Support polynomial exponents and variable bases in the growth domain

problemreductions-expr/tests/fixtures/sympy_oracle.json

@@ -849,6 +849,111 @@
       "right": "exp(n)",
       "ratio_limit": "0",
       "relation": "right_dominates"
+    },
+    {
+      "name": "polynomial_exponent",
+      "left": "2^(n^2)",
+      "right": "3^n",
+      "ratio_limit": "oo",
+      "relation": "left_dominates"
+    },
+    {
+      "name": "sqrt_exponent_over_polynomial",
+      "left": "2^sqrt(n)",
+      "right": "n^100",
+      "ratio_limit": "oo",
+      "relation": "left_dominates"
+    },
+    {
+      "name": "exponential_over_sqrt_exponent",
+      "left": "1.0001^n",
+      "right": "2^sqrt(n)",
+      "ratio_limit": "oo",
+      "relation": "left_dominates"
+    },
+    {
+      "name": "quasi_polynomial",
+      "left": "2^(log(n)^2)",
+      "right": "n^100",
+      "ratio_limit": "oo",
+      "relation": "left_dominates"
+    },
+    {
+      "name": "self_power_over_binary_power",
+      "left": "n^n",
+      "right": "2^(n * log(n))",
+      "ratio_limit": "oo",
+      "relation": "left_dominates"
+    },
+    {
+      "name": "variable_base_rate",
+      "left": "n^(2 * n)",
+      "right": "n^n",
+      "ratio_limit": "oo",
+      "relation": "left_dominates"
+    },
+    {
+      "name": "mixed_base_product",
+      "left": "2^(2 * n) * 3^n",
+      "right": "2^n * 4^n",
+      "ratio_limit": "oo",
+      "relation": "left_dominates"
+    },
+    {
+      "name": "close_exponential_rates",
+      "left": "2^(0.773 * n)",
+      "right": "1.1996^n",
+      "ratio_limit": "oo",
+      "relation": "left_dominates"
+    },
+    {
+      "name": "exponent_cancellation",
+      "left": "2^((n + 1)^2 - n^2)",
+      "right": "2^(2 * n)",
+      "ratio_limit": "2",
+      "relation": "equivalent"
+    },
+    {
+      "name": "decaying_factor",
+      "left": "2^n * 0.5^n",
+      "right": "1",
+      "ratio_limit": "1",
+      "relation": "equivalent"
+    },
+    {
+      "name": "reverse_variable_base",
+      "left": "2^n",
+      "right": "n^n",
+      "ratio_limit": "0",
+      "relation": "right_dominates"
+    },
+    {
+      "name": "stirling_factorial",
+      "left": "factorial(n)",
+      "right": "n^n * sqrt(n) * exp(-n)",
+      "ratio_limit": "sqrt(2)*sqrt(pi)",
+      "relation": "equivalent"
+    },
+    {
+      "name": "factorial_below_self_power",
+      "left": "n^n",
+      "right": "factorial(n)",
+      "ratio_limit": "oo",
+      "relation": "left_dominates"
+    },
+    {
+      "name": "factorial_above_base_e_power",
+      "left": "factorial(n)",
+      "right": "(n / 3)^n",
+      "ratio_limit": "oo",
+      "relation": "left_dominates"
+    },
+    {
+      "name": "scaled_factorial",
+      "left": "factorial(2 * n)",
+      "right": "(2 * n)^(2 * n) * sqrt(n) * exp(-2 * n)",
+      "ratio_limit": "2*sqrt(pi)",
+      "relation": "equivalent"
     }
   ],
   "factorial_domain_cases": [

scripts/generate_symbolic_expr_fixture.py

@@ -148,6 +148,21 @@
     ("exponential_poly_tie_break", "2^n * n", "2^n"),
     ("reverse_polynomial_degree", "n", "n^2"),
     ("reverse_exponential", "n^100", "exp(n)"),
+    ("polynomial_exponent", "2^(n^2)", "3^n"),
+    ("sqrt_exponent_over_polynomial", "2^sqrt(n)", "n^100"),
+    ("exponential_over_sqrt_exponent", "1.0001^n", "2^sqrt(n)"),
+    ("quasi_polynomial", "2^(log(n)^2)", "n^100"),
+    ("self_power_over_binary_power", "n^n", "2^(n * log(n))"),
+    ("variable_base_rate", "n^(2 * n)", "n^n"),
+    ("mixed_base_product", "2^(2 * n) * 3^n", "2^n * 4^n"),
+    ("close_exponential_rates", "2^(0.773 * n)", "1.1996^n"),
+    ("exponent_cancellation", "2^((n + 1)^2 - n^2)", "2^(2 * n)"),
+    ("decaying_factor", "2^n * 0.5^n", "1"),
+    ("reverse_variable_base", "2^n", "n^n"),
+    ("stirling_factorial", "factorial(n)", "n^n * sqrt(n) * exp(-n)"),
+    ("factorial_below_self_power", "n^n", "factorial(n)"),
+    ("factorial_above_base_e_power", "factorial(n)", "(n / 3)^n"),
+    ("scaled_factorial", "factorial(2 * n)", "(2 * n)^(2 * n) * sqrt(n) * exp(-2 * n)"),
 ]