diff --git a/cirq-core/cirq/study/resolver.py b/cirq-core/cirq/study/resolver.py
index d0ee7aae51d..aaf2343b90f 100644
--- a/cirq-core/cirq/study/resolver.py
+++ b/cirq-core/cirq/study/resolver.py
@@ -75,9 +75,20 @@ def __init__(self, param_dict: cirq.ParamResolverOrSimilarType = None) -> None:
 
         self._param_hash: int | None = None
         self._param_dict = cast(ParamDictType, {} if param_dict is None else param_dict)
+        self._param_dict_with_str_keys = self._param_dict
+        generate_str_keys = False
         for key in self._param_dict:
-            if isinstance(key, sympy.Expr) and not isinstance(key, sympy.Symbol):
-                raise TypeError(f'ParamResolver keys cannot be (non-symbol) formulas ({key})')
+            if isinstance(key, sympy.Expr):
+                if isinstance(key, sympy.Symbol):
+                    generate_str_keys = True
+                else:
+                    raise TypeError(f'ParamResolver keys cannot be (non-symbol) formulas ({key})')
+        if generate_str_keys:
+            # Remake dictionary with string keys for faster access
+            self._param_dict_with_str_keys = {
+                (key.name if isinstance(key, sympy.Symbol) else key): value
+                for key, value in self._param_dict.items()
+            }
         self._deep_eval_map: ParamDictType = {}
 
     @property
@@ -119,22 +130,23 @@ def value_of(
         """
 
         # Handle string or symbol
-        if isinstance(value, (str, sympy.Symbol)):
-            string = value if isinstance(value, str) else value.name
-            param_value = self._param_dict.get(string, _NOT_FOUND)
+        original_value = value
+        if isinstance(value, sympy.Symbol):
+            value = value.name
+        if isinstance(value, str):
+            param_value = self._param_dict_with_str_keys.get(value, _NOT_FOUND)
+            if isinstance(param_value, float):
+                return param_value
             if param_value is _NOT_FOUND:
-                symbol = value if isinstance(value, sympy.Symbol) else sympy.Symbol(value)
-                param_value = self._param_dict.get(symbol, _NOT_FOUND)
-                if param_value is _NOT_FOUND:
-                    # Symbol or string cannot be resolved if not in param dict; return as symbol.
-                    return symbol
+                # Symbol or string cannot be resolved if not in param dict; return as symbol.
+                return sympy.Symbol(value)
             v = _resolve_value(param_value)
             if v is not NotImplemented:
                 return v
             if isinstance(param_value, str):
                 param_value = sympy.Symbol(param_value)
             elif not isinstance(param_value, sympy.Basic):
-                return value
+                return original_value
             if recursive:
                 param_value = self._value_of_recursive(value)
             return param_value
@@ -210,7 +222,7 @@ def _value_of_recursive(self, value: cirq.TParamKey) -> cirq.TParamValComplex:
         self._deep_eval_map[value] = _RECURSION_FLAG
 
         v = self.value_of(value, recursive=False)
-        if v == value:
+        if v == value or (isinstance(v, sympy.Symbol) and v.name == value):
             self._deep_eval_map[value] = v
         else:
             self._deep_eval_map[value] = self.value_of(v, recursive=True)
@@ -278,7 +290,7 @@ def _from_json_dict_(cls, param_dict, **kwargs):
 
 
 def _resolve_value(val: Any) -> Any:
-    if val is None or isinstance(val, float):
+    if isinstance(val, float) or val is None:
         return val
     if isinstance(val, numbers.Number) and not isinstance(val, sympy.Basic):
         return val