[Eval] Calculate area enclosed by path

[AhmedA77]

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Eval details 📑

Eval name

path_enclosed_area

Eval description

This eval tests the model's ability to calculate the total area enclosed by a path walked on a flat plane; the path moves only north, south, east, or west. These problems are extremely simple for any human, but the model has a lot of difficulty with them.

The paths were hand constructed to test across a variety of scenarios including:

• One path with multiple discrete enclosed areas
• One path with zero enclosed areas
• Irrelevant segmentation of an enclosed area into smaller enclosed areas
• Going back and forth across the same segment
• Different initial directions
• Symmetrical and asymmetrical

What makes this a useful eval?

This kind of geometric reasoning and calculation is important for simple tasks across mathematics, game design, engineering, and various other fields.

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Eval JSON data

Since we are using Git LFS, we are asking eval submitters to add in as many Eval Samples (at least 5) from their contribution here:

View evals in JSON

Eval

{"input": [{"role": "system", "content": "On a flat plane, I walk 5 miles north, 3 miles east, 2 miles south, 2 miles east, 4 miles south, 6 miles west. What is the area, in square miles, of the area that is completely enclosed by my path? If no area is completely enclosed, then there are 0 square miles enclosed. If multiple discrete areas are enclosed, then please sum their areas for the final answer. Explain your reasoning step-by-step, and then provide your final answer in the exact following format surrounded by brackets: \"[X square miles]\" where X is the integer number of total square miles enclosed by the path, and where miles should be written as mile if X=1."}], "ideal": "[0 square miles]"}
{"input": [{"role": "system", "content": "On a flat plane, I walk 3 miles east, 3 miles south, 2 miles east, 3 miles west, 1 mile east, 5 miles north, 4 miles west. What is the area, in square miles, of the area that is completely enclosed by my path? If no area is completely enclosed, then there are 0 square miles enclosed. If multiple discrete areas are enclosed, then please sum their areas for the final answer. Explain your reasoning step-by-step, and then provide your final answer in the exact following format surrounded by brackets: \"[X square miles]\" where X is the integer number of total square miles enclosed by the path, and where miles should be written as mile if X=1."}], "ideal": "[0 square miles]"}
{"input": [{"role": "system", "content": "On a flat plane, I walk 5 miles north, 3 miles east, 2 miles south, 1 mile east, 2 miles south, 5 miles west. What is the area, in square miles, of the area that is completely enclosed by my path? If no area is completely enclosed, then there are 0 square miles enclosed. If multiple discrete areas are enclosed, then please sum their areas for the final answer. Explain your reasoning step-by-step, and then provide your final answer in the exact following format surrounded by brackets: \"[X square miles]\" where X is the integer number of total square miles enclosed by the path, and where miles should be written as mile if X=1."}], "ideal": "[14 square miles]"}
{"input": [{"role": "system", "content": "On a flat plane, I walk 2 miles south, 3 miles west, 2 miles north, 2 miles east, 2 miles south, 1 mile west, 2 miles north, 2 miles east. What is the area, in square miles, of the area that is completely enclosed by my path? If no area is completely enclosed, then there are 0 square miles enclosed. If multiple discrete areas are enclosed, then please sum their areas for the final answer. Explain your reasoning step-by-step, and then provide your final answer in the exact following format surrounded by brackets: \"[X square miles]\" where X is the integer number of total square miles enclosed by the path, and where miles should be written as mile if X=1."}], "ideal": "[6 square miles]"}
{"input": [{"role": "system", "content": "On a flat plane, I walk 3 miles south, 2 miles east, 1 mile north, 3 miles west, 1 mile north, 2 miles east, 4 miles south. What is the area, in square miles, of the area that is completely enclosed by my path? If no area is completely enclosed, then there are 0 square miles enclosed. If multiple discrete areas are enclosed, then please sum their areas for the final answer. Explain your reasoning step-by-step, and then provide your final answer in the exact following format surrounded by brackets: \"[X square miles]\" where X is the integer number of total square miles enclosed by the path, and where miles should be written as mile if X=1."}], "ideal": "[4 square miles]"}
{"input": [{"role": "system", "content": "On a flat plane, I walk 1 mile west, 1 mile north, 1 mile east, 1 mile south, 1 mile east, 1 mile north, 1 mile west, 2 miles north. What is the area, in square miles, of the area that is completely enclosed by my path? If no area is completely enclosed, then there are 0 square miles enclosed. If multiple discrete areas are enclosed, then please sum their areas for the final answer. Explain your reasoning step-by-step, and then provide your final answer in the exact following format surrounded by brackets: \"[X square miles]\" where X is the integer number of total square miles enclosed by the path, and where miles should be written as mile if X=1."}], "ideal": "[2 square miles]"}
{"input": [{"role": "system", "content": "On a flat plane, I walk 1 mile south, 1 mile east, 1 mile south, 1 mile east, 1 mile south, 1 mile east, 2 miles north, 1 mile east, 1 mile north, 4 miles west. What is the area, in square miles, of the area that is completely enclosed by my path? If no area is completely enclosed, then there are 0 square miles enclosed. If multiple discrete areas are enclosed, then please sum their areas for the final answer. Explain your reasoning step-by-step, and then provide your final answer in the exact following format surrounded by brackets: \"[X square miles]\" where X is the integer number of total square miles enclosed by the path, and where miles should be written as mile if X=1."}], "ideal": "[7 square miles]"}
{"input": [{"role": "system", "content": "On a flat plane, I walk 1 mile west, 1 mile south, 1 mile north, 2 miles east, 1 mile north, 3 miles west, 3 miles south, 1 mile east, 1 mile south, 1 mile west, 2 miles north. What is the area, in square miles, of the area that is completely enclosed by my path? If no area is completely enclosed, then there are 0 square miles enclosed. If multiple discrete areas are enclosed, then please sum their areas for the final answer. Explain your reasoning step-by-step, and then provide your final answer in the exact following format surrounded by brackets: \"[X square miles]\" where X is the integer number of total square miles enclosed by the path, and where miles should be written as mile if X=1."}], "ideal": "[1 square mile]"}
{"input": [{"role": "system", "content": "On a flat plane, I walk 1 mile north, 2 miles east, 1 mile north, 1 mile east, 3 miles south, 2 miles west, 2 miles north. What is the area, in square miles, of the area that is completely enclosed by my path? If no area is completely enclosed, then there are 0 square miles enclosed. If multiple discrete areas are enclosed, then please sum their areas for the final answer. Explain your reasoning step-by-step, and then provide your final answer in the exact following format surrounded by brackets: \"[X square miles]\" where X is the integer number of total square miles enclosed by the path, and where miles should be written as mile if X=1."}], "ideal": "[5 square miles]"}
{"input": [{"role": "system", "content": "On a flat plane, I walk 1 mile east, 1 mile north, 1 mile west, 1 mile north, 1 mile east, 1 mile north, 1 mile west, 1 mile north, 1 mile east, 5 miles south. What is the area, in square miles, of the area that is completely enclosed by my path? If no area is completely enclosed, then there are 0 square miles enclosed. If multiple discrete areas are enclosed, then please sum their areas for the final answer. Explain your reasoning step-by-step, and then provide your final answer in the exact following format surrounded by brackets: \"[X square miles]\" where X is the integer number of total square miles enclosed by the path, and where miles should be written as mile if X=1."}], "ideal": "[2 square miles]"}
{"input": [{"role": "system", "content": "On a flat plane, I walk 5 miles south, 5 miles east, 4 miles north, 4 miles west, 3 miles south, 3 miles east, 2 miles north, 2 miles west, 1 mile south, 1 mile east, 3 miles north. What is the area, in square miles, of the area that is completely enclosed by my path? If no area is completely enclosed, then there are 0 square miles enclosed. If multiple discrete areas are enclosed, then please sum their areas for the final answer. Explain your reasoning step-by-step, and then provide your final answer in the exact following format surrounded by brackets: \"[X square miles]\" where X is the integer number of total square miles enclosed by the path, and where miles should be written as mile if X=1."}], "ideal": "[8 square miles]"}
{"input": [{"role": "system", "content": "On a flat plane, I walk 1 mile west, 1 mile south, 1 mile north, 1 mile south, 1 mile east, 1 mile south, 1 mile west, 1 mile south, 2 miles east, 3 miles north. What is the area, in square miles, of the area that is completely enclosed by my path? If no area is completely enclosed, then there are 0 square miles enclosed. If multiple discrete areas are enclosed, then please sum their areas for the final answer. Explain your reasoning step-by-step, and then provide your final answer in the exact following format surrounded by brackets: \"[X square miles]\" where X is the integer number of total square miles enclosed by the path, and where miles should be written as mile if X=1."}], "ideal": "[0 square miles]"}
{"input": [{"role": "system", "content": "On a flat plane, I walk 4 miles north, 2 miles south, 2 miles west, 4 miles east, 1 mile west, 1 mile north, 2 miles west, 2 miles south, 1 mile east. What is the area, in square miles, of the area that is completely enclosed by my path? If no area is completely enclosed, then there are 0 square miles enclosed. If multiple discrete areas are enclosed, then please sum their areas for the final answer. Explain your reasoning step-by-step, and then provide your final answer in the exact following format surrounded by brackets: \"[X square miles]\" where X is the integer number of total square miles enclosed by the path, and where miles should be written as mile if X=1."}], "ideal": "[3 square miles]"}
{"input": [{"role": "system", "content": "On a flat plane, I walk 2 miles south, 1 mile east, 1 mile north, 1 mile south, 1 mile east, 1 mile north, 1 mile south, 1 mile east, 2 miles north, 1 mile east, 1 mile south, 3 miles west. What is the area, in square miles, of the area that is completely enclosed by my path? If no area is completely enclosed, then there are 0 square miles enclosed. If multiple discrete areas are enclosed, then please sum their areas for the final answer. Explain your reasoning step-by-step, and then provide your final answer in the exact following format surrounded by brackets: \"[X square miles]\" where X is the integer number of total square miles enclosed by the path, and where miles should be written as mile if X=1."}], "ideal": "[3 square miles]"}
{"input": [{"role": "system", "content": "On a flat plane, I walk 3 miles east, 1 mile south, 1 mile west, 1 mile south, 1 mile east, 1 mile south, 3 miles west, 1 mile north, 1 mile east, 1 mile north, 1 mile west, 2 miles north, 1 mile west. What is the area, in square miles, of the area that is completely enclosed by my path? If no area is completely enclosed, then there are 0 square miles enclosed. If multiple discrete areas are enclosed, then please sum their areas for the final answer. Explain your reasoning step-by-step, and then provide your final answer in the exact following format surrounded by brackets: \"[X square miles]\" where X is the integer number of total square miles enclosed by the path, and where miles should be written as mile if X=1."}], "ideal": "[7 square miles]"}
{"input": [{"role": "system", "content": "On a flat plane, I walk 1 mile south, 1 mile east, 1 mile north, 2 miles west, 2 miles south, 3 miles east, 2 miles north, 1 mile west. What is the area, in square miles, of the area that is completely enclosed by my path? If no area is completely enclosed, then there are 0 square miles enclosed. If multiple discrete areas are enclosed, then please sum their areas for the final answer. Explain your reasoning step-by-step, and then provide your final answer in the exact following format surrounded by brackets: \"[X square miles]\" where X is the integer number of total square miles enclosed by the path, and where miles should be written as mile if X=1."}], "ideal": "[6 square miles]"}
{"input": [{"role": "system", "content": "On a flat plane, I walk 1 mile south, 1 mile east, 1 mile north, 1 mile west. What is the area, in square miles, of the area that is completely enclosed by my path? If no area is completely enclosed, then there are 0 square miles enclosed. If multiple discrete areas are enclosed, then please sum their areas for the final answer. Explain your reasoning step-by-step, and then provide your final answer in the exact following format surrounded by brackets: \"[X square miles]\" where X is the integer number of total square miles enclosed by the path, and where miles should be written as mile if X=1."}], "ideal": "[1 square mile]"}

[usama-openai]

Thanks for submitting this eval! This PR looks good. I'm approving this PR.

[usama-openai]

You should see GPT-4 API access enabled in your account in the next few days.

[AhmedA77]

You should see GPT-4 API access enabled in your account in the next few days.

@usama-openai Hi, wanted to check in and make sure you have the right email because still don't seem to have GPT-4 API access on my account. The email is [email protected]. Per instructions, this is also the email associated with my Github I used for eval submission.

Thank you.

[usama-openai]

@usama-openai Hi, wanted to check in and make sure you have the right email because still don't seem to have GPT-4 API access on my account. The email is [email protected]. Per instructions, this is also the email associated with my Github I used for eval submission.

Thank you.

Sorry for the confusion. The GPT-4 access is provided to the email id associated with the commits, which is [email protected] in this case. Definitely, this is an invalid ID. Kindly send an email to [email protected] with details.

[AhmedA77]

[email protected]
Ah, my fault. Thanks

@usama-openai Hi, wanted to check in and make sure you have the right email because still don't seem to have GPT-4 API access on my account. The email is [email protected]. Per instructions, this is also the email associated with my Github I used for eval submission.
Thank you.

Sorry for the confusion. The GPT-4 access is provided to the email id associated with the commits, which is [email protected] in this case. Definitely, this is an invalid ID. Kindly send an email to [email protected] with details.

Ah, my fault. Thank you for your help -- just emailed him.