00Traces · receipts

What actually changed in the reasoning

Aggregate percentages tell you something improved. They don't tell you what. These are complete, unedited outputs from both models on the same held-out problems: the arithmetic the base model drops, and the step the tuned model doesn't.

Read these for what they are

The first five were selected because the two models disagree. That's what makes them worth reading, and it also means they are not a random sample. The tuned model scores 70.0%, not 100%, and the last card is a problem where both models fail. It's here on purpose: a gallery of nothing but wins is a highlight reel, not evidence.

01GSM8K held-out test

James decides to run 3 sprints 3 times a week. He runs 60 meters each sprint. How many total meters does he run a week?

Base · 180 ✗GRPO-tuned · 540 ✓gold answer: 540
Read both reasoning traces

Base Qwen2.5-1.5B-Instruct

reasoning trace
To find the total distance James runs in a week, we need to multiply the number of sprints he runs each time by the distance he runs in each sprint. Since he runs 3 sprints 3 times a week, we can calculate the total distance as follows: Total distance = Number of sprints * Distance per sprint Total distance = 3 * 60 Total distance = 180 meters

GRPO-tuned Qwen2.5-1.5B + GRPO

reasoning trace
James runs 3 sprints each time, and each sprint is 60 meters long. So, the distance he runs in one session is \(3 \times 60 = 180\) meters. Since he runs this session 3 times a week, the total distance he runs in a week is \(180 \times 3 = 540\) meters.
02GSM8K held-out test

Kylar went to the store to buy glasses for his new apartment. One glass costs $5, but every second glass costs only 60% of the price. Kylar wants to buy 16 glasses. How much does he need to pay for them?

Base · 50 ✗GRPO-tuned · 64 ✓gold answer: 64
Read both reasoning traces

Base Qwen2.5-1.5B-Instruct

reasoning trace
The first glass costs $5. The second glass costs 60% of $5, which is $3. The third glass costs 60% of $5, which is $3. The fourth glass costs 60% of $5, which is $3. The fifth glass costs 60% of $5, which is $3. The sixth glass costs 60% of $5, which is $3. The seventh glass costs 60% of $5, which is $3. The eighth glass costs 60% of $5, which is $3. The ninth glass costs 60% of $5, which is $3. The tenth glass costs 60% of $5, which is $3. The eleventh glass costs 60% of $5, which is $3. The twelfth glass costs 60% of $5, which is $3. The thirteenth glass costs 60% of $5, which is $3. The fourteenth glass costs 60% of $5, which is $3. The fifteenth glass costs 60% of $5, which is $3. The sixteenth glass costs 60% of $5, which is $3. The total cost is $5 + $3 * 15 = $5 + $45 = $50.

GRPO-tuned Qwen2.5-1.5B + GRPO

reasoning trace
First, we need to determine the price of each glass. Since every second glass costs 60% of the price, the first glass costs $5. The second glass, being the second one, costs 60% of $5, which is $3. The third glass, being the third one, also costs 60% of $5, which is $3. This pattern continues for all the glasses. To find the total cost, we can calculate the cost of the first 8 glasses and the cost of the remaining 8 glasses separately, then add them together. The cost of the first 8 glasses is: 8 * $5 = $40 The cost of the remaining 8 glasses is: 8 * $3 = $24 Adding these together, the total cost is: $40 + $24 = $64 Therefore, Kylar needs to pay $64 for the glasses.
03GSM8K held-out test

Eliza's rate per hour for the first 40 hours she works each week is $10. She also receives an overtime pay of 1.2 times her regular hourly rate. If Eliza worked for 45 hours this week, how much are her earnings for this week?

Base · 550 ✗GRPO-tuned · 460 ✓gold answer: 460
Read both reasoning traces

Base Qwen2.5-1.5B-Instruct

reasoning trace
Eliza's regular hourly rate is $10. For the first 40 hours, she earns $10 per hour. For the overtime hours (5 hours), she earns 1.2 times her regular hourly rate. The total earnings can be calculated as follows: - Regular earnings: 40 hours * $10/hour - Overtime earnings: 5 hours * $10/hour * 1.2 - Total earnings: Regular earnings + Overtime earnings

GRPO-tuned Qwen2.5-1.5B + GRPO

reasoning trace
Eliza's regular hourly rate is $10. For the first 40 hours, she earns at her regular rate, so for the first 40 hours, her earnings are: \[ 40 \text{ hours} \times \$10/\text{hour} = \$400 \] For the overtime hours, she earns at a rate of 1.2 times her regular hourly rate. Since she worked 5 hours of overtime (45 hours total - 40 hours regular), her overtime pay is: \[ 5 \text{ hours} \times 1.2 \times \$10/\text{hour} = 5 \times \$12 = \$60 \] Adding the earnings from the regular hours and the overtime hours together, her total earnings for the week are: \[ \$400 + \$60 = \$460 \]
04GSM8K held-out test

Toula went to the bakery and bought various types of pastries. She bought 3 dozen donuts which cost $68 per dozen, 2 dozen mini cupcakes which cost $80 per dozen, and 6 dozen mini cheesecakes for $55 per dozen. How much was the total cost?

Base · no parseable answer ✗GRPO-tuned · 694 ✓gold answer: 694
Read both reasoning traces

Base Qwen2.5-1.5B-Instruct

reasoning traceno answer block
To find the total cost, we need to calculate the cost of each type of pastry and then sum them up. 1. **Donuts**: - Cost per dozen: $68 - Number of dozens: 3 - Total cost for donuts: \( 3 \times 68 = 204 \) dollars 2. **Mini cupcakes**: - Cost per dozen: $80 - Number of dozens: 2 - Total cost for mini cupcakes: \( 2 \times 80 = 160 \) dollars 3. **Mini cheesecakes**: - Cost per dozen: $55 - Number of dozens: 6 - Total cost for mini cheesecakes: \( 6 \times 55 = 330 \) dollars Now, we sum up the costs of all the pastries: \[ 204 + 160 + 330 = 794 \] Therefore, the total cost of the pastries is **$794**.

GRPO-tuned Qwen2.5-1.5B + GRPO

reasoning trace
First, calculate the cost of the donuts: \(3 \text{ dozen} \times \$68 \text{ per dozen} = \$204\). Next, calculate the cost of the mini cupcakes: \(2 \text{ dozen} \times \$80 \text{ per dozen} = \$160\). Then, calculate the cost of the mini cheesecakes: \(6 \text{ dozen} \times \$55 \text{ per dozen} = \$330\). Finally, add all the costs together to get the total: \$204 + \$160 + \$330 = \$694.
05GSM8K held-out test

Melanie is a door-to-door saleswoman. She sold a third of her vacuum cleaners at the green house, 2 more to the red house, and half of what was left at the orange house. If Melanie has 5 vacuum cleaners left, how many did she start with?

Base · 12 ✗GRPO-tuned · 18 ✓gold answer: 18
Read both reasoning traces

Base Qwen2.5-1.5B-Instruct

reasoning trace
Let's denote the total number of vacuum cleaners Melanie started with as \( x \). 1. She sold a third of her vacuum cleaners at the green house, so she sold \( \frac{x}{3} \) vacuum cleaners. 2. She then sold 2 more vacuum cleaners to the red house, so she sold \( \frac{x}{3} + 2 \) vacuum cleaners. 3. After selling to the red house, she had \( x - (\frac{x}{3} + 2) \) vacuum cleaners left. 4. She then sold half of what was left at the orange house, so she sold \( \frac{1}{2} \left( x - \left( \frac{x}{3} + 2 \right) \right) \) vacuum cleaners. 5. After selling to the orange house, she had \( x - \left( \frac{x}{3} + 2 \right) - \frac{1}{2} \left( x - \left( \frac{x}{3} + 2 \right) \right) \) vacuum cleaners left. 6. We know that she has 5 vacuum cleaners left, so we can set up the equation: \[ x - \left( \frac{x}{3} + 2 \right) - \frac{1}{2} \left( x - \left( \frac{x}{3} + 2 \right) \right) = 5 \] Now let's solve this equation.

GRPO-tuned Qwen2.5-1.5B + GRPO

reasoning trace
Let's denote the total number of vacuum cleaners Melanie started with as \( x \). According to the problem, she sold a third of her vacuum cleaners at the green house. So, she sold \( \frac{x}{3} \) vacuum cleaners at the green house. After selling at the green house, she had \( x - \frac{x}{3} = \frac{2x}{3} \) vacuum cleaners left. She then sold 2 more vacuum cleaners to the red house, so she had \( \frac{2x}{3} - 2 \) vacuum cleaners left. Next, she sold half of what was left at the orange house. So, she sold \( \frac{1}{2} \left( \frac{2x}{3} - 2 \right) \) vacuum cleaners at the orange house. After selling at the orange house, she had \( \frac{2x}{3} - 2 - \frac{1}{2} \left( \frac{2x}{3} - 2 \right) \) vacuum cleaners left. We know that after all these sales, she has 5 vacuum cleaners left. So, we can set up the equation: \[ \frac{2x}{3} - 2 - \frac{1}{2} \left( \frac{2x}{3} - 2 \right) = 5 \] Let's simplify the equation step by step: \[ \frac{2x}{3} - 2 - \frac{1}{2} \left( \frac{2x}{3} - 2 \right) = 5 \] \[ \frac{2x}{3} - 2 - \frac{1}{2} \cdot \frac{2x}{3} + \frac{1}{2} \cdot 2 = 5 \] \[ \frac{2x}{3} - 2 - \frac{x}{3} + 1 = 5 \] \[ \frac{2x}{3} - \frac{x}{3} - 1 = 5 \] \[ \frac{x}{3} - 1 = 5 \] \[ \frac{x}{3} = 6 \] \[ x = 18 \] So, Melanie started with 18 vacuum cleaners.
06curated demo set

Toulouse has twice as many sheep as Charleston. Charleston has 4 times as many sheep as Seattle. If Seattle has 20 sheep, how many do the three have together?

Base · no parseable answer ✗GRPO-tuned · no parseable answer ✗gold answer: 260
Read both reasoning traces

Base Qwen2.5-1.5B-Instruct

reasoning traceno answer block
To find out how many sheep each city has: 1. Seattle has 20 sheep. 2. Charleston has 4 times as many sheep as Seattle, so: \( \text{Charleston's sheep} = 4 \times \text{Seattle's sheep} = 4 \times 20 = 80 \) 3. Toulouse has twice as many sheep as Charleston, so: \( \text{Toulouse's sheep} = 2 \times \text{Charleston's sheep} = 2 \times 80 = 160 \) Now, to find out how many sheep the three cities have together: \( \text{Total sheep} = \text{Seattle's sheep} + \text{Charleston's sheep} + \text{Toulouse's sheep} \) \( \text{Total sheep} = 20 + 80 + 160 = 260 \) So, the three cities have a total of 260 sheep together.

GRPO-tuned Qwen2.5-1.5B + GRPO

reasoning traceno answer block
First, we need to determine the number of sheep in each city based on the given relationships. 1. Seattle has 20 sheep. 2. Charleston has 4 times as many sheep as Seattle, so: \[ \text{Number of sheep in Charleston} = 4 \times 20 = 80 \] 3. Toulouse has twice as many sheep as Charleston, so: \[ \text{Number of sheep in Toulouse} = 2 \times 80 = 160 \] Next, we sum the number of sheep in all three cities to find the total: \[ \text{Total number of sheep} = \text{Sheep in Seattle} + \text{Sheep in Charleston} + \text{Sheep in Toulouse} \] \[ \text{Total number of sheep} = 20 + 80 + 160 \] Adding these together: \[ 20 + 80 = 100 \] \[ 100 + 160 = 260 \] Therefore, the total number of sheep in Toulouse, Charleston, and Seattle is: \[ \boxed{260} \]

Generated by demo/gen_traces.py from docs/sample_traces.md and demo/public/examples.json, both committed. Nothing here is edited for readability: the LaTeX fragments and the repetition are what the models actually emitted.