Dolphin Math Data Generator

Purpose

This project, generates synthetic math problems covering various arithmetic and algebra topics. Crucially, it also generates detailed, step-by-step solutions intended to mimic the process a human would follow when solving the problem manually (like a "visible scratchpad").

The output is designed for training language models to perform multi-step mathematical reasoning.

It works for both SFT and RL. You should generate separate datasets for SFT and RL. SFT teaches it the syntax, RL teaches it to git gud at it.

Features

Generates problems and detailed steps for the following types:

• Basic Arithmetic:
  • Long Division (with remainder)
  • Decimal Multiplication
  • Decimal Addition
  • Decimal Subtraction
  • Decimal Division
  • Fraction Addition (common and uncommon denominators)
  • Fraction Subtraction (common and uncommon denominators)
  • Fraction Multiplication
  • Fraction Division
• Algebra:
  • Simple Linear Equations (e.g., ax + b = c)
  • Complex Linear Equations (e.g., ax + b = cx + d)
  • Quadratic Equations (using the quadratic formula)
  • Simplifying Algebraic Expressions (with distribution)
  • Evaluating Algebraic Expressions (substituting variable values)
  • Proportional Relationships
• Geometry:
  • Pythagorean Theorem (finding hypotenuse)
• Percentages:
  • Finding the part (e.g., "What is 25% of 80?")
  • Finding the percent (e.g., "15 is what percent of 50?")
  • Finding the whole (e.g., "20 is 50% of what number?")
• Tools/Methods:
  • Abacus-style Addition (column-by-column with carries)

Usage

Generating Samples

To see one sample output from each generator type:

python dolphin_math_datagen.py --sample

You can optionally specify a random seed using -s or --seed.

Generating a Dataset

To generate a full dataset file in JSON Lines format:

python dolphin_math_datagen.py -n <number_of_examples> -o <output_file.jsonl>

Example: Generate 50,000 examples with seed 123:

# Specify output file explicitly:
python dolphin_math_datagen.py -n 50000 -o my_dataset.jsonl -s 123

# Use default output filename (dolphin_math_50000.jsonl):
python dolphin_math_datagen.py -n 50000 -s 123

Default values are 10,000 examples (outputting to dolphin_math_10000.jsonl by default if -o is omitted), and seed 42 if arguments are omitted.

Running Tests

Unit tests are provided for each generator. To run all tests:

python -m unittest discover tests

Op-Code Legend

The steps field in the output JSON contains a list of strings, each representing a step in the solution. Steps are formatted as OP_CODE|arg1|arg2|....

• Arithmetic:
  • D: Divide (dividend, divisor, quotient_digit)
  • M: Multiply (factor1, factor2, product)
  • S: Subtract (minuend, subtrahend, difference)
  • A: Add (addend1, addend2, sum)
  • B: Bring down (remainder_before, digit_down, new_num_to_divide)
  • R: Remainder (final_remainder)
  • C: Convert fraction for LCD (orig_frac_str, lcd, converted_frac_str)
  • L: LCD calculation (denominator1, denominator2, lcd)
  • I: Invert fraction (orig_frac_str, inverted_frac_str)
  • F: Fraction simplification (unsimplified_frac_str, simplified_frac_str)
• Decimal Add/Sub:
  • DEC_ALIGN: Align numbers by decimal point (num1_aligned, num2_aligned)
  • DEC_ADD_COL: Add column (col_name, details_str, result_str)
  • DEC_SUB_COL: Subtract column (col_name, details_str, result_str)
  • DEC_CARRY_FINAL: Final carry digit from leftmost column (carry_digit)
• Decimal Multiplication:
  • MUL_SETUP: Setup integer multiplication (int1_str, int2_str)
  • MUL_PARTIAL: Multiply by digit for partial product (digit, top_int_str, partial_product_shifted_str)
  • ADD_PARTIALS: Sum the partial products (sum_expression_str, result_sum_str)
  • COUNT_DP: Count total decimal places in original factors (dp1, dp2, total_dp)
  • PLACE_DP: Place decimal point in the final integer sum (sum_int_str, total_dp, final_result_str)
• Decimal Division:
  • DEC_SHIFT: Shift decimal points (orig_expr, shifted_expr, shift_places)
  • DIV_SETUP: Setup long division (integer_dividend, integer_divisor)
  • PLACE_DP_Q: Place decimal in quotient (quotient_digits_str, dp_position_from_left_in_shifted_dividend)
  • (Reuses B, D, M, S from Arithmetic)
• Percentages:
  • PERCENT_TO_DEC: Convert percent to decimal (percent_str, decimal_val)
  • SETUP_PERCENT_EQ: Show the equation setup (equation_str)
  • REARRANGE_EQ: Show rearranged equation (rearranged_equation_str)
  • PERCENT_CALC_PART: Calculate the part (percent_dec, whole, part_result) - Only for find_part
  • DEC_TO_PERCENT: Convert decimal result back to percent (decimal_val, percent_str) - Only for find_percent
  • (Uses division steps internally for find_percent/find_whole)
• Algebra:
  • DISC: Discriminant calculation (b_squared, four_ac, discriminant)
  • ROOT: Square root calculation (number, root)
  • Q1/Q2: Quadratic formula roots (neg_b, sqrt_disc, two_a, root_value)
  • DIST: Distribute term (factor, expr_in_parens, result_expr)
  • REWRITE: Rewrite expression/equation after step (new_form_string)
  • COMB_X: Combine X terms (term1, term2, result_term)
  • COMB_CONST: Combine Constant terms (const1, const2, result_const)
  • SUBST: Substitute value (var_name, value, resulting_expr)
  • MOVE_TERM: Move term across equals sign (term_moved, target_side, resulting_equation_str)
  • DIV_COEFF: Divide by coefficient (numerator, denominator, result_str)
• Geometry:
  • E: Exponent/Power (base, exponent, result)
  • (Reuses ROOT)
• Algebra+:
  • PROP_SETUP: Setup proportion (proportion_str)
• Tools/Methods (Abacus):
  • AB_SET: Set initial number (number)
  • AB_INFO: Informational text (text)
  • AB_ADD_DGT: Add digits in a column (col_name, details_str, column_sum)
  • AB_CARRY: Show carry propagation (from_col, carry_value, to_col)
  • AB_CARRY_FINAL: Final carry from leftmost column (carry_value)
• Final Answer:
  • Z: Contains the final formatted answer string (final_answer_str)

Dependencies

• Python 3 (tested with 3.9+)