diff --git a/onnxscript/function_libs/torch_lib/ops/core.py b/onnxscript/function_libs/torch_lib/ops/core.py
index 535da66d0..b2138d4e6 100644
--- a/onnxscript/function_libs/torch_lib/ops/core.py
+++ b/onnxscript/function_libs/torch_lib/ops/core.py
@@ -1585,14 +1585,14 @@ def aten_cdist(
     raise NotImplementedError()
 
 
-@torch_op("aten::ceil")
+@torch_op("aten::ceil", traceable=True)
 def aten_ceil(self: TFloat) -> TFloat:
     """ceil(Tensor self) -> Tensor"""
 
     return op.Ceil(self)
 
 
-@torch_op("math::ceil")
+@torch_op("math::ceil", traceable=True)
 def python_math_ceil(self: TFloat) -> TInt:
     """ceil(Tensor self) -> Tensor"""
     ceil = op.Ceil(self)
@@ -1764,13 +1764,6 @@ def aten_combinations(
     raise NotImplementedError()
 
 
-@torch_op("aten::complex", private=True)
-def _aten_complex(real: TFloat, imag: TFloat) -> TFloat:
-    """Non-broadcasting complex constructor."""
-
-    return op.Concat(op.Unsqueeze(real, axes=[-1]), op.Unsqueeze(imag, axes=[-1]), axis=-1)
-
-
 @torch_op("aten::complex", trace_only=True)
 def aten_complex(real: TFloat, imag: TFloat) -> TFloat:
     """complex(Tensor real, Tensor imag) -> Tensor"""
@@ -1780,7 +1773,7 @@ def aten_complex(real: TFloat, imag: TFloat) -> TFloat:
     real = op.Expand(real, broadcasted_shape)
     imag = op.Expand(imag, broadcasted_shape)
 
-    return _aten_complex(real, imag)
+    return op.Concat(op.Unsqueeze(real, axes=[-1]), op.Unsqueeze(imag, axes=[-1]), axis=-1)
 
 
 @torch_op("aten::conj", trace_only=True)
@@ -1790,7 +1783,6 @@ def aten_conj(self: TTensor) -> TTensor:
     return op.Identity(self)
 
 
-@torch_op("aten::conj", complex=True, private=True)
 def _complex_conjugate(self: TFloat) -> TFloat:
     zero = op.Constant(value_ints=[0])
     one = op.Constant(value_ints=[1])
@@ -1809,8 +1801,6 @@ def _complex_conjugate(self: TFloat) -> TFloat:
 def aten_conj_complex(self: TFloat) -> TFloat:
     """conj(Tensor(a) self) -> Tensor(a)"""
 
-    # TODO(#834): Allow calling scripted functions from other
-    # scripted functions and remove trace only.
     return _complex_conjugate(self)
 
 
@@ -5071,9 +5061,6 @@ def aten_mH(self: TRealOrUInt8) -> TRealOrUInt8:
 def aten_mH_complex(self: TFloat) -> TFloat:
     """mH(Tensor(a) self) -> Tensor(a)"""
 
-    # TODO(#834): Allow calling scripted functions from other
-    # scripted functions and remove trace only.
-
     # c is the last dimension being the real and imaginary parts
     trasposed = op.Einsum(self, equation="...ijc->...jic")
     return _complex_conjugate(trasposed)