[Eval] Calculate area enclosed by path (#1137)

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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:

<details>
  <summary>View evals in JSON</summary>

  ### Eval
  ```jsonl
{"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]"}
  ```
</details>

Co-authored-by: Ahmed Allawi <[email protected]>

Author: AhmedA77

evals/registry/data/path_enclosed_area/samples.jsonl

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:64c4304d7469a8bdda1148eae2250efe0b228d10ea077df94f787e3a067cc0a2
+size 12643

evals/registry/evals/path_enclosed_area.yaml

@@ -0,0 +1,9 @@
+path_enclosed_area:
+  id: path_enclosed_area.dev.v0
+  description: Geometric calculation of the total area enclosed by a given path on a flat plane
+  metrics: [accuracy]
+
+path_enclosed_area.dev.v0:
+  class: evals.elsuite.basic.includes:Includes
+  args:
+    samples_jsonl: path_enclosed_area/samples.jsonl