pymlex/calculator

Arithmetic Expression Dataset Generator

Overview

This is a synthetic deterministic dataset with nested arithmetic expressions and step-by-step solutions. We provide examples of bracketed arithmetic expressions using:

• parentheses: ()
• square brackets: []
• curly braces: {}

and operators: +, -, *.

The dataset is balanced across reduction depths from 1 to 15 and is intended for SLMs that learn structured mathematical reasoning from examples.

Content

Each sample contains:

• expression — the original arithmetic expression
• prompt — the input prompt for the model
• completion — the target answer in <think> ... </think> and <answer> ... </answer> format
• answer — the final numeric result
• steps — the number of reduction steps
• text — the full formatted training sample

Counts

• Train examples: 15000
• Validation examples: 750
• Test examples: 3000
• Total examples: 18750

Each step from 1 to 15 appears exactly:

• 1000 times in train
• 50 times in validation
• 200 times in test

The symbol-length distribution:

Example

### Expression
Calculate: {([20 - 9] - 3) * ({[8 + {{2 * 18} - (12 * 19)}] - {(15 * 13) - 12}} + 11)}

### Answer
<think>
Start: {([20 - 9] - 3) * ({[8 + {{2 * 18} - (12 * 19)}] - {(15 * 13) - 12}} + 11)}
1. (20 - 9) = 11
2. (11 - 3) = 8
3. (2 * 18) = 36
4. (12 * 19) = 228
5. (36 - 228) = -192
6. (8 + -192) = -184
7. (15 * 13) = 195
8. (195 - 12) = 183
9. (-184 - 183) = -367
10. (-367 + 11) = -356
11. (8 * -356) = -2848
</think>
<answer>-2848</answer>

Evaluation on Qwen2.5-Math

We used this dataset to evaluate the mathematical abilities of models from the Qwen2.5-Math family. The plot shows that the accuracy of models without integrated calculation tools decreases approximately quadratically:

We propose a weighted accuracy metric where results for problems requiring more steps are weighted by the square of the step count:

$$\text{weighted\_score}=\frac{\sum _{s=1}^{N_{cls}}(\text{mean}({\text{correct}}_s)\cdot s^2)}{\sum _{s=1}^{N_{cls}}{s}^2},N_{cls}=15\backslash text\{weighted\backslash \_score\}\; =\; \backslash frac\{\backslash sum\backslash limits\_\{s=1\}^\{N\_\{cls\}\}\; (\backslash text\{mean\}(\backslash text\{correct\}\_s)\; \backslash cdot\; s^2)\}\{\backslash sum\backslash limits\_\{s=1\}^\{N\_\{cls\}\}\; s^2\},\; \backslash quad\; N\_\{cls\}\; =\; 15$$

Comparison table:

model_id	overall_acc	weighted_score
Qwen/Qwen2.5-Math-1.5B-Instruct	0.758333	0.571052
Qwen/Qwen2.5-Math-7B-Instruct	0.803667	0.651044