problem stringlengths 16 2.02k | solution stringlengths 29 4.45k | answer stringlengths 1 69 | subject stringclasses 7
values | level int64 1 5 | unique_id stringlengths 20 40 | idx int64 0 7k | ete_solution stringlengths 198 2.15k | gen_length int64 512 512 | num_steps int64 14 212 | pareto_index int64 0 33 | sampling_params stringclasses 34
values | worst_case_steps int64 15 232 | best_case_steps int64 13 202 | explore_failures int64 0 0 | explore_count int64 0 10 | solution_reward float64 1 1 | extracted_pred_answer stringlengths 10 264 | extracted_gold_answer stringlengths 10 168 | is_solution_correct bool 1
class | sequence_0 listlengths 512 512 | sequence_1 listlengths 512 512 | sequence_2 listlengths 512 512 | sequence_3 listlengths 512 512 | sequence_4 listlengths 512 512 | sequence_5 listlengths 512 512 | sequence_6 listlengths 512 512 | sequence_7 listlengths 512 512 | sequence_8 listlengths 512 512 | sequence_9 listlengths 512 512 | sequence_10 listlengths 512 512 | sequence_11 listlengths 512 512 | sequence_12 listlengths 512 512 | sequence_13 listlengths 512 512 | sequence_14 listlengths 512 512 | sequence_15 listlengths 512 512 ⌀ | sequence_16 listlengths 512 512 ⌀ | sequence_17 listlengths 512 512 ⌀ | sequence_18 listlengths 512 512 ⌀ | sequence_19 listlengths 512 512 ⌀ | sequence_20 listlengths 512 512 ⌀ | sequence_21 listlengths 512 512 ⌀ | sequence_22 listlengths 512 512 ⌀ | sequence_23 listlengths 512 512 ⌀ | sequence_24 listlengths 512 512 ⌀ | sequence_25 listlengths 512 512 ⌀ | sequence_26 listlengths 512 512 ⌀ | sequence_27 listlengths 512 512 ⌀ | sequence_28 listlengths 512 512 ⌀ | sequence_29 listlengths 512 512 ⌀ | sequence_30 listlengths 512 512 ⌀ | sequence_31 listlengths 512 512 ⌀ | sequence_32 listlengths 512 512 ⌀ | sequence_33 listlengths 512 512 ⌀ | sequence_34 listlengths 512 512 ⌀ | sequence_35 listlengths 512 512 ⌀ | sequence_36 listlengths 512 512 ⌀ | sequence_37 listlengths 512 512 ⌀ | sequence_38 listlengths 512 512 ⌀ | sequence_39 listlengths 512 512 ⌀ | sequence_40 listlengths 512 512 ⌀ | sequence_41 listlengths 512 512 ⌀ | sequence_42 listlengths 512 512 ⌀ | sequence_43 listlengths 512 512 ⌀ | sequence_44 listlengths 512 512 ⌀ | sequence_45 listlengths 512 512 ⌀ | sequence_46 listlengths 512 512 ⌀ | sequence_47 listlengths 512 512 ⌀ | sequence_48 listlengths 512 512 ⌀ | sequence_49 listlengths 512 512 ⌀ | sequence_50 listlengths 512 512 ⌀ | sequence_51 listlengths 512 512 ⌀ | sequence_52 listlengths 512 512 ⌀ | sequence_53 listlengths 512 512 ⌀ | sequence_54 listlengths 512 512 ⌀ | sequence_55 listlengths 512 512 ⌀ |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
"Let \\[f(x) = \\left\\{\n\\begin{array}{cl} ax+3, &\\text{ if }x>2, \\\\\nx-5 &\\text{ if } -2 \\le(...TRUNCATED) | "For the piecewise function to be continuous, the cases must \"meet\" at $2$ and $-2$. For example, (...TRUNCATED) | 0 | Algebra | 5 | train/algebra/0.json | 0 | "To ensure that the piecewise function \\( f(x) \\) is continuous, we need to ensure that the left-h(...TRUNCATED) | 512 | 55 | 11 | "{\"accumulative_error_tolerance\": 0.2, \"alpha\": 0.86, \"block_length\": 64, \"compute_log_probs\(...TRUNCATED) | 75 | 45 | 0 | 10 | 1 | ['0', '0'] | ['0', '0'] | true | [126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,1(...TRUNCATED) | [126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,1(...TRUNCATED) | [126336,126336,126336,126336,117254,126336,126336,126336,126336,126336,126336,126336,126336,126336,1(...TRUNCATED) | [2088,5034,126336,268,117254,1399,126336,126336,126336,126336,126336,126336,126336,126336,126336,126(...TRUNCATED) | [2088,5034,378,268,117254,1399,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336(...TRUNCATED) | [2088,5034,378,268,117254,1399,126336,126336,126336,126336,126336,341,126336,126336,126336,126336,12(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,126336,126336,126336,126336,126336,1(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,126336,126336,126336,126336,12633(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,126336,126336,126336,126336,378,1(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,126336,(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,126336,(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,126336,(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) |
"Let \\[f(x) = \\left\\{\n\\begin{array}{cl} ax+3, &\\text{ if }x>2, \\\\\nx-5 &\\text{ if } -2 \\le(...TRUNCATED) | "For the piecewise function to be continuous, the cases must \"meet\" at $2$ and $-2$. For example, (...TRUNCATED) | 0 | Algebra | 5 | train/algebra/0.json | 0 | "To ensure that the piecewise function \\( f(x) \\) is continuous, we need to ensure that the left-h(...TRUNCATED) | 512 | 55 | 13 | "{\"accumulative_error_tolerance\": 0.2, \"alpha\": 0.86, \"block_length\": 64, \"compute_log_probs\(...TRUNCATED) | 75 | 45 | 0 | 10 | 1 | ['0', '0'] | ['0', '0'] | true | [126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,1(...TRUNCATED) | [126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,1(...TRUNCATED) | [126336,126336,126336,126336,117254,126336,126336,126336,126336,126336,126336,126336,126336,126336,1(...TRUNCATED) | [2088,5034,126336,268,117254,1399,126336,126336,126336,126336,126336,126336,126336,126336,126336,126(...TRUNCATED) | [2088,5034,378,268,117254,1399,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336(...TRUNCATED) | [2088,5034,378,268,117254,1399,126336,126336,126336,126336,126336,341,126336,126336,126336,126336,12(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,126336,126336,126336,126336,126336,1(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,126336,126336,126336,126336,12633(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,126336,126336,126336,126336,378,1(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,126336,(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,126336,(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,126336,(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) |
"Let \\[f(x) = \\left\\{\n\\begin{array}{cl} ax+3, &\\text{ if }x>2, \\\\\nx-5 &\\text{ if } -2 \\le(...TRUNCATED) | "For the piecewise function to be continuous, the cases must \"meet\" at $2$ and $-2$. For example, (...TRUNCATED) | 0 | Algebra | 5 | train/algebra/0.json | 0 | "To ensure that the piecewise function \\( f(x) \\) is continuous, we need to ensure that the left-h(...TRUNCATED) | 512 | 57 | 14 | "{\"accumulative_error_tolerance\": 0.2, \"alpha\": 0.86, \"block_length\": 64, \"compute_log_probs\(...TRUNCATED) | 77 | 47 | 0 | 10 | 1 | ['0', '0'] | ['0', '0'] | true | [126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,1(...TRUNCATED) | [126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,1(...TRUNCATED) | [126336,126336,126336,126336,117254,126336,126336,126336,126336,126336,126336,126336,126336,126336,1(...TRUNCATED) | [2088,5034,126336,268,117254,1399,126336,126336,126336,126336,126336,126336,126336,126336,126336,126(...TRUNCATED) | [2088,5034,378,268,117254,1399,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336(...TRUNCATED) | [2088,5034,378,268,117254,1399,126336,126336,126336,126336,126336,341,126336,126336,126336,126336,12(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,126336,126336,126336,126336,126336,1(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,126336,126336,126336,126336,12633(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,126336,126336,126336,126336,378,1(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,126336,(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,126336,(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,126336,(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) |
"Let \\[f(x) = \\left\\{\n\\begin{array}{cl} ax+3, &\\text{ if }x>2, \\\\\nx-5 &\\text{ if } -2 \\le(...TRUNCATED) | "For the piecewise function to be continuous, the cases must \"meet\" at $2$ and $-2$. For example, (...TRUNCATED) | 0 | Algebra | 5 | train/algebra/0.json | 0 | "To ensure that the piecewise function \\( f(x) \\) is continuous, we need to make sure that the val(...TRUNCATED) | 512 | 102 | 23 | "{\"accumulative_error_tolerance\": 0.2, \"alpha\": 0.86, \"block_length\": 64, \"compute_log_probs\(...TRUNCATED) | 121 | 91 | 0 | 10 | 1 | ['0', '0'] | ['0', '0'] | true | [126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,1(...TRUNCATED) | [126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,1(...TRUNCATED) | [126336,126336,126336,126336,117254,126336,126336,126336,126336,126336,126336,126336,126336,126336,1(...TRUNCATED) | [126336,5034,126336,268,117254,1399,126336,126336,126336,126336,126336,126336,126336,126336,126336,1(...TRUNCATED) | [2088,5034,378,268,117254,1399,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336(...TRUNCATED) | [2088,5034,378,268,117254,1399,126336,126336,126336,126336,126336,341,126336,126336,126336,126336,12(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,126336,70685,341,12629,126336,126336,126336,126336,126(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,126336,126336,126336,126336,126336,1(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,126336,126336,126336,297,126336,1263(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,126336,126336,126336(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,126336,126336,126336(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,126336,126336,1(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,12(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,12(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,12(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,12(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) |
"Let \\[f(x) = \\left\\{\n\\begin{array}{cl} ax+3, &\\text{ if }x>2, \\\\\nx-5 &\\text{ if } -2 \\le(...TRUNCATED) | "For the piecewise function to be continuous, the cases must \"meet\" at $2$ and $-2$. For example, (...TRUNCATED) | 0 | Algebra | 5 | train/algebra/0.json | 0 | "To ensure that the piecewise function \\( f(x) \\) is continuous, we need to make sure that the val(...TRUNCATED) | 512 | 102 | 24 | "{\"accumulative_error_tolerance\": 0.2, \"alpha\": 0.86, \"block_length\": 64, \"compute_log_probs\(...TRUNCATED) | 121 | 91 | 0 | 10 | 1 | ['0', '0'] | ['0', '0'] | true | [126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,1(...TRUNCATED) | [126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,1(...TRUNCATED) | [126336,126336,126336,126336,117254,126336,126336,126336,126336,126336,126336,126336,126336,126336,1(...TRUNCATED) | [126336,5034,126336,268,117254,1399,126336,126336,126336,126336,126336,126336,126336,126336,126336,1(...TRUNCATED) | [2088,5034,378,268,117254,1399,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336(...TRUNCATED) | [2088,5034,378,268,117254,1399,126336,126336,126336,126336,126336,341,126336,126336,126336,126336,12(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,126336,70685,341,12629,126336,126336,126336,126336,126(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,126336,126336,126336,126336,126336,1(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,126336,126336,126336,297,126336,1263(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,126336,126336,126336(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,126336,126336,126336(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,126336,126336,1(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,12(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,12(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,12(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,12(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) |
"Let \\[f(x) = \\left\\{\n\\begin{array}{cl} ax+3, &\\text{ if }x>2, \\\\\nx-5 &\\text{ if } -2 \\le(...TRUNCATED) | "For the piecewise function to be continuous, the cases must \"meet\" at $2$ and $-2$. For example, (...TRUNCATED) | 0 | Algebra | 5 | train/algebra/0.json | 0 | "To ensure that the piecewise function \\( f(x) \\) is continuous, we need to make sure that the val(...TRUNCATED) | 512 | 101 | 25 | "{\"accumulative_error_tolerance\": 0.2, \"alpha\": 0.86, \"block_length\": 64, \"compute_log_probs\(...TRUNCATED) | 121 | 91 | 0 | 10 | 1 | ['0', '0'] | ['0', '0'] | true | [126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,1(...TRUNCATED) | [126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,1(...TRUNCATED) | [126336,126336,126336,126336,117254,126336,126336,126336,126336,126336,126336,126336,126336,126336,1(...TRUNCATED) | [126336,5034,126336,268,117254,1399,126336,126336,126336,126336,126336,126336,126336,126336,126336,1(...TRUNCATED) | [2088,5034,378,268,117254,1399,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336(...TRUNCATED) | [2088,5034,378,268,117254,1399,126336,126336,126336,126336,126336,341,126336,126336,126336,126336,12(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,126336,70685,341,12629,126336,126336,126336,126336,126(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,126336,126336,126336,126336,126336,1(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,126336,126336,126336,297,126336,1263(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,126336,126336,126336(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,126336,126336,126336(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,126336,126336,1(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,12(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,12(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,12(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,12(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED) |
"Let \\[f(x) = \\left\\{\n\\begin{array}{cl} ax+3, &\\text{ if }x>2, \\\\\nx-5 &\\text{ if } -2 \\le(...TRUNCATED) | "For the piecewise function to be continuous, the cases must \"meet\" at $2$ and $-2$. For example, (...TRUNCATED) | 0 | Algebra | 5 | train/algebra/0.json | 0 | "To ensure that the piecewise function \\( f(x) \\) is continuous, we need to ensure that the left-h(...TRUNCATED) | 512 | 108 | 31 | "{\"accumulative_error_tolerance\": 0.2, \"alpha\": 0.86, \"block_length\": 64, \"compute_log_probs\(...TRUNCATED) | 118 | 98 | 0 | 10 | 1 | ['0', '0'] | ['0', '0'] | true | [126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,1(...TRUNCATED) | [126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,1(...TRUNCATED) | [126336,5034,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126(...TRUNCATED) | [2088,5034,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,12633(...TRUNCATED) | [2088,5034,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,12633(...TRUNCATED) | [2088,5034,126336,126336,117254,126336,126336,126336,126336,126336,126336,126336,126336,126336,12633(...TRUNCATED) | [2088,5034,378,126336,117254,1399,126336,126336,126336,126336,126336,126336,126336,126336,126336,126(...TRUNCATED) | [2088,5034,378,268,117254,1399,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336(...TRUNCATED) | [2088,5034,378,268,117254,1399,126336,126336,126336,126336,126336,341,126336,126336,126336,126336,12(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,126336,3698,126336,126336,341,12629,126336,126336,126336,126336(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,126336,3698,126336,70685,341,12629,126336,126336,126336,126336,(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,126336,3698,126336,70685,341,12629,126336,126336,1050,126336,12(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,126336,126336,126336(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,126336,126336,126336(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,126336,126336,268,12(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,126336,126336,268,12(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,126336,126336,268,12(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,126336,268,1263(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,126336,(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,126336,(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,126336,(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) |
"Let \\[f(x) = \\left\\{\n\\begin{array}{cl} ax+3, &\\text{ if }x>2, \\\\\nx-5 &\\text{ if } -2 \\le(...TRUNCATED) | "For the piecewise function to be continuous, the cases must \"meet\" at $2$ and $-2$. For example, (...TRUNCATED) | 0 | Algebra | 5 | train/algebra/0.json | 0 | "To ensure that the piecewise function \\( f(x) \\) is continuous, we need to ensure that the left-h(...TRUNCATED) | 512 | 108 | 32 | "{\"accumulative_error_tolerance\": 0.2, \"alpha\": 0.86, \"block_length\": 64, \"compute_log_probs\(...TRUNCATED) | 118 | 98 | 0 | 10 | 1 | ['0', '0'] | ['0', '0'] | true | [126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,1(...TRUNCATED) | [126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,1(...TRUNCATED) | [126336,5034,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126(...TRUNCATED) | [2088,5034,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,12633(...TRUNCATED) | [2088,5034,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,12633(...TRUNCATED) | [2088,5034,126336,126336,117254,126336,126336,126336,126336,126336,126336,126336,126336,126336,12633(...TRUNCATED) | [2088,5034,378,126336,117254,1399,126336,126336,126336,126336,126336,126336,126336,126336,126336,126(...TRUNCATED) | [2088,5034,378,268,117254,1399,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336(...TRUNCATED) | [2088,5034,378,268,117254,1399,126336,126336,126336,126336,126336,341,126336,126336,126336,126336,12(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,126336,3698,126336,126336,341,12629,126336,126336,126336,126336(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,126336,3698,126336,70685,341,12629,126336,126336,126336,126336,(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,126336,3698,126336,70685,341,12629,126336,126336,1050,126336,12(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,126336,126336,126336(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,126336,126336,126336(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,126336,126336,268,12(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,126336,126336,268,12(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,126336,126336,268,12(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,126336,268,1263(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,126336,(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,126336,(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,126336,(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) | [2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED) |
What is the area of the triangle bounded by the lines $y=x,$ $y=-x,$ and $y=6$? | "[asy]\nsize(200); defaultpen(linewidth(0.8));\nxlimits(-8,8); ylimits(-1,10);\nxaxis(Label(\"$x$\")(...TRUNCATED) | 36 | Geometry | 3 | train/geometry/218.json | 1 | "To find the area of the triangle bounded by the lines \\( y = x \\), \\( y = -x \\), and \\( y = 6 (...TRUNCATED) | 512 | 77 | 31 | "{\"accumulative_error_tolerance\": 0.2, \"alpha\": 0.86, \"block_length\": 64, \"compute_log_probs\(...TRUNCATED) | 87 | 67 | 0 | 10 | 1 | ['36', '36'] | ['36', '36'] | true | [126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,1(...TRUNCATED) | [2088,126336,126336,126336,300,268,23079,26707,527,268,6039,24946,126336,373,126336,126336,126336,12(...TRUNCATED) | [2088,1491,268,2993,300,268,23079,26707,527,268,6039,24946,126336,373,1529,126336,943,24946,126336,3(...TRUNCATED) | [2088,1491,268,2993,300,268,23079,26707,527,268,6039,24946,340,373,1529,795,943,24946,340,373,537,87(...TRUNCATED) | [2088,1491,268,2993,300,268,23079,26707,527,268,6039,24946,340,373,1529,795,943,24946,340,373,537,87(...TRUNCATED) | [2088,1491,268,2993,300,268,23079,26707,527,268,6039,24946,340,373,1529,795,943,24946,340,373,537,87(...TRUNCATED) | [2088,1491,268,2993,300,268,23079,26707,527,268,6039,24946,340,373,1529,795,943,24946,340,373,537,87(...TRUNCATED) | [2088,1491,268,2993,300,268,23079,26707,527,268,6039,24946,340,373,1529,795,943,24946,340,373,537,87(...TRUNCATED) | [2088,1491,268,2993,300,268,23079,26707,527,268,6039,24946,340,373,1529,795,943,24946,340,373,537,87(...TRUNCATED) | [2088,1491,268,2993,300,268,23079,26707,527,268,6039,24946,340,373,1529,795,943,24946,340,373,537,87(...TRUNCATED) | [2088,1491,268,2993,300,268,23079,26707,527,268,6039,24946,340,373,1529,795,943,24946,340,373,537,87(...TRUNCATED) | [2088,1491,268,2993,300,268,23079,26707,527,268,6039,24946,340,373,1529,795,943,24946,340,373,537,87(...TRUNCATED) | [2088,1491,268,2993,300,268,23079,26707,527,268,6039,24946,340,373,1529,795,943,24946,340,373,537,87(...TRUNCATED) | [2088,1491,268,2993,300,268,23079,26707,527,268,6039,24946,340,373,1529,795,943,24946,340,373,537,87(...TRUNCATED) | [2088,1491,268,2993,300,268,23079,26707,527,268,6039,24946,340,373,1529,795,943,24946,340,373,537,87(...TRUNCATED) | [2088,1491,268,2993,300,268,23079,26707,527,268,6039,24946,340,373,1529,795,943,24946,340,373,537,87(...TRUNCATED) | [2088,1491,268,2993,300,268,23079,26707,527,268,6039,24946,340,373,1529,795,943,24946,340,373,537,87(...TRUNCATED) | [2088,1491,268,2993,300,268,23079,26707,527,268,6039,24946,340,373,1529,795,943,24946,340,373,537,87(...TRUNCATED) | [2088,1491,268,2993,300,268,23079,26707,527,268,6039,24946,340,373,1529,795,943,24946,340,373,537,87(...TRUNCATED) | [2088,1491,268,2993,300,268,23079,26707,527,268,6039,24946,340,373,1529,795,943,24946,340,373,537,87(...TRUNCATED) | [2088,1491,268,2993,300,268,23079,26707,527,268,6039,24946,340,373,1529,795,943,24946,340,373,537,87(...TRUNCATED) | [2088,1491,268,2993,300,268,23079,26707,527,268,6039,24946,340,373,1529,795,943,24946,340,373,537,87(...TRUNCATED) | [2088,1491,268,2993,300,268,23079,26707,527,268,6039,24946,340,373,1529,795,943,24946,340,373,537,87(...TRUNCATED) | [2088,1491,268,2993,300,268,23079,26707,527,268,6039,24946,340,373,1529,795,943,24946,340,373,537,87(...TRUNCATED) | [2088,1491,268,2993,300,268,23079,26707,527,268,6039,24946,340,373,1529,795,943,24946,340,373,537,87(...TRUNCATED) | [2088,1491,268,2993,300,268,23079,26707,527,268,6039,24946,340,373,1529,795,943,24946,340,373,537,87(...TRUNCATED) | [2088,1491,268,2993,300,268,23079,26707,527,268,6039,24946,340,373,1529,795,943,24946,340,373,537,87(...TRUNCATED) | [2088,1491,268,2993,300,268,23079,26707,527,268,6039,24946,340,373,1529,795,943,24946,340,373,537,87(...TRUNCATED) | [2088,1491,268,2993,300,268,23079,26707,527,268,6039,24946,340,373,1529,795,943,24946,340,373,537,87(...TRUNCATED) | [2088,1491,268,2993,300,268,23079,26707,527,268,6039,24946,340,373,1529,795,943,24946,340,373,537,87(...TRUNCATED) | [2088,1491,268,2993,300,268,23079,26707,527,268,6039,24946,340,373,1529,795,943,24946,340,373,537,87(...TRUNCATED) | [2088,1491,268,2993,300,268,23079,26707,527,268,6039,24946,340,373,1529,795,943,24946,340,373,537,87(...TRUNCATED) | [2088,1491,268,2993,300,268,23079,26707,527,268,6039,24946,340,373,1529,795,943,24946,340,373,537,87(...TRUNCATED) | [2088,1491,268,2993,300,268,23079,26707,527,268,6039,24946,340,373,1529,795,943,24946,340,373,537,87(...TRUNCATED) | [2088,1491,268,2993,300,268,23079,26707,527,268,6039,24946,340,373,1529,795,943,24946,340,373,537,87(...TRUNCATED) | [2088,1491,268,2993,300,268,23079,26707,527,268,6039,24946,340,373,1529,795,943,24946,340,373,537,87(...TRUNCATED) | [2088,1491,268,2993,300,268,23079,26707,527,268,6039,24946,340,373,1529,795,943,24946,340,373,537,87(...TRUNCATED) | [2088,1491,268,2993,300,268,23079,26707,527,268,6039,24946,340,373,1529,795,943,24946,340,373,537,87(...TRUNCATED) | [2088,1491,268,2993,300,268,23079,26707,527,268,6039,24946,340,373,1529,795,943,24946,340,373,537,87(...TRUNCATED) | [2088,1491,268,2993,300,268,23079,26707,527,268,6039,24946,340,373,1529,795,943,24946,340,373,537,87(...TRUNCATED) | [2088,1491,268,2993,300,268,23079,26707,527,268,6039,24946,340,373,1529,795,943,24946,340,373,537,87(...TRUNCATED) | [2088,1491,268,2993,300,268,23079,26707,527,268,6039,24946,340,373,1529,795,943,24946,340,373,537,87(...TRUNCATED) | [2088,1491,268,2993,300,268,23079,26707,527,268,6039,24946,340,373,1529,795,943,24946,340,373,537,87(...TRUNCATED) | [2088,1491,268,2993,300,268,23079,26707,527,268,6039,24946,340,373,1529,795,943,24946,340,373,537,87(...TRUNCATED) | [2088,1491,268,2993,300,268,23079,26707,527,268,6039,24946,340,373,1529,795,943,24946,340,373,537,87(...TRUNCATED) | [2088,1491,268,2993,300,268,23079,26707,527,268,6039,24946,340,373,1529,795,943,24946,340,373,537,87(...TRUNCATED) | [2088,1491,268,2993,300,268,23079,26707,527,268,6039,24946,340,373,1529,795,943,24946,340,373,537,87(...TRUNCATED) | [2088,1491,268,2993,300,268,23079,26707,527,268,6039,24946,340,373,1529,795,943,24946,340,373,537,87(...TRUNCATED) | [2088,1491,268,2993,300,268,23079,26707,527,268,6039,24946,340,373,1529,795,943,24946,340,373,537,87(...TRUNCATED) | [2088,1491,268,2993,300,268,23079,26707,527,268,6039,24946,340,373,1529,795,943,24946,340,373,537,87(...TRUNCATED) | [2088,1491,268,2993,300,268,23079,26707,527,268,6039,24946,340,373,1529,795,943,24946,340,373,537,87(...TRUNCATED) | [2088,1491,268,2993,300,268,23079,26707,527,268,6039,24946,340,373,1529,795,943,24946,340,373,537,87(...TRUNCATED) | [2088,1491,268,2993,300,268,23079,26707,527,268,6039,24946,340,373,1529,795,943,24946,340,373,537,87(...TRUNCATED) | [2088,1491,268,2993,300,268,23079,26707,527,268,6039,24946,340,373,1529,795,943,24946,340,373,537,87(...TRUNCATED) | [2088,1491,268,2993,300,268,23079,26707,527,268,6039,24946,340,373,1529,795,943,24946,340,373,537,87(...TRUNCATED) | [2088,1491,268,2993,300,268,23079,26707,527,268,6039,24946,340,373,1529,795,943,24946,340,373,537,87(...TRUNCATED) |
Twenty-seven increased by twice a number is 39. What is the number? | "We are asked to solve $27+2x=39$ for $x$. We subtract 27 from both sides and then multiply both si(...TRUNCATED) | 6 | Prealgebra | 1 | train/prealgebra/1915.json | 2 | "To solve the problem, let's denote the unknown number by \\( x \\).\n\nStep 1: TranslateTwenty-seve(...TRUNCATED) | 512 | 17 | 0 | "{\"accumulative_error_tolerance\": 0.2, \"alpha\": 0.86, \"block_length\": 64, \"compute_log_probs\(...TRUNCATED) | 23 | 14 | 0 | 3 | 1 | ['6', '6'] | ['6', '6'] | true | [126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,1(...TRUNCATED) | [2088,9237,268,3214,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126(...TRUNCATED) | [2088,9237,268,3214,126336,126336,698,126336,126336,126336,126336,126336,126336,126336,126336,126336(...TRUNCATED) | [2088,9237,268,3214,11,1993,698,22978,268,12398,1788,527,24946,1529,795,931,198,198,126336,126336,12(...TRUNCATED) | [2088,9237,268,3214,11,1993,698,22978,268,12398,1788,527,24946,1529,795,931,198,198,8963,220,16,25,6(...TRUNCATED) | [2088,9237,268,3214,11,1993,698,22978,268,12398,1788,527,24946,1529,795,931,198,198,8963,220,16,25,6(...TRUNCATED) | [2088,9237,268,3214,11,1993,698,22978,268,12398,1788,527,24946,1529,795,931,198,198,8963,220,16,25,6(...TRUNCATED) | [2088,9237,268,3214,11,1993,698,22978,268,12398,1788,527,24946,1529,795,931,198,198,8963,220,16,25,6(...TRUNCATED) | [2088,9237,268,3214,11,1993,698,22978,268,12398,1788,527,24946,1529,795,931,198,198,8963,220,16,25,6(...TRUNCATED) | [2088,9237,268,3214,11,1993,698,22978,268,12398,1788,527,24946,1529,795,931,198,198,8963,220,16,25,6(...TRUNCATED) | [2088,9237,268,3214,11,1993,698,22978,268,12398,1788,527,24946,1529,795,931,198,198,8963,220,16,25,6(...TRUNCATED) | [2088,9237,268,3214,11,1993,698,22978,268,12398,1788,527,24946,1529,795,931,198,198,8963,220,16,25,6(...TRUNCATED) | [2088,9237,268,3214,11,1993,698,22978,268,12398,1788,527,24946,1529,795,931,198,198,8963,220,16,25,6(...TRUNCATED) | [2088,9237,268,3214,11,1993,698,22978,268,12398,1788,527,24946,1529,795,931,198,198,8963,220,16,25,6(...TRUNCATED) | [2088,9237,268,3214,11,1993,698,22978,268,12398,1788,527,24946,1529,795,931,198,198,8963,220,16,25,6(...TRUNCATED) | [2088,9237,268,3214,11,1993,698,22978,268,12398,1788,527,24946,1529,795,931,198,198,8963,220,16,25,6(...TRUNCATED) | [2088,9237,268,3214,11,1993,698,22978,268,12398,1788,527,24946,1529,795,931,198,198,8963,220,16,25,6(...TRUNCATED) | [2088,9237,268,3214,11,1993,698,22978,268,12398,1788,527,24946,1529,795,931,198,198,8963,220,16,25,6(...TRUNCATED) | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
End of preview. Expand in Data Studio
No dataset card yet
- Downloads last month
- 10