code: def test_distance_paraboloid():
      test_cases = [
          TestCase("z = x^2 + y^2 + 2", [0, 0, 2], 0.0),
          TestCase(
              "z = 2x^2 + y^2 + 2", [0, 11, 151], 1.2055445093982982
          ),  # https://www.wolframalpha.com/input?i=minimize+x%5E2+%2B+%28y+-+11%29%5E2+%2B+%28%282x%5E2+%2B+y%5E2+%2B+2%29+-+151%29%5E2  # noqa
          TestCase(
              "z = 2x^2 + 2y^2 + 2", [0, 0, 6], 1.3919410907075054
          ),  # https://www.wolframalpha.com/input?i=minimize+x%5E2+%2By%5E2+%2B+%28%282x%5E2+%2B+2y%5E2+%2B+2%29+-+6%29%5E2  # noqa
          TestCase(
              "z = x^2 + y^2 + 2", [0, 0, 20], 4.2130748865881795
          ),  # https://www.wolframalpha.com/input?i=x%5E2+%2B+y%5E2+%2B+%28%28x%5E2+%2B+y%5E2+%2B+2%29+-+20%29%5E2
          TestCase(
              "z = 2x^2 + xy + y^2 + 4",
              [6, 19, 519],
              0.5290904095503263,
          ),
          TestCase(
              "z = 2x^2 + xy + 2y^2 + 3",
              [0, 14, 380],
              0.26248531385619783,
          ),
          TestCase(
              "z = x^2 + 2y^2 + 1", [5, 14, 4], 13.354544558906934
          ),
          TestCase(
              "z = x^2 + xy + 2y^2 + 4",
              [3, 20, 1001],
              1.4206031238856873,
          ),
          TestCase("z = x^2 + xy + 2y^2 + 4", [0, 0, 55], 51.0),
          TestCase(
              "z = x^2 + xy + 2y^2 + 4", [0, 9, 55], 3.8558889386410757
          ),
          TestCase(
              "z = 2x^2 + 2y^2 + 1", [8, 9, 289], 0.04158555512549898
          ),
          TestCase("z = 2x^2 + 2y^2 + 1", [8, 9, 291], 0.0),
          TestCase(
              "z = x^2 + 2xy + 5y^2 + 4", [0, 9, 55], 5.7150737847649244
          ),
      ]
      check_test_cases(test_cases, distance_paraboloid)
  
file_path: H2O/h2o_hf/helm/src/helm/benchmark/metrics/test_numeracy_metrics.py
imports: from dataclasses import dataclass
  from typing import List, Callable
  from helm.benchmark.scenarios.numeracy_scenario import distance_linear, distance_parabola, distance_plane, distance_paraboloid
label_desc: Use image node_id 5 for calling a global function with example usage: test_distance_paraboloid() without return types