diff --git a/jax/experimental/checkify.py b/jax/experimental/checkify.py
index 4365f4c64..39d314f77 100644
--- a/jax/experimental/checkify.py
+++ b/jax/experimental/checkify.py
@@ -15,7 +15,7 @@
 from dataclasses import dataclass
 from functools import partial
 import itertools as it
-from typing import Union, Optional, Callable, Dict
+from typing import Union, Optional, Callable, Dict, Tuple, TypeVar
 
 import numpy as np
 
@@ -86,7 +86,7 @@ def assert_func(error: Error, pred: Bool, msg: str) -> Error:
 
 ## Checkify transformation for plumbing functional error values.
 
-class ErrorTracer(core.Tracer):
+class CheckifyTracer(core.Tracer):
   def __init__(self, trace, val):
     self._trace = trace
     self.val = val
@@ -94,11 +94,11 @@ class ErrorTracer(core.Tracer):
   aval = property(lambda self: core.get_aval(self.val))
   full_lower = lambda self: self
 
-class ErrorTrace(core.Trace):
-  pure = lift = lambda self, val: ErrorTracer(self, val)
+class CheckifyTrace(core.Trace):
+  pure = lift = lambda self, val: CheckifyTracer(self, val)
 
   def sublift(self, tracer):
-    return ErrorTracer(self, tracer.val)
+    return CheckifyTracer(self, tracer.val)
 
   def process_primitive(self, primitive, tracers, params):
     in_vals = [t.val for t in tracers]
@@ -108,23 +108,23 @@ class ErrorTrace(core.Trace):
     else:
       out = primitive.bind(*in_vals, **params)
     if primitive.multiple_results:
-      return [ErrorTracer(self, x) for x in out]
+      return [CheckifyTracer(self, x) for x in out]
     else:
-      return ErrorTracer(self, out)
+      return CheckifyTracer(self, out)
 
   def process_call(self, primitive, f, tracers, params):
     in_vals = [t.val for t in tracers]
     e = popattr(self.main, 'error')
-    f, msgs = check_errors_subtrace(f, self.main, tuple(e.msgs.items()))
+    f, msgs = checkify_subtrace(f, self.main, tuple(e.msgs.items()))
     params_ = dict(params, donated_invars=(False, False, *params['donated_invars']))
     err, code, *out_vals = primitive.bind(f, e.err, e.code, *in_vals, **params_)
     setnewattr(self.main, 'error', Error(err, code, msgs()))
-    return [ErrorTracer(self, x) for x in out_vals]
+    return [CheckifyTracer(self, x) for x in out_vals]
 
   def process_map(self, primitive, f, tracers, params):
     in_vals = [t.val for t in tracers]
     e = popattr(self.main, 'error')
-    f, msgs = check_errors_subtrace(f, self.main, tuple(e.msgs.items()))
+    f, msgs = checkify_subtrace(f, self.main, tuple(e.msgs.items()))
 
     @as_hashable_function(closure=params['out_axes_thunk'])
     def new_out_axes_thunk():
@@ -136,7 +136,7 @@ class ErrorTrace(core.Trace):
     errs, codes, *outs = primitive.bind(f, e.err, e.code, *in_vals, **params_)
     err, code = _reduce_any_error(errs, codes)
     setnewattr(self.main, 'error', Error(err, code, msgs()))
-    return [ErrorTracer(self, x) for x in outs]
+    return [CheckifyTracer(self, x) for x in outs]
 
   def post_process_call(self, primitive, tracers, params):
     vals = [t.val for t in tracers]
@@ -146,7 +146,7 @@ class ErrorTrace(core.Trace):
     def todo(vals):
       trace = main.with_cur_sublevel()
       err, code, *vals = vals
-      return [ErrorTracer(trace, x) for x in vals]
+      return [CheckifyTracer(trace, x) for x in vals]
     return (err, code, *vals), todo
 
   def post_process_map(self, primitive, tracers, params):
@@ -157,7 +157,7 @@ class ErrorTrace(core.Trace):
     def todo(vals):
       trace = main.with_cur_sublevel()
       err, code, *vals = vals
-      return [ErrorTracer(trace, x) for x in vals]
+      return [CheckifyTracer(trace, x) for x in vals]
     def out_axes_transform(out_axes):
       return (0, 0, *out_axes)
     return (err, code, *vals), (todo, out_axes_transform)
@@ -169,26 +169,24 @@ def _reduce_any_error(errs, codes):
 ErrorCheckRule = Callable
 error_checks: Dict[core.Primitive, ErrorCheckRule] = {}
 
-def check_errors_flat(fun: lu.WrappedFun, *args):
-  fun, msgs = check_errors_subtrace(fun)
-  fun = check_errors_toplevel(fun)
-  err, code, *out_vals = fun.call_wrapped(*args)
-  return (err, code, out_vals), msgs()
+def checkify_flat(fun: lu.WrappedFun, *args):
+  fun, msgs = checkify_subtrace(fun)
+  fun = checkify_traceable(fun, tuple(init_error.msgs.items()))
+  err, code, *outvals = fun.call_wrapped(init_error.err, init_error.code, *args)
+  return (err, code, outvals), msgs()
 
 @lu.transformation
-def check_errors_toplevel(*args):
-  error = init_error
-  with core.new_main(ErrorTrace) as main:
-    msgs = tuple(error.msgs.items())
-    outs = yield (main, msgs, error.err, error.code, *args), {}
+def checkify_traceable(msgs, err, code, *args):
+  with core.new_main(CheckifyTrace) as main:
+    outs = yield (main, msgs, err, code, *args), {}
     del main
   yield outs
 
 @lu.transformation_with_aux
-def check_errors_subtrace(main, msgs, err, code, *args):
+def checkify_subtrace(main, msgs, err, code, *args):
   setnewattr(main, 'error', Error(err, code, dict(msgs)))
   trace = main.with_cur_sublevel()
-  in_tracers = [ErrorTracer(trace, x) for x in args]
+  in_tracers = [CheckifyTracer(trace, x) for x in args]
   out = yield in_tracers, {}
   out_tracers = map(trace.full_raise, out)
   out_vals = [t.val for t in out_tracers]
@@ -196,27 +194,20 @@ def check_errors_subtrace(main, msgs, err, code, *args):
   del main.error
   yield (err, code, *out_vals), msgs
 
-def checkify_fun_to_jaxpr(f, error, in_avals):
-  f, msgs = check_errors_subtrace(f)
-  f = check_errors_traceable(f, tuple(error.msgs.items()))
-  err_aval = core.raise_to_shaped(core.get_aval(error.err))
-  code_aval = core.raise_to_shaped(core.get_aval(error.code))
-  avals_in = [err_aval, code_aval, *in_avals]
-  jaxpr_out, _, literals_out = pe.trace_to_jaxpr_dynamic(f, avals_in)
-  return core.ClosedJaxpr(jaxpr_out, literals_out), msgs()
 
 # TODO take (error_aval, code_aval) instead of error here?
 def checkify_jaxpr(jaxpr, error):
   f = lu.wrap_init(core.jaxpr_as_fun(jaxpr))
   return checkify_fun_to_jaxpr(f, error, jaxpr.in_avals)
 
-# TODO dedup with check_errors_toplevel
-@lu.transformation
-def check_errors_traceable(msgs, err, code, *args):
-  with core.new_main(ErrorTrace) as main:
-    outs = yield (main, msgs, err, code, *args), {}
-    del main
-  yield outs
+def checkify_fun_to_jaxpr(f, error, in_avals):
+  f, msgs = checkify_subtrace(f)
+  f = checkify_traceable(f, tuple(error.msgs.items()))
+  err_aval = core.raise_to_shaped(core.get_aval(error.err))
+  code_aval = core.raise_to_shaped(core.get_aval(error.code))
+  avals_in = [err_aval, code_aval, *in_avals]
+  jaxpr_out, _, literals_out = pe.trace_to_jaxpr_dynamic(f, avals_in)
+  return core.ClosedJaxpr(jaxpr_out, literals_out), msgs()
 
 
 ## assert primitive
@@ -398,30 +389,6 @@ def while_loop_error_check(error, *in_flat, cond_nconsts, cond_jaxpr, body_ncons
   return out, Error(err, code, new_msgs)
 error_checks[lax.while_p] = while_loop_error_check
 
-# TODO(mattjj,lenamartens): currently we bundle effectful-assert-discharging
-# with the error-check-adding transformation (checkify), but they could be
-# separated into two orthogonal transformations.
-def assert_discharge_rule(error, pred, code, *, msgs):
-  out_err = error.err | jnp.logical_not(pred)
-  out_code = lax.select(error.err, error.code, code)
-  return [], Error(out_err, out_code, {**error.msgs, **msgs})
-error_checks[assert_p] = assert_discharge_rule
-
-
-## checkify api
-
-def checkify(fun: Callable) -> Callable:
-  @traceback_util.api_boundary
-  def checked_fun(*args, **kwargs):
-    args_flat, in_tree = tree_flatten((args, kwargs))
-    f, out_tree = flatten_fun(lu.wrap_init(fun), in_tree)
-    (err, code, out_flat), msgs = check_errors_flat(f, *args_flat)
-    out = tree_unflatten(out_tree(), out_flat)
-    return Error(err, code, msgs), out
-  return checked_fun
-
-## NaN error rule table
-
 def add_nan_check(prim):
   error_checks[prim] = partial(nan_error_check, prim)
 
@@ -485,3 +452,23 @@ add_nan_check(lax.abs_p)
 add_nan_check(lax.select_p)
 add_nan_check(lax.max_p)
 add_nan_check(lax.min_p)
+
+def assert_discharge_rule(error, pred, code, *, msgs):
+  out_err = error.err | jnp.logical_not(pred)
+  out_code = lax.select(error.err, error.code, code)
+  return [], Error(out_err, out_code, {**error.msgs, **msgs})
+error_checks[assert_p] = assert_discharge_rule
+
+
+## checkify api
+
+Out = TypeVar('Out')
+def checkify(fun: Callable[..., Out]) -> Callable[..., Tuple[Error, Out]]:
+  @traceback_util.api_boundary
+  def checked_fun(*args, **kwargs):
+    args_flat, in_tree = tree_flatten((args, kwargs))
+    f, out_tree = flatten_fun(lu.wrap_init(fun), in_tree)
+    (err, code, out_flat), msgs = checkify_flat(f, *args_flat)
+    out = tree_unflatten(out_tree(), out_flat)
+    return Error(err, code, msgs), out
+  return checked_fun