPPI'?",
+      "expected": "34650",
+      "predicted": "34650",
+      "full_response": "34650",
+      "correct": true,
+      "time_s": 1.17,
+      "tokens": 2
+    },
+    {
+      "question": "Find the area of a circle with circumference $8\\pi$.",
+      "expected": "16\\pi",
+      "predicted": "16",
+      "full_response": "$16\\pi$",
+      "correct": true,
+      "time_s": 1.11,
+      "tokens": 3
+    },
+    {
+      "question": "If $\\log_2(x) + \\log_2(x-2) = 3$, find $x$.",
+      "expected": "4",
+      "predicted": "4",
+      "full_response": "4",
+      "correct": true,
+      "time_s": 0.82,
+      "tokens": 1
+    },
+    {
+      "question": "A geometric sequence has first term 3 and common ratio 2. What is the 8th term?",
+      "expected": "384",
+      "predicted": "384",
+      "full_response": "384",
+      "correct": true,
+      "time_s": 1.01,
+      "tokens": 2
+    },
+    {
+      "question": "How many ways can 5 people be arranged in a line?",
+      "expected": "120",
+      "predicted": "120",
+      "full_response": "120",
+      "correct": true,
+      "time_s": 0.85,
+      "tokens": 2
+    }
+  ]
+}