data/v0.1.0_tiny_cleanvars_binary.jsonl

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{"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.736842105263, "p_not_A": 0.263157894737}}, "gold_argmax": "A", "gold_distribution": {"A": 0.736842105263, "not_A": 0.263157894737}, "instance_id": "explicit_probability__seed_000056__repr_prose", "latent_instance_id": "explicit_probability__seed_000056", "outcomes": ["A", "not_A"], "probability_band": "(0.70,0.90]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "prose", "seed": 56, "state": {"description": "The state fully determines the target distribution. The probability of A is 0.736842105263, and the remaining probability belongs to the other outcome. {'p_A': 0.736842105263, 'p_not_A': 0.263157894737}", "representation": "natural_language"}}
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{"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.789473684211, "p_not_A": 0.21052631578900005}}, "gold_argmax": "A", "gold_distribution": {"A": 0.789473684211, "not_A": 0.21052631578900005}, "instance_id": "explicit_probability__seed_000057__repr_prose", "latent_instance_id": "explicit_probability__seed_000057", "outcomes": ["A", "not_A"], "probability_band": "(0.70,0.90]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "prose", "seed": 57, "state": {"description": "The state fully determines the target distribution. The probability of A is 0.789473684211, and the remaining probability belongs to the other outcome. {'p_A': 0.789473684211, 'p_not_A': 0.21052631578900005}", "representation": "natural_language"}}
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{"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.842105263158, "p_not_A": 0.15789473684199995}}, "gold_argmax": "A", "gold_distribution": {"A": 0.842105263158, "not_A": 0.15789473684199995}, "instance_id": "explicit_probability__seed_000058__repr_prose", "latent_instance_id": "explicit_probability__seed_000058", "outcomes": ["A", "not_A"], "probability_band": "(0.70,0.90]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "prose", "seed": 58, "state": {"description": "The state fully determines the target distribution. The probability of A is 0.842105263158, and the remaining probability belongs to the other outcome. {'p_A': 0.842105263158, 'p_not_A': 0.15789473684199995}", "representation": "natural_language"}}
{"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.842105263158, "p_not_A": 0.15789473684199995}}, "gold_argmax": "A", "gold_distribution": {"A": 0.842105263158, "not_A": 0.15789473684199995}, "instance_id": "explicit_probability__seed_000058__repr_distractor", "latent_instance_id": "explicit_probability__seed_000058", "outcomes": ["A", "not_A"], "probability_band": "(0.70,0.90]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "distractor", "seed": 58, "state": {"irrelevant": {"batch_code": "ZX-058", "container_temperature_c": 17.4, "operator_shift": "swing", "sensor_revision": "rev-4", "warehouse_lane": "E"}, "representation": "distractor", "sufficient_statistics": {"p_A": 0.842105263158, "p_not_A": 0.15789473684199995}}}
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{"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.894736842105, "p_not_A": 0.10526315789499996}}, "gold_argmax": "A", "gold_distribution": {"A": 0.894736842105, "not_A": 0.10526315789499996}, "instance_id": "explicit_probability__seed_000059__repr_prose", "latent_instance_id": "explicit_probability__seed_000059", "outcomes": ["A", "not_A"], "probability_band": "(0.70,0.90]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "prose", "seed": 59, "state": {"description": "The state fully determines the target distribution. The probability of A is 0.894736842105, and the remaining probability belongs to the other outcome. {'p_A': 0.894736842105, 'p_not_A': 0.10526315789499996}", "representation": "natural_language"}}
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{"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.947368421053, "p_not_A": 0.05263157894699999}}, "gold_argmax": "A", "gold_distribution": {"A": 0.947368421053, "not_A": 0.05263157894699999}, "instance_id": "explicit_probability__seed_000060__repr_prose", "latent_instance_id": "explicit_probability__seed_000060", "outcomes": ["A", "not_A"], "probability_band": "(0.90,0.99]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "prose", "seed": 60, "state": {"description": "The state fully determines the target distribution. The probability of A is 0.947368421053, and the remaining probability belongs to the other outcome. {'p_A': 0.947368421053, 'p_not_A': 0.05263157894699999}", "representation": "natural_language"}}
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{"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 1.0, "p_not_A": 0.0}}, "gold_argmax": "A", "gold_distribution": {"A": 1.0, "not_A": 0.0}, "instance_id": "explicit_probability__seed_000061__repr_ratio", "latent_instance_id": "explicit_probability__seed_000061", "outcomes": ["A", "not_A"], "probability_band": "1", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "ratio", "seed": 61, "state": {"probability_ratio_A_to_not_A": "1:0", "representation": "ratio"}}
{"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 1.0, "p_not_A": 0.0}}, "gold_argmax": "A", "gold_distribution": {"A": 1.0, "not_A": 0.0}, "instance_id": "explicit_probability__seed_000061__repr_prose", "latent_instance_id": "explicit_probability__seed_000061", "outcomes": ["A", "not_A"], "probability_band": "1", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "prose", "seed": 61, "state": {"description": "The state fully determines the target distribution. The probability of A is 1, and the remaining probability belongs to the other outcome. {'p_A': 1.0, 'p_not_A': 0.0}", "representation": "natural_language"}}
{"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 1.0, "p_not_A": 0.0}}, "gold_argmax": "A", "gold_distribution": {"A": 1.0, "not_A": 0.0}, "instance_id": "explicit_probability__seed_000061__repr_distractor", "latent_instance_id": "explicit_probability__seed_000061", "outcomes": ["A", "not_A"], "probability_band": "1", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "distractor", "seed": 61, "state": {"irrelevant": {"batch_code": "ZX-061", "container_temperature_c": 19.5, "operator_shift": "swing", "sensor_revision": "rev-2", "warehouse_lane": "B"}, "representation": "distractor", "sufficient_statistics": {"p_A": 1.0, "p_not_A": 0.0}}}
{"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 10, "zor": 40}, "reduced_counts": {"nif": 1, "zor": 4}}}, "gold_argmax": "zor", "gold_distribution": {"nif": 0.2, "zor": 0.8}, "instance_id": "frequency__seed_000042__repr_counts", "latent_instance_id": "frequency__seed_000042", "outcomes": ["zor", "nif"], "probability_band": "(0.70,0.90]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "counts", "seed": 42, "state": {"counts": {"nif": 200, "zor": 800}, "representation": "counts", "sampling": "uniform"}}
{"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 10, "zor": 40}, "reduced_counts": {"nif": 1, "zor": 4}}}, "gold_argmax": "zor", "gold_distribution": {"nif": 0.2, "zor": 0.8}, "instance_id": "frequency__seed_000042__repr_scaled_counts", "latent_instance_id": "frequency__seed_000042", "outcomes": ["zor", "nif"], "probability_band": "(0.70,0.90]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "scaled_counts", "seed": 42, "state": {"counts": {"nif": 20000, "zor": 80000}, "representation": "counts", "sampling": "uniform"}}
{"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 10, "zor": 40}, "reduced_counts": {"nif": 1, "zor": 4}}}, "gold_argmax": "zor", "gold_distribution": {"nif": 0.2, "zor": 0.8}, "instance_id": "frequency__seed_000042__repr_ratio", "latent_instance_id": "frequency__seed_000042", "outcomes": ["zor", "nif"], "probability_band": "(0.70,0.90]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "ratio", "seed": 42, "state": {"probability_ratio_zor_to_nif": "4:1", "representation": "ratio"}}
{"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 10, "zor": 40}, "reduced_counts": {"nif": 1, "zor": 4}}}, "gold_argmax": "zor", "gold_distribution": {"nif": 0.2, "zor": 0.8}, "instance_id": "frequency__seed_000042__repr_table", "latent_instance_id": "frequency__seed_000042", "outcomes": ["zor", "nif"], "probability_band": "(0.70,0.90]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "table", "seed": 42, "state": {"representation": "table", "state": {"counts": {"nif": 10, "zor": 40}, "sampling": "uniform"}, "table": [{"count": 40, "label": "zor"}, {"count": 10, "label": "nif"}]}}
{"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 10, "zor": 40}, "reduced_counts": {"nif": 1, "zor": 4}}}, "gold_argmax": "zor", "gold_distribution": {"nif": 0.2, "zor": 0.8}, "instance_id": "frequency__seed_000042__repr_prose", "latent_instance_id": "frequency__seed_000042", "outcomes": ["zor", "nif"], "probability_band": "(0.70,0.90]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "prose", "seed": 42, "state": {"description": "The state fully determines the target distribution. The probability of zor is 0.8, and the remaining probability belongs to the other outcome. {'counts': {'zor': 40, 'nif': 10}, 'sampling': 'uniform'}", "representation": "natural_language"}}
{"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 10, "zor": 40}, "reduced_counts": {"nif": 1, "zor": 4}}}, "gold_argmax": "zor", "gold_distribution": {"nif": 0.2, "zor": 0.8}, "instance_id": "frequency__seed_000042__repr_distractor", "latent_instance_id": "frequency__seed_000042", "outcomes": ["zor", "nif"], "probability_band": "(0.70,0.90]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "distractor", "seed": 42, "state": {"irrelevant": {"batch_code": "ZX-042", "container_temperature_c": 18.1, "operator_shift": "morning", "sensor_revision": "rev-3", "warehouse_lane": "A"}, "representation": "distractor", "sufficient_statistics": {"counts": {"nif": 10, "zor": 40}, "sampling": "uniform"}}}
{"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 7, "zor": 13}, "reduced_counts": {"nif": 7, "zor": 13}}}, "gold_argmax": "zor", "gold_distribution": {"nif": 0.35, "zor": 0.65}, "instance_id": "frequency__seed_000046__repr_counts", "latent_instance_id": "frequency__seed_000046", "outcomes": ["zor", "nif"], "probability_band": "(0.55,0.70]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "counts", "seed": 46, "state": {"counts": {"nif": 350, "zor": 650}, "representation": "counts", "sampling": "uniform"}}
{"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 7, "zor": 13}, "reduced_counts": {"nif": 7, "zor": 13}}}, "gold_argmax": "zor", "gold_distribution": {"nif": 0.35, "zor": 0.65}, "instance_id": "frequency__seed_000046__repr_scaled_counts", "latent_instance_id": "frequency__seed_000046", "outcomes": ["zor", "nif"], "probability_band": "(0.55,0.70]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "scaled_counts", "seed": 46, "state": {"counts": {"nif": 35000, "zor": 65000}, "representation": "counts", "sampling": "uniform"}}
{"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 7, "zor": 13}, "reduced_counts": {"nif": 7, "zor": 13}}}, "gold_argmax": "zor", "gold_distribution": {"nif": 0.35, "zor": 0.65}, "instance_id": "frequency__seed_000046__repr_ratio", "latent_instance_id": "frequency__seed_000046", "outcomes": ["zor", "nif"], "probability_band": "(0.55,0.70]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "ratio", "seed": 46, "state": {"probability_ratio_zor_to_nif": "13:7", "representation": "ratio"}}
{"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 7, "zor": 13}, "reduced_counts": {"nif": 7, "zor": 13}}}, "gold_argmax": "zor", "gold_distribution": {"nif": 0.35, "zor": 0.65}, "instance_id": "frequency__seed_000046__repr_table", "latent_instance_id": "frequency__seed_000046", "outcomes": ["zor", "nif"], "probability_band": "(0.55,0.70]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "table", "seed": 46, "state": {"representation": "table", "state": {"counts": {"nif": 7, "zor": 13}, "sampling": "uniform"}, "table": [{"count": 13, "label": "zor"}, {"count": 7, "label": "nif"}]}}
{"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 7, "zor": 13}, "reduced_counts": {"nif": 7, "zor": 13}}}, "gold_argmax": "zor", "gold_distribution": {"nif": 0.35, "zor": 0.65}, "instance_id": "frequency__seed_000046__repr_prose", "latent_instance_id": "frequency__seed_000046", "outcomes": ["zor", "nif"], "probability_band": "(0.55,0.70]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "prose", "seed": 46, "state": {"description": "The state fully determines the target distribution. The probability of zor is 0.65, and the remaining probability belongs to the other outcome. {'counts': {'zor': 13, 'nif': 7}, 'sampling': 'uniform'}", "representation": "natural_language"}}
{"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 7, "zor": 13}, "reduced_counts": {"nif": 7, "zor": 13}}}, "gold_argmax": "zor", "gold_distribution": {"nif": 0.35, "zor": 0.65}, "instance_id": "frequency__seed_000046__repr_distractor", "latent_instance_id": "frequency__seed_000046", "outcomes": ["zor", "nif"], "probability_band": "(0.55,0.70]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "distractor", "seed": 46, "state": {"irrelevant": {"batch_code": "ZX-046", "container_temperature_c": 20.9, "operator_shift": "swing", "sensor_revision": "rev-2", "warehouse_lane": "E"}, "representation": "distractor", "sufficient_statistics": {"counts": {"nif": 7, "zor": 13}, "sampling": "uniform"}}}
{"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 71, "zor": 29}, "reduced_counts": {"nif": 71, "zor": 29}}}, "gold_argmax": "nif", "gold_distribution": {"nif": 0.71, "zor": 0.29}, "instance_id": "frequency__seed_000050__repr_counts", "latent_instance_id": "frequency__seed_000050", "outcomes": ["zor", "nif"], "probability_band": "(0.10,0.30]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "counts", "seed": 50, "state": {"counts": {"nif": 710, "zor": 290}, "representation": "counts", "sampling": "uniform"}}
{"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 71, "zor": 29}, "reduced_counts": {"nif": 71, "zor": 29}}}, "gold_argmax": "nif", "gold_distribution": {"nif": 0.71, "zor": 0.29}, "instance_id": "frequency__seed_000050__repr_scaled_counts", "latent_instance_id": "frequency__seed_000050", "outcomes": ["zor", "nif"], "probability_band": "(0.10,0.30]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "scaled_counts", "seed": 50, "state": {"counts": {"nif": 71000, "zor": 29000}, "representation": "counts", "sampling": "uniform"}}
{"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 71, "zor": 29}, "reduced_counts": {"nif": 71, "zor": 29}}}, "gold_argmax": "nif", "gold_distribution": {"nif": 0.71, "zor": 0.29}, "instance_id": "frequency__seed_000050__repr_ratio", "latent_instance_id": "frequency__seed_000050", "outcomes": ["zor", "nif"], "probability_band": "(0.10,0.30]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "ratio", "seed": 50, "state": {"probability_ratio_zor_to_nif": "29:71", "representation": "ratio"}}
{"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 71, "zor": 29}, "reduced_counts": {"nif": 71, "zor": 29}}}, "gold_argmax": "nif", "gold_distribution": {"nif": 0.71, "zor": 0.29}, "instance_id": "frequency__seed_000050__repr_table", "latent_instance_id": "frequency__seed_000050", "outcomes": ["zor", "nif"], "probability_band": "(0.10,0.30]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "table", "seed": 50, "state": {"representation": "table", "state": {"counts": {"nif": 71, "zor": 29}, "sampling": "uniform"}, "table": [{"count": 29, "label": "zor"}, {"count": 71, "label": "nif"}]}}
{"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 71, "zor": 29}, "reduced_counts": {"nif": 71, "zor": 29}}}, "gold_argmax": "nif", "gold_distribution": {"nif": 0.71, "zor": 0.29}, "instance_id": "frequency__seed_000050__repr_prose", "latent_instance_id": "frequency__seed_000050", "outcomes": ["zor", "nif"], "probability_band": "(0.10,0.30]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "prose", "seed": 50, "state": {"description": "The state fully determines the target distribution. The probability of zor is 0.29, and the remaining probability belongs to the other outcome. {'counts': {'zor': 29, 'nif': 71}, 'sampling': 'uniform'}", "representation": "natural_language"}}
{"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 71, "zor": 29}, "reduced_counts": {"nif": 71, "zor": 29}}}, "gold_argmax": "nif", "gold_distribution": {"nif": 0.71, "zor": 0.29}, "instance_id": "frequency__seed_000050__repr_distractor", "latent_instance_id": "frequency__seed_000050", "outcomes": ["zor", "nif"], "probability_band": "(0.10,0.30]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "distractor", "seed": 50, "state": {"irrelevant": {"batch_code": "ZX-050", "container_temperature_c": 23.7, "operator_shift": "night", "sensor_revision": "rev-1", "warehouse_lane": "C"}, "representation": "distractor", "sufficient_statistics": {"counts": {"nif": 71, "zor": 29}, "sampling": "uniform"}}}
{"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 16, "zor": 4}, "reduced_counts": {"nif": 4, "zor": 1}}}, "gold_argmax": "nif", "gold_distribution": {"nif": 0.8, "zor": 0.2}, "instance_id": "frequency__seed_000054__repr_counts", "latent_instance_id": "frequency__seed_000054", "outcomes": ["zor", "nif"], "probability_band": "(0.10,0.30]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "counts", "seed": 54, "state": {"counts": {"nif": 800, "zor": 200}, "representation": "counts", "sampling": "uniform"}}
{"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 16, "zor": 4}, "reduced_counts": {"nif": 4, "zor": 1}}}, "gold_argmax": "nif", "gold_distribution": {"nif": 0.8, "zor": 0.2}, "instance_id": "frequency__seed_000054__repr_scaled_counts", "latent_instance_id": "frequency__seed_000054", "outcomes": ["zor", "nif"], "probability_band": "(0.10,0.30]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "scaled_counts", "seed": 54, "state": {"counts": {"nif": 80000, "zor": 20000}, "representation": "counts", "sampling": "uniform"}}
{"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 16, "zor": 4}, "reduced_counts": {"nif": 4, "zor": 1}}}, "gold_argmax": "nif", "gold_distribution": {"nif": 0.8, "zor": 0.2}, "instance_id": "frequency__seed_000054__repr_ratio", "latent_instance_id": "frequency__seed_000054", "outcomes": ["zor", "nif"], "probability_band": "(0.10,0.30]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "ratio", "seed": 54, "state": {"probability_ratio_zor_to_nif": "1:4", "representation": "ratio"}}
{"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 16, "zor": 4}, "reduced_counts": {"nif": 4, "zor": 1}}}, "gold_argmax": "nif", "gold_distribution": {"nif": 0.8, "zor": 0.2}, "instance_id": "frequency__seed_000054__repr_table", "latent_instance_id": "frequency__seed_000054", "outcomes": ["zor", "nif"], "probability_band": "(0.10,0.30]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "table", "seed": 54, "state": {"representation": "table", "state": {"counts": {"nif": 16, "zor": 4}, "sampling": "uniform"}, "table": [{"count": 4, "label": "zor"}, {"count": 16, "label": "nif"}]}}
{"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 16, "zor": 4}, "reduced_counts": {"nif": 4, "zor": 1}}}, "gold_argmax": "nif", "gold_distribution": {"nif": 0.8, "zor": 0.2}, "instance_id": "frequency__seed_000054__repr_prose", "latent_instance_id": "frequency__seed_000054", "outcomes": ["zor", "nif"], "probability_band": "(0.10,0.30]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "prose", "seed": 54, "state": {"description": "The state fully determines the target distribution. The probability of zor is 0.2, and the remaining probability belongs to the other outcome. {'counts': {'zor': 4, 'nif': 16}, 'sampling': 'uniform'}", "representation": "natural_language"}}
{"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 16, "zor": 4}, "reduced_counts": {"nif": 4, "zor": 1}}}, "gold_argmax": "nif", "gold_distribution": {"nif": 0.8, "zor": 0.2}, "instance_id": "frequency__seed_000054__repr_distractor", "latent_instance_id": "frequency__seed_000054", "outcomes": ["zor", "nif"], "probability_band": "(0.10,0.30]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "distractor", "seed": 54, "state": {"irrelevant": {"batch_code": "ZX-054", "container_temperature_c": 14.6, "operator_shift": "morning", "sensor_revision": "rev-5", "warehouse_lane": "A"}, "representation": "distractor", "sufficient_statistics": {"counts": {"nif": 16, "zor": 4}, "sampling": "uniform"}}}
{"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 44, "zor": 6}, "reduced_counts": {"nif": 22, "zor": 3}}}, "gold_argmax": "nif", "gold_distribution": {"nif": 0.88, "zor": 0.12}, "instance_id": "frequency__seed_000058__repr_counts", "latent_instance_id": "frequency__seed_000058", "outcomes": ["zor", "nif"], "probability_band": "(0.10,0.30]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "counts", "seed": 58, "state": {"counts": {"nif": 880, "zor": 120}, "representation": "counts", "sampling": "uniform"}}
{"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 44, "zor": 6}, "reduced_counts": {"nif": 22, "zor": 3}}}, "gold_argmax": "nif", "gold_distribution": {"nif": 0.88, "zor": 0.12}, "instance_id": "frequency__seed_000058__repr_scaled_counts", "latent_instance_id": "frequency__seed_000058", "outcomes": ["zor", "nif"], "probability_band": "(0.10,0.30]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "scaled_counts", "seed": 58, "state": {"counts": {"nif": 88000, "zor": 12000}, "representation": "counts", "sampling": "uniform"}}
{"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 44, "zor": 6}, "reduced_counts": {"nif": 22, "zor": 3}}}, "gold_argmax": "nif", "gold_distribution": {"nif": 0.88, "zor": 0.12}, "instance_id": "frequency__seed_000058__repr_ratio", "latent_instance_id": "frequency__seed_000058", "outcomes": ["zor", "nif"], "probability_band": "(0.10,0.30]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "ratio", "seed": 58, "state": {"probability_ratio_zor_to_nif": "3:22", "representation": "ratio"}}
{"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 44, "zor": 6}, "reduced_counts": {"nif": 22, "zor": 3}}}, "gold_argmax": "nif", "gold_distribution": {"nif": 0.88, "zor": 0.12}, "instance_id": "frequency__seed_000058__repr_table", "latent_instance_id": "frequency__seed_000058", "outcomes": ["zor", "nif"], "probability_band": "(0.10,0.30]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "table", "seed": 58, "state": {"representation": "table", "state": {"counts": {"nif": 44, "zor": 6}, "sampling": "uniform"}, "table": [{"count": 6, "label": "zor"}, {"count": 44, "label": "nif"}]}}
{"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 44, "zor": 6}, "reduced_counts": {"nif": 22, "zor": 3}}}, "gold_argmax": "nif", "gold_distribution": {"nif": 0.88, "zor": 0.12}, "instance_id": "frequency__seed_000058__repr_prose", "latent_instance_id": "frequency__seed_000058", "outcomes": ["zor", "nif"], "probability_band": "(0.10,0.30]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "prose", "seed": 58, "state": {"description": "The state fully determines the target distribution. The probability of zor is 0.12, and the remaining probability belongs to the other outcome. {'counts': {'zor': 6, 'nif': 44}, 'sampling': 'uniform'}", "representation": "natural_language"}}
{"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 44, "zor": 6}, "reduced_counts": {"nif": 22, "zor": 3}}}, "gold_argmax": "nif", "gold_distribution": {"nif": 0.88, "zor": 0.12}, "instance_id": "frequency__seed_000058__repr_distractor", "latent_instance_id": "frequency__seed_000058", "outcomes": ["zor", "nif"], "probability_band": "(0.10,0.30]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "distractor", "seed": 58, "state": {"irrelevant": {"batch_code": "ZX-058", "container_temperature_c": 17.4, "operator_shift": "swing", "sensor_revision": "rev-4", "warehouse_lane": "E"}, "representation": "distractor", "sufficient_statistics": {"counts": {"nif": 44, "zor": 6}, "sampling": "uniform"}}}
{"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"p_A": 0.07458, "query": "not_A", "subtask": "complement"}}, "gold_argmax": "target", "gold_distribution": {"not_target": 0.07457999999999998, "target": 0.92542}, "instance_id": "compound__seed_000042__repr_direct", "latent_instance_id": "compound__seed_000042", "outcomes": ["target", "not_target"], "probability_band": "(0.90,0.99]", "prompt": "Event A has the supplied probability. What is the probability that A does not occur? Return a normalized probability for each of: target, not_target.", "representation": "direct", "seed": 42, "state": {"representation": "direct", "sufficient_statistics": {"p_A": 0.07458, "query": "not_A", "subtask": "complement"}}}
{"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"p_A": 0.07458, "query": "not_A", "subtask": "complement"}}, "gold_argmax": "target", "gold_distribution": {"not_target": 0.07457999999999998, "target": 0.92542}, "instance_id": "compound__seed_000042__repr_table", "latent_instance_id": "compound__seed_000042", "outcomes": ["target", "not_target"], "probability_band": "(0.90,0.99]", "prompt": "Event A has the supplied probability. What is the probability that A does not occur? Return a normalized probability for each of: target, not_target.", "representation": "table", "seed": 42, "state": {"representation": "table", "state": {"p_A": 0.07458, "query": "not_A", "subtask": "complement"}, "table": [{"field": "subtask", "value": "complement"}, {"field": "p_A", "value": 0.07458}, {"field": "query", "value": "not_A"}]}}
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{"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"independent": true, "p_A": 0.200973, "p_B": 0.665751, "query": "A_and_B", "subtask": "intersection"}}, "gold_argmax": "not_target", "gold_distribution": {"not_target": 0.866202024277, "target": 0.133797975723}, "instance_id": "compound__seed_000043__repr_direct", "latent_instance_id": "compound__seed_000043", "outcomes": ["target", "not_target"], "probability_band": "(0.10,0.30]", "prompt": "Events A and B are independent. What is the probability that both occur? Return a normalized probability for each of: target, not_target.", "representation": "direct", "seed": 43, "state": {"representation": "direct", "sufficient_statistics": {"independent": true, "p_A": 0.200973, "p_B": 0.665751, "query": "A_and_B", "subtask": "intersection"}}}
{"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"independent": true, "p_A": 0.200973, "p_B": 0.665751, "query": "A_and_B", "subtask": "intersection"}}, "gold_argmax": "not_target", "gold_distribution": {"not_target": 0.866202024277, "target": 0.133797975723}, "instance_id": "compound__seed_000043__repr_table", "latent_instance_id": "compound__seed_000043", "outcomes": ["target", "not_target"], "probability_band": "(0.10,0.30]", "prompt": "Events A and B are independent. What is the probability that both occur? Return a normalized probability for each of: target, not_target.", "representation": "table", "seed": 43, "state": {"representation": "table", "state": {"independent": true, "p_A": 0.200973, "p_B": 0.665751, "query": "A_and_B", "subtask": "intersection"}, "table": [{"field": "subtask", "value": "intersection"}, {"field": "p_A", "value": 0.200973}, {"field": "p_B", "value": 0.665751}, {"field": "independent", "value": true}, {"field": "query", "value": "A_and_B"}]}}
{"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"independent": true, "p_A": 0.200973, "p_B": 0.665751, "query": "A_and_B", "subtask": "intersection"}}, "gold_argmax": "not_target", "gold_distribution": {"not_target": 0.866202024277, "target": 0.133797975723}, "instance_id": "compound__seed_000043__repr_prose", "latent_instance_id": "compound__seed_000043", "outcomes": ["target", "not_target"], "probability_band": "(0.10,0.30]", "prompt": "Events A and B are independent. What is the probability that both occur? Return a normalized probability for each of: target, not_target.", "representation": "prose", "seed": 43, "state": {"description": "The state fully determines the target distribution. The probability of target is 0.133797975723, and the remaining probability belongs to the other outcome. {'subtask': 'intersection', 'p_A': 0.200973, 'p_B': 0.665751, 'independent': True, 'query': 'A_and_B'}", "representation": "natural_language"}}
{"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"independent": true, "p_A": 0.387226, "p_B": 0.989146, "query": "A_or_B", "subtask": "union"}}, "gold_argmax": "target", "gold_distribution": {"not_target": 0.0066510489960001085, "target": 0.9933489510039999}, "instance_id": "compound__seed_000044__repr_direct", "latent_instance_id": "compound__seed_000044", "outcomes": ["target", "not_target"], "probability_band": "(0.99,1)", "prompt": "Events A and B are independent. What is the probability that at least one occurs? Return a normalized probability for each of: target, not_target.", "representation": "direct", "seed": 44, "state": {"representation": "direct", "sufficient_statistics": {"independent": true, "p_A": 0.387226, "p_B": 0.989146, "query": "A_or_B", "subtask": "union"}}}
{"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"independent": true, "p_A": 0.387226, "p_B": 0.989146, "query": "A_or_B", "subtask": "union"}}, "gold_argmax": "target", "gold_distribution": {"not_target": 0.0066510489960001085, "target": 0.9933489510039999}, "instance_id": "compound__seed_000044__repr_table", "latent_instance_id": "compound__seed_000044", "outcomes": ["target", "not_target"], "probability_band": "(0.99,1)", "prompt": "Events A and B are independent. What is the probability that at least one occurs? Return a normalized probability for each of: target, not_target.", "representation": "table", "seed": 44, "state": {"representation": "table", "state": {"independent": true, "p_A": 0.387226, "p_B": 0.989146, "query": "A_or_B", "subtask": "union"}, "table": [{"field": "subtask", "value": "union"}, {"field": "p_A", "value": 0.387226}, {"field": "p_B", "value": 0.989146}, {"field": "independent", "value": true}, {"field": "query", "value": "A_or_B"}]}}
{"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"independent": true, "p_A": 0.387226, "p_B": 0.989146, "query": "A_or_B", "subtask": "union"}}, "gold_argmax": "target", "gold_distribution": {"not_target": 0.0066510489960001085, "target": 0.9933489510039999}, "instance_id": "compound__seed_000044__repr_prose", "latent_instance_id": "compound__seed_000044", "outcomes": ["target", "not_target"], "probability_band": "(0.99,1)", "prompt": "Events A and B are independent. What is the probability that at least one occurs? Return a normalized probability for each of: target, not_target.", "representation": "prose", "seed": 44, "state": {"description": "The state fully determines the target distribution. The probability of target is 0.993348951004, and the remaining probability belongs to the other outcome. {'subtask': 'union', 'p_A': 0.387226, 'p_B': 0.989146, 'independent': True, 'query': 'A_or_B'}", "representation": "natural_language"}}
{"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"k": 3, "n": 7, "query": "exactly_k_successes", "subtask": "repeated_exact", "success_probability": 0.490136}}, "gold_argmax": "not_target", "gold_distribution": {"not_target": 0.7214935573757005, "target": 0.27850644262429947}, "instance_id": "compound__seed_000045__repr_direct", "latent_instance_id": "compound__seed_000045", "outcomes": ["target", "not_target"], "probability_band": "(0.10,0.30]", "prompt": "Independent Bernoulli trials use the supplied success probability. What is the probability of exactly k successes? Return a normalized probability for each of: target, not_target.", "representation": "direct", "seed": 45, "state": {"representation": "direct", "sufficient_statistics": {"k": 3, "n": 7, "query": "exactly_k_successes", "subtask": "repeated_exact", "success_probability": 0.490136}}}
{"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"k": 3, "n": 7, "query": "exactly_k_successes", "subtask": "repeated_exact", "success_probability": 0.490136}}, "gold_argmax": "not_target", "gold_distribution": {"not_target": 0.7214935573757005, "target": 0.27850644262429947}, "instance_id": "compound__seed_000045__repr_table", "latent_instance_id": "compound__seed_000045", "outcomes": ["target", "not_target"], "probability_band": "(0.10,0.30]", "prompt": "Independent Bernoulli trials use the supplied success probability. What is the probability of exactly k successes? Return a normalized probability for each of: target, not_target.", "representation": "table", "seed": 45, "state": {"representation": "table", "state": {"k": 3, "n": 7, "query": "exactly_k_successes", "subtask": "repeated_exact", "success_probability": 0.490136}, "table": [{"field": "subtask", "value": "repeated_exact"}, {"field": "n", "value": 7}, {"field": "k", "value": 3}, {"field": "success_probability", "value": 0.490136}, {"field": "query", "value": "exactly_k_successes"}]}}
{"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"k": 3, "n": 7, "query": "exactly_k_successes", "subtask": "repeated_exact", "success_probability": 0.490136}}, "gold_argmax": "not_target", "gold_distribution": {"not_target": 0.7214935573757005, "target": 0.27850644262429947}, "instance_id": "compound__seed_000045__repr_prose", "latent_instance_id": "compound__seed_000045", "outcomes": ["target", "not_target"], "probability_band": "(0.10,0.30]", "prompt": "Independent Bernoulli trials use the supplied success probability. What is the probability of exactly k successes? Return a normalized probability for each of: target, not_target.", "representation": "prose", "seed": 45, "state": {"description": "The state fully determines the target distribution. The probability of target is 0.278506442624, and the remaining probability belongs to the other outcome. {'subtask': 'repeated_exact', 'n': 7, 'k': 3, 'success_probability': 0.490136, 'query': 'exactly_k_successes'}", "representation": "natural_language"}}
{"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"bad": 14, "draws_without_replacement": 4, "good": 6, "k_good": 2, "subtask": "hypergeometric"}}, "gold_argmax": "not_target", "gold_distribution": {"not_target": 0.7182662538699691, "target": 0.28173374613003094}, "instance_id": "compound__seed_000046__repr_direct", "latent_instance_id": "compound__seed_000046", "outcomes": ["target", "not_target"], "probability_band": "(0.10,0.30]", "prompt": "A sample is drawn without replacement. What is the probability of exactly k good items? Return a normalized probability for each of: target, not_target.", "representation": "direct", "seed": 46, "state": {"representation": "direct", "sufficient_statistics": {"bad": 14, "draws_without_replacement": 4, "good": 6, "k_good": 2, "subtask": "hypergeometric"}}}
{"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"bad": 14, "draws_without_replacement": 4, "good": 6, "k_good": 2, "subtask": "hypergeometric"}}, "gold_argmax": "not_target", "gold_distribution": {"not_target": 0.7182662538699691, "target": 0.28173374613003094}, "instance_id": "compound__seed_000046__repr_table", "latent_instance_id": "compound__seed_000046", "outcomes": ["target", "not_target"], "probability_band": "(0.10,0.30]", "prompt": "A sample is drawn without replacement. What is the probability of exactly k good items? Return a normalized probability for each of: target, not_target.", "representation": "table", "seed": 46, "state": {"representation": "table", "state": {"bad": 14, "draws_without_replacement": 4, "good": 6, "k_good": 2, "subtask": "hypergeometric"}, "table": [{"field": "subtask", "value": "hypergeometric"}, {"field": "good", "value": 6}, {"field": "bad", "value": 14}, {"field": "draws_without_replacement", "value": 4}, {"field": "k_good", "value": 2}]}}
{"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"bad": 14, "draws_without_replacement": 4, "good": 6, "k_good": 2, "subtask": "hypergeometric"}}, "gold_argmax": "not_target", "gold_distribution": {"not_target": 0.7182662538699691, "target": 0.28173374613003094}, "instance_id": "compound__seed_000046__repr_prose", "latent_instance_id": "compound__seed_000046", "outcomes": ["target", "not_target"], "probability_band": "(0.10,0.30]", "prompt": "A sample is drawn without replacement. What is the probability of exactly k good items? Return a normalized probability for each of: target, not_target.", "representation": "prose", "seed": 46, "state": {"description": "The state fully determines the target distribution. The probability of target is 0.28173374613, and the remaining probability belongs to the other outcome. {'subtask': 'hypergeometric', 'good': 6, 'bad': 14, 'draws_without_replacement': 4, 'k_good': 2}", "representation": "natural_language"}}
{"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"p_A": 0.84647, "query": "not_A", "subtask": "complement"}}, "gold_argmax": "not_target", "gold_distribution": {"not_target": 0.84647, "target": 0.15353000000000006}, "instance_id": "compound__seed_000047__repr_direct", "latent_instance_id": "compound__seed_000047", "outcomes": ["target", "not_target"], "probability_band": "(0.10,0.30]", "prompt": "Event A has the supplied probability. What is the probability that A does not occur? Return a normalized probability for each of: target, not_target.", "representation": "direct", "seed": 47, "state": {"representation": "direct", "sufficient_statistics": {"p_A": 0.84647, "query": "not_A", "subtask": "complement"}}}
{"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"p_A": 0.84647, "query": "not_A", "subtask": "complement"}}, "gold_argmax": "not_target", "gold_distribution": {"not_target": 0.84647, "target": 0.15353000000000006}, "instance_id": "compound__seed_000047__repr_table", "latent_instance_id": "compound__seed_000047", "outcomes": ["target", "not_target"], "probability_band": "(0.10,0.30]", "prompt": "Event A has the supplied probability. What is the probability that A does not occur? Return a normalized probability for each of: target, not_target.", "representation": "table", "seed": 47, "state": {"representation": "table", "state": {"p_A": 0.84647, "query": "not_A", "subtask": "complement"}, "table": [{"field": "subtask", "value": "complement"}, {"field": "p_A", "value": 0.84647}, {"field": "query", "value": "not_A"}]}}
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{"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"independent": true, "p_A": 0.933733, "p_B": 0.403957, "query": "A_and_B", "subtask": "intersection"}}, "gold_argmax": "not_target", "gold_distribution": {"not_target": 0.622812018519, "target": 0.377187981481}, "instance_id": "compound__seed_000048__repr_direct", "latent_instance_id": "compound__seed_000048", "outcomes": ["target", "not_target"], "probability_band": "(0.30,0.45]", "prompt": "Events A and B are independent. What is the probability that both occur? Return a normalized probability for each of: target, not_target.", "representation": "direct", "seed": 48, "state": {"representation": "direct", "sufficient_statistics": {"independent": true, "p_A": 0.933733, "p_B": 0.403957, "query": "A_and_B", "subtask": "intersection"}}}
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{"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"independent": true, "p_A": 0.031994, "p_B": 0.588463, "query": "A_or_B", "subtask": "union"}}, "gold_argmax": "target", "gold_distribution": {"not_target": 0.39837028522200013, "target": 0.6016297147779999}, "instance_id": "compound__seed_000049__repr_direct", "latent_instance_id": "compound__seed_000049", "outcomes": ["target", "not_target"], "probability_band": "(0.55,0.70]", "prompt": "Events A and B are independent. What is the probability that at least one occurs? Return a normalized probability for each of: target, not_target.", "representation": "direct", "seed": 49, "state": {"representation": "direct", "sufficient_statistics": {"independent": true, "p_A": 0.031994, "p_B": 0.588463, "query": "A_or_B", "subtask": "union"}}}
{"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"independent": true, "p_A": 0.031994, "p_B": 0.588463, "query": "A_or_B", "subtask": "union"}}, "gold_argmax": "target", "gold_distribution": {"not_target": 0.39837028522200013, "target": 0.6016297147779999}, "instance_id": "compound__seed_000049__repr_table", "latent_instance_id": "compound__seed_000049", "outcomes": ["target", "not_target"], "probability_band": "(0.55,0.70]", "prompt": "Events A and B are independent. What is the probability that at least one occurs? Return a normalized probability for each of: target, not_target.", "representation": "table", "seed": 49, "state": {"representation": "table", "state": {"independent": true, "p_A": 0.031994, "p_B": 0.588463, "query": "A_or_B", "subtask": "union"}, "table": [{"field": "subtask", "value": "union"}, {"field": "p_A", "value": 0.031994}, {"field": "p_B", "value": 0.588463}, {"field": "independent", "value": true}, {"field": "query", "value": "A_or_B"}]}}
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{"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"bad": 13, "draws_without_replacement": 4, "good": 13, "k_good": 4, "subtask": "hypergeometric"}}, "gold_argmax": "not_target", "gold_distribution": {"not_target": 0.9521739130434783, "target": 0.04782608695652174}, "instance_id": "compound__seed_000061__repr_direct", "latent_instance_id": "compound__seed_000061", "outcomes": ["target", "not_target"], "probability_band": "[0.01,0.10]", "prompt": "A sample is drawn without replacement. What is the probability of exactly k good items? Return a normalized probability for each of: target, not_target.", "representation": "direct", "seed": 61, "state": {"representation": "direct", "sufficient_statistics": {"bad": 13, "draws_without_replacement": 4, "good": 13, "k_good": 4, "subtask": "hypergeometric"}}}
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{"benchmark_version": "0.1.0", "difficulty": 5, "family": "bayes", "generator_metadata": {"parameters": {"likelihood_event": {"H": 0.439104, "not_H": 0.774864}, "observed_event": true, "priors": {"H": 0.07458, "not_H": 0.92542}}}, "gold_argmax": "not_H", "gold_distribution": {"H": 0.04367480789658851, "not_H": 0.9563251921034115}, "instance_id": "bayes__seed_000042__repr_table", "latent_instance_id": "bayes__seed_000042", "outcomes": ["H", "not_H"], "probability_band": "[0.01,0.10]", "prompt": "Given the prior probabilities and likelihoods, what is the posterior distribution after observing the event? Return a normalized probability for each of: H, not_H.", "representation": "table", "seed": 42, "state": {"representation": "table", "state": {"likelihood_event": {"H": 0.439104, "not_H": 0.774864}, "observed_event": true, "priors": {"H": 0.07458, "not_H": 0.92542}}, "table": [{"P(E|hypothesis)": 0.439104, "hypothesis": "H", "prior": 0.07458}, {"P(E|hypothesis)": 0.774864, "hypothesis": "not_H", "prior": 0.92542}]}}
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{"benchmark_version": "0.1.0", "difficulty": 5, "family": "bayes", "generator_metadata": {"parameters": {"likelihood_event": {"H": 0.780272, "not_H": 0.101396}, "observed_event": true, "priors": {"H": 0.480479, "not_H": 0.519521}}}, "gold_argmax": "H", "gold_distribution": {"H": 0.8768016590833436, "not_H": 0.12319834091665638}, "instance_id": "bayes__seed_000045__repr_table", "latent_instance_id": "bayes__seed_000045", "outcomes": ["H", "not_H"], "probability_band": "(0.70,0.90]", "prompt": "Given the prior probabilities and likelihoods, what is the posterior distribution after observing the event? Return a normalized probability for each of: H, not_H.", "representation": "table", "seed": 45, "state": {"representation": "table", "state": {"likelihood_event": {"H": 0.780272, "not_H": 0.101396}, "observed_event": true, "priors": {"H": 0.480479, "not_H": 0.519521}}, "table": [{"P(E|hypothesis)": 0.780272, "hypothesis": "H", "prior": 0.480479}, {"P(E|hypothesis)": 0.101396, "hypothesis": "not_H", "prior": 0.519521}]}}
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{"benchmark_version": "0.1.0", "difficulty": 5, "family": "bayes", "generator_metadata": {"parameters": {"likelihood_event": {"H": 0.23861, "not_H": 0.681894}, "observed_event": true, "priors": {"H": 0.933733, "not_H": 0.06626699999999996}}}, "gold_argmax": "H", "gold_distribution": {"H": 0.8313821568498233, "not_H": 0.1686178431501767}, "instance_id": "bayes__seed_000048__repr_counts", "latent_instance_id": "bayes__seed_000048", "outcomes": ["H", "not_H"], "probability_band": "(0.70,0.90]", "prompt": "Given the prior probabilities and likelihoods, what is the posterior distribution after observing the event? Return a normalized probability for each of: H, not_H.", "representation": "counts", "seed": 48, "state": {"event_counts_by_hypothesis": {"H": 223, "not_H": 45}, "observed_event": true, "prior_counts": {"H": 934, "not_H": 66}, "representation": "bayes_counts"}}
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{"benchmark_version": "0.1.0", "difficulty": 5, "family": "bayes", "generator_metadata": {"parameters": {"likelihood_event": {"H": 0.64129, "not_H": 0.013968}, "observed_event": true, "priors": {"H": 0.410511, "not_H": 0.5894889999999999}}}, "gold_argmax": "H", "gold_distribution": {"H": 0.9696712044107276, "not_H": 0.030328795589272373}, "instance_id": "bayes__seed_000051__repr_table", "latent_instance_id": "bayes__seed_000051", "outcomes": ["H", "not_H"], "probability_band": "(0.90,0.99]", "prompt": "Given the prior probabilities and likelihoods, what is the posterior distribution after observing the event? Return a normalized probability for each of: H, not_H.", "representation": "table", "seed": 51, "state": {"representation": "table", "state": {"likelihood_event": {"H": 0.64129, "not_H": 0.013968}, "observed_event": true, "priors": {"H": 0.410511, "not_H": 0.5894889999999999}}, "table": [{"P(E|hypothesis)": 0.64129, "hypothesis": "H", "prior": 0.410511}, {"P(E|hypothesis)": 0.013968, "hypothesis": "not_H", "prior": 0.5894889999999999}]}}
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