import itertools
import torch
from collections import defaultdict, namedtuple
from operator import attrgetter
class EventList(list):
"""A list of Events (for pretty printing)"""
def __init__(self, *args, **kwargs):
super(EventList, self).__init__(*args, **kwargs)
self._cpu_children_populated = False
def __str__(self):
return self.table()
def populate_cpu_children(self):
"""Populates child events into each underlying FunctionEvent object.
One event is a child of another if [s1, e1) is inside [s2, e2). Where
s1 and e1 would be start and end of the child event's interval. And
s2 and e2 start and end of the parent event's interval
Example: In event list [[0, 10], [1, 3], [3, 4]] would have make [0, 10]
be a parent of two other intervals.
If for any reason two intervals intersect only partialy, this function
will not record a parent child relationship between then.
"""
if self.cpu_children_populated:
return
events = sorted(
self,
key=attrgetter("thread"),
)
threads = itertools.groupby(events, key=attrgetter("thread"))
# For each thread we keep a stack of current nested parents.
# We maintain the invariant that each interval is a subset of all other
# intervals lower in the stack.
#
# First we sort the intervals by their start time. Then we iterate over them.
# Every time we see a new interval we remove several parents from
# the top until we restore the invariant. Then parent child relationship
# if recorded if the stack is not empty.
# Finally we add new interval to the list
#
# Algorithm has O(N * log(N)) complexity where N is number of
# intervals
for thread_id, thread_events in threads:
thread_events = sorted(
thread_events,
key=lambda event: [event.cpu_interval.start, -event.cpu_interval.end],
)
current_events = []
cur_end = 0
for event in thread_events:
while len(current_events) > 0:
parent = current_events[-1]
if event.cpu_interval.start >= parent.cpu_interval.end or \
event.cpu_interval.end > parent.cpu_interval.end:
# this can't be a parent
current_events.pop()
else:
parent.append_cpu_child(event)
break
current_events.append(event)
self._cpu_children_populated = True
@property
def self_cpu_time_total(self):
return sum([event.self_cpu_time_total for event in self])
@property
def cpu_children_populated(self):
return self._cpu_children_populated
def table(self, sort_by=None, row_limit=100, header=None):
"""Prints an EventList as a nicely formatted table.
Arguments:
sort_by (str, optional): Attribute used to sort entries. By default
they are printed in the same order as they were registered.
Valid keys include: ``cpu_time``, ``cuda_time``, ``cpu_time_total``,
``cuda_time_total``, ``count``.
Returns:
A string containing the table.
"""
return build_table(
self, sort_by=sort_by, row_limit=row_limit, header=header)
def export_chrome_trace(self, path):
"""Exports an EventList as a Chrome tracing tools file.
The checkpoint can be later loaded and inspected under ``chrome://tracing`` URL.
Arguments:
path (str): Path where the trace will be written.
"""
import json
with open(path, 'w') as f:
chrome_events = []
next_id = 0
for evt in self:
chrome_events.append(dict(
name=evt.name,
ph='X',
ts=evt.cpu_interval.start,
dur=evt.cpu_interval.elapsed_us(),
tid=evt.thread,
pid='CPU functions',
args={},
))
for k in evt.kernels:
# 's' and 'f' draw Flow arrows from
# the CPU launch to the GPU kernel
chrome_events.append(dict(
name=evt.name,
ph='s',
ts=evt.cpu_interval.start,
tid=evt.thread,
pid='CPU functions',
id=next_id,
cat='cpu_to_cuda',
args={},
))
chrome_events.append(dict(
name=k.name,
ph='f',
ts=k.interval.start,
tid=k.device,
pid='CUDA functions',
id=next_id,
cat='cpu_to_cuda',
args={},
))
chrome_events.append(dict(
name=k.name,
ph='X',
ts=k.interval.start,
dur=k.interval.elapsed_us(),
tid=k.device,
pid='CUDA functions',
args={},
))
next_id += 1
json.dump(chrome_events, f)
def key_averages(self, group_by_input_shapes=False):
"""Averages all function events over their keys.
@param group_by_input_shapes The key would become
(event name, input dimensions) rather than just event name.
This is useful to see which dimensionality contributes to the runtime
the most and may help with dimension specific optimizations or
choosing best candidates for quantization (aka fitting a roof line)
Returns:
An EventList containing FunctionEventAvg objects.
"""
self.populate_cpu_children()
stats = defaultdict(FunctionEventAvg)
def get_key(event, group_by_input_shapes):
if not group_by_input_shapes:
return event.key
return (event.key, str(event.input_shapes))
for evt in self:
stats[get_key(evt, group_by_input_shapes)].add(
evt, group_by_input_shapes)
return EventList(stats.values())
def total_average(self):
"""Averages all events.
Returns:
A FunctionEventAvg object.
"""
total_stat = FunctionEventAvg()
for evt in self:
total_stat += evt
total_stat.key = None
total_stat.key = 'Total'
return total_stat
[docs]class profile(object):
"""Context manager that manages autograd profiler state and holds a summary of results.
Under the hood it just records events of functions being executed in C++ and
exposes those events to Python. You can wrap any code into it and it will
only report runtime of PyTorch functions.
Arguments:
enabled (bool, optional): Setting this to False makes this context manager a no-op.
Default: ``True``.
use_cuda (bool, optional): Enables timing of CUDA events as well using the cudaEvent API.
Adds approximately 4us of overhead to each tensor operation.
Default: ``False``
record_shapes (bool, optional): If shapes recording is set, information
about input dimensions will be collected. This allows one to see which
dimensions have been used under the hood and further group by them
using prof.key_averages(group_by_input_shape=True). Please note that
shape recording might skew your profiling data. It is recommended to
use separate runs with and without shape recording to validate the timing.
Most likely the skew will be negligible for bottom most events (in a case
of nested function calls). But for higher level functions the total
self cpu time might be artificially increased because of the shape
collection.
.. warning:
This context managers should not be called recursively, i.e. at most one
instance should be enabled at any given time.
Example:
>>> x = torch.randn((1, 1), requires_grad=True)
>>> with torch.autograd.profiler.profile() as prof:
>>> for _ in range(100): # any normal python code, really!
>>> y = x ** 2
>> y.backward()
>>> # NOTE: some columns were removed for brevity
>>> print(prof.key_averages().table(sort_by="self_cpu_time_total"))
----------------------------------- --------------- --------------- ---------------
Name Self CPU total CPU time avg Number of Calls
----------------------------------- --------------- --------------- ---------------
mul 32.048ms 32.048ms 200
pow 27.041ms 27.041ms 200
PowBackward0 9.727ms 55.483ms 100
torch::autograd::AccumulateGrad 9.148ms 9.148ms 100
torch::autograd::GraphRoot 691.816us 691.816us 100
----------------------------------- --------------- --------------- ---------------
"""
def __init__(self, enabled=True, use_cuda=False, record_shapes=False):
self.enabled = enabled
self.use_cuda = use_cuda
self.function_events = None
if not self.enabled:
return
self.entered = False
self.record_shapes = record_shapes
def __enter__(self):
if not self.enabled:
return
if self.entered:
raise RuntimeError("autograd profiler traces are not reentrant")
self.entered = True
profiler_kind = torch.autograd.ProfilerState.CUDA if self.use_cuda \
else torch.autograd.ProfilerState.CPU
torch.autograd._enable_profiler(
torch.autograd.ProfilerConfig(profiler_kind, self.record_shapes))
return self
def __exit__(self, exc_type, exc_val, exc_tb):
if not self.enabled:
return
records = torch.autograd._disable_profiler()
self.function_events = EventList(parse_cpu_trace(records))
return False
def __repr__(self):
if self.function_events is None:
return '<unfinished torch.autograd.profile>'
return repr(self.function_events)
def __str__(self):
if self.function_events is None:
return '<unfinished torch.autograd.profile>'
return str(self.function_events)
def _check_finish(self):
if self.function_events is None:
raise RuntimeError("can't export a trace that didn't finish running")
self.function_events.populate_cpu_children()
[docs] def table(self, sort_by=None, row_limit=100, header=None):
self._check_finish()
return self.function_events.table(
sort_by=sort_by, row_limit=row_limit, header=header)
table.__doc__ = EventList.table.__doc__
[docs] def export_chrome_trace(self, path):
self._check_finish()
return self.function_events.export_chrome_trace(path)
export_chrome_trace.__doc__ = EventList.export_chrome_trace.__doc__
[docs] def key_averages(self, group_by_input_shape=False):
self._check_finish()
return self.function_events.key_averages(group_by_input_shape)
key_averages.__doc__ = EventList.key_averages.__doc__
[docs] def total_average(self):
self._check_finish()
return self.function_events.total_average()
total_average.__doc__ = EventList.total_average.__doc__
@property
def self_cpu_time_total(self):
""" Returns total time spent on CPU obtained as a sum of
all self times across all the events.
"""
self._check_finish()
return self.function_events.self_cpu_time_total
[docs]class emit_nvtx(object):
"""Context manager that makes every autograd operation emit an NVTX range.
It is useful when running the program under nvprof::
nvprof --profile-from-start off -o trace_name.prof -- <regular command here>
Unfortunately, there's no way to force nvprof to flush the data it collected
to disk, so for CUDA profiling one has to use this context manager to annotate
nvprof traces and wait for the process to exit before inspecting them.
Then, either NVIDIA Visual Profiler (nvvp) can be used to visualize the timeline, or
:func:`torch.autograd.profiler.load_nvprof` can load the results for inspection
e.g. in Python REPL.
.. warning:
This context manager should not be called recursively, i.e. at most one
instance should be enabled at any given time.
Arguments:
enabled (bool, optional, default=True): Setting ``enabled=False`` makes this context manager a no-op.
Default: ``True``.
record_shapes (bool, optional, default=False): If ``record_shapes=True``, the nvtx range wrapping
each autograd op will append information about the sizes of Tensor arguments received
by that op, in the following format:
``[[arg0.size(0), arg0.size(1), ...], [arg1.size(0), arg1.size(1), ...], ...]``
Non-tensor arguments will be represented by ``[]``.
Arguments will be listed in the order they are received by the backend op.
Please note that this order may not match the order in which those arguments were passed
on the Python side. Also note that shape recording may increase the overhead of nvtx range creation.
Example:
>>> with torch.cuda.profiler.profile():
... model(x) # Warmup CUDA memory allocator and profiler
... with torch.autograd.profiler.emit_nvtx():
... model(x)
**Forward-backward correlation**
When viewing a profile created using :class:`emit_nvtx` in the Nvidia Visual Profiler,
correlating each backward-pass op with the corresponding forward-pass op can be difficult.
To ease this task, :class:`emit_nvtx` appends sequence number information to the ranges it
generates.
During the forward pass, each function range is decorated with ``seq=<N>``. ``seq`` is a running
counter, incremented each time a new backward Function object is created and stashed for backward.
Thus, the ``seq=<N>`` annotation associated with each forward function range tells you that
if a backward Function object is created by this forward function,
the backward object will receive sequence number N.
During the backward pass, the top-level range wrapping each C++ backward Function's
``apply()`` call is decorated with ``stashed seq=<M>``. ``M`` is the sequence number that
the backward object was created with. By comparing ``stashed seq`` numbers in backward with ``seq``
numbers in forward, you can track down which forward op created each backward Function.
Any functions executed during the backward pass are also decorated with ``seq=<N>``. During
default backward (with ``create_graph=False``) this information is irrelevant, and in fact,
``N`` may simply be 0 for all such functions. Only the top-level ranges associated with
backward Function objects' ``apply()`` methods are useful, as a way to correlate these Function
objects with the earlier forward pass.
**Double-backward**
If, on the other hand, a backward pass with ``create_graph=True`` is underway (in other words,
if you are setting up for a double-backward), each function's execution during backward
is given a nonzero, useful ``seq=<N>``. Those functions may themselves create Function objects
to be executed later during double-backward, just as the original functions in the forward pass did.
The relationship between backward and double-backward is conceptually the same as the relationship
between forward and backward: The functions still emit current-sequence-number-tagged ranges,
the Function objects they create still stash those sequence numbers, and during the eventual
double-backward, the Function objects' ``apply()`` ranges are still tagged with ``stashed seq``
numbers, which can be compared to `seq` numbers from the backward pass.
.. warning:
The sequence number is thread-local, and some forward functions don't create an associated
backward Function object (instead delegating that to sub-functions further down the call chain).
For these reasons, the correspondence of stashed sequence numbers in
backward Function ``apply()`` ranges with `seq` numbers in forward-pass ranges is
not guaranteed to be 1 to 1. The sequence numbers alone may not be enough to fully
disambiguate which forward function created which
backward Function object. You may need to make a judgment based on analytic knowledge of what
the expected correspondence should be.
"""
def __init__(self, enabled=True, record_shapes=False):
self.enabled = enabled
self.entered = False
self.record_shapes = record_shapes
def __enter__(self):
if not self.enabled:
return
if self.entered:
raise RuntimeError("NVTX annotation context manager is not reentrant")
self.entered = True
torch.cuda.synchronize()
torch.autograd._enable_profiler(
torch.autograd.ProfilerConfig(
torch.autograd.ProfilerState.NVTX,
self.record_shapes
)
)
return self
def __exit__(self, exc_type, exc_val, exc_tb):
if not self.enabled:
return
torch.cuda.synchronize()
torch.autograd._disable_profiler()
return False
[docs]def load_nvprof(path):
"""Opens an nvprof trace file and parses autograd annotations.
Arguments:
path (str): path to nvprof trace
"""
return EventList(parse_nvprof_trace(path))
################################################################################
# FunctionEvent
def format_time(time_us):
"""Defines how to format time in FunctionEvent"""
US_IN_SECOND = 1000.0 * 1000.0
US_IN_MS = 1000.0
if time_us >= US_IN_SECOND:
return '{:.3f}s'.format(time_us / US_IN_SECOND)
if time_us >= US_IN_MS:
return '{:.3f}ms'.format(time_us / US_IN_MS)
return '{:.3f}us'.format(time_us)
def format_time_share(time_us, total_time_us):
"""Defines how to format time in FunctionEvent"""
if total_time_us == 0:
assert(time_us == 0)
return "NaN"
return '{:.2f}%'.format(time_us * 100.0 / total_time_us)
def attr_formatter(name):
return property(lambda self: format_time(getattr(self, name)))
class FormattedTimesMixin(object):
"""Helpers for FunctionEvent and FunctionEventAvg.
The subclass should define `*_time_total` and `count` attributes.
"""
cpu_time_str = attr_formatter('cpu_time')
cuda_time_str = attr_formatter('cuda_time')
cpu_time_total_str = attr_formatter('cpu_time_total')
cuda_time_total_str = attr_formatter('cuda_time_total')
self_cpu_time_total_str = attr_formatter('self_cpu_time_total')
@property
def cpu_time(self):
return 0.0 if self.count == 0 else 1.0 * self.cpu_time_total / self.count
@property
def cuda_time(self):
return 0.0 if self.count == 0 else 1.0 * self.cuda_time_total / self.count
class Interval(object):
def __init__(self, start, end):
self.start = start
self.end = end
def elapsed_us(self):
return self.end - self.start
Kernel = namedtuple('Kernel', ['name', 'device', 'interval'])
# TODO: record TID too
class FunctionEvent(FormattedTimesMixin):
"""Profiling information about a single function."""
def __init__(self, id, name, thread, cpu_start, cpu_end, input_shapes=None):
self.id = id
self.name = name
self.cpu_interval = Interval(cpu_start, cpu_end)
self.thread = thread
self.kernels = []
self.count = 1
self.cpu_children = []
self.input_shapes = input_shapes
def append_kernel(self, name, device, start, end):
self.kernels.append(Kernel(name, device, Interval(start, end)))
def append_cpu_child(self, child):
"""Append a CPU child of type FunctionEvent.
One is supposed to append only dirrect children to the event to have
correct self cpu time being reported.
"""
assert(isinstance(child, FunctionEvent))
self.cpu_children.append(child)
@property
def self_cpu_time_total(self):
return self.cpu_time_total - sum(
[child.cpu_time_total for child in self.cpu_children]
)
@property
def cuda_time_total(self):
return sum(kinfo.interval.elapsed_us() for kinfo in self.kernels)
@property
def cpu_time_total(self):
return self.cpu_interval.elapsed_us()
@property
def key(self):
return self.name
def __repr__(self):
return (
'<FunctionEvent id={} cpu_time={} cpu_start={} cpu_end={} '
'cpu_children={} cuda_time={} name={} thread={} input_shapes={}>'.format(
self.id,
self.cpu_time_str,
self.cpu_interval.start,
self.cpu_interval.end,
str([child.id for child in self.cpu_children]),
self.cuda_time_str,
self.name,
self.thread,
str(self.input_shapes),
)
)
class FunctionEventAvg(FormattedTimesMixin):
"""Used to average stats over multiple FunctionEvent objects."""
def __init__(self):
self.key = None
self.count = 0
self.cpu_time_total = 0
self.cuda_time_total = 0
self.self_cpu_time_total = 0
self.input_shapes = None
def add(self, other, group_by_input_shapes=False):
if self.key is None:
self.key = other.key
if group_by_input_shapes:
self.input_shapes = other.input_shapes
assert (
not group_by_input_shapes or
other.input_shapes == self.input_shapes
)
assert isinstance(other, FunctionEvent)
assert other.key == self.key
self.cpu_time_total += other.cpu_time
self.cuda_time_total += other.cuda_time
self.self_cpu_time_total += other.self_cpu_time_total
self.count += 1
return self
def __repr__(self):
return (
'<FunctionEventAvg key={} self_cpu_time={} cpu_time={} '
'cuda_time={} input_shapes={}>'.format(
self.key,
self.self_cpu_time_total_str,
self.cpu_time_str,
self.cuda_time_str,
str(self.input_shapes),
)
)
################################################################################
# Utilities
class StringTable(defaultdict):
def __missing__(self, key):
self[key] = torch._C._demangle(key)
return self[key]
################################################################################
# CPU checkpoints
def parse_cpu_trace(thread_records):
next_id = 0
start_record = None
cuda_records = {}
functions = []
record_stack = []
string_table = StringTable()
# cuda start events and the overall profiler start event don't happen
# at exactly the same time because we need to record an event on each device
# and each record takes ~4us. So we adjust here by the difference
# adding the difference in CPU time between the profiler start event
# and the CPU time of the cuda start event for the device
def adjusted_time(cuda_record):
assert cuda_record.device() != -1
cuda_time_0 = cuda_records[cuda_record.device()]
return cuda_time_0.cuda_elapsed_us(cuda_record) + start_record.cpu_elapsed_us(cuda_time_0)
# '__start_profile' is not guarenteed to be first, so we must find it here
for record in itertools.chain(*thread_records):
if record.name() == '__start_profile':
start_record = record
elif record.name() == '__cuda_start_event':
assert record.device() != -1
cuda_records[record.device()] = record
assert start_record is not None
for record in itertools.chain(*thread_records):
if record.kind() == 'mark':
continue
elif record.kind() == 'push':
record_stack.append((next_id, record))
next_id += 1
elif record.kind() == 'pop':
function_id, start = record_stack.pop()
fe = FunctionEvent(
id=function_id,
name=string_table[start.name()],
thread=start.thread_id(),
cpu_start=start_record.cpu_elapsed_us(start),
cpu_end=start_record.cpu_elapsed_us(record),
input_shapes=start.shapes())
if start.has_cuda():
cuda_start = adjusted_time(start)
cuda_end = adjusted_time(record)
fe.append_kernel(start.name(),
start.device(),
cuda_start,
cuda_end)
functions.append(fe)
functions.sort(key=lambda evt: evt.cpu_interval.start)
return functions
################################################################################
# CUDA checkpoints
class EnforceUnique(object):
"""Raises an error if a key is seen more than once."""
def __init__(self):
self.seen = set()
def see(self, *key):
if key in self.seen:
raise RuntimeError('duplicate key: ' + str(key))
self.seen.add(key)
def parse_nvprof_trace(path):
import sqlite3
conn = sqlite3.connect(path)
conn.row_factory = sqlite3.Row
# Parse strings table
strings = {}
for r in conn.execute("SELECT _id_ as id, value FROM StringTable"):
strings[r["id"]] = torch._C._demangle(r["value"])
# First, find all functions and create FunctionEvents for them
marker_query = """
SELECT
start.id AS marker_id, start.name, start.timestamp AS start_time, end.timestamp AS end_time
FROM
CUPTI_ACTIVITY_KIND_MARKER AS start INNER JOIN CUPTI_ACTIVITY_KIND_MARKER AS end
ON start.id = end.id
WHERE
start.name != 0 AND end.name = 0
"""
functions = []
functions_map = {}
unique = EnforceUnique()
for row in conn.execute(marker_query):
unique.see(row['marker_id'])
evt = FunctionEvent(id=row['marker_id'],
name=strings[row['name']],
cpu_start=row['start_time'],
cpu_end=row['end_time'],
thread=0) # TODO: find in sqlite database
functions.append(evt)
functions_map[evt.id] = evt
# Now, correlate all kernels with FunctionEvents
kernel_query = """
SELECT
start.id AS marker_id, start.name, start.timestamp, end.timestamp,
runtime._id_ AS runtime_id, runtime.cbid, runtime.start AS runtime_start, runtime.end AS runtime_end,
kernel.start AS kernel_start, kernel.end AS kernel_end, kernel.name AS kernel_name
FROM
CUPTI_ACTIVITY_KIND_MARKER AS start
INNER JOIN CUPTI_ACTIVITY_KIND_MARKER AS end
ON start.id = end.id
INNER JOIN CUPTI_ACTIVITY_KIND_RUNTIME as runtime
ON (start.timestamp < runtime.start AND runtime.end < end.timestamp)
INNER JOIN CUPTI_ACTIVITY_KIND_CONCURRENT_KERNEL AS kernel
ON kernel.correlationId = runtime.correlationId
"""
unique = EnforceUnique()
for row in conn.execute(kernel_query):
unique.see(row['marker_id'], row['runtime_id'])
assert row['cbid'] == 13 # 13 == Launch
evt = functions_map[row['marker_id']]
evt.append_kernel(row['kernel_name'],
0,
row['kernel_start'],
row['kernel_end'])
functions.sort(key=lambda evt: evt.cpu_interval.start)
return functions
################################################################################
# Pretty printer
def build_table(events, sort_by=None, header=None, row_limit=100):
"""Prints a summary of events (which can be a list of FunctionEvent or FunctionEventAvg)."""
if len(events) == 0:
return ""
if sort_by is not None:
events = EventList(sorted(
events, key=lambda evt: getattr(evt, sort_by), reverse=True
))
has_input_shapes = any(
[event.input_shapes is not None for event in events])
name_column_width = max([len(evt.key) for evt in events]) + 4
DEFAULT_COLUMN_WIDTH = 15
SHAPES_COLUMN_WIDTH = 35
headers = [
'Name',
'Self CPU total %',
'Self CPU total',
'CPU total %',
'CPU total',
'CPU time avg',
'CUDA total %',
'CUDA total',
'CUDA time avg',
'Number of Calls',
]
# Have to use a list because nonlocal is Py3 only...
SPACING_SIZE = 2
row_format = [""]
header_sep = [""]
line_length = [-SPACING_SIZE]
def add_column(padding):
row_format[0] += '{: <' + str(padding) + '} '
header_sep[0] += '-' * padding + ' '
line_length[0] += padding + SPACING_SIZE
add_column(name_column_width)
for _ in headers[1:]:
add_column(DEFAULT_COLUMN_WIDTH)
if has_input_shapes:
headers.append('Input Shapes')
add_column(SHAPES_COLUMN_WIDTH)
row_format = row_format[0]
header_sep = header_sep[0]
line_length = line_length[0]
add_column = None
# Have to use a list because nonlocal is Py3 only...
result = []
def append(s):
result.append(s)
result.append('\n') # Yes, newline after the end as well
self_cpu_time_total = sum([event.self_cpu_time_total for event in events])
cuda_time_total = sum([evt.cuda_time_total for evt in events])
# Actual printing
if header is not None:
append('=' * line_length)
append(header)
append(header_sep)
append(row_format.format(*headers))
append(header_sep)
for evt in events[:row_limit]:
row_values = [
evt.key, # Name
# Self CPU total %
format_time_share(evt.self_cpu_time_total,
self_cpu_time_total),
evt.self_cpu_time_total_str, # Self CPU total
# CPU total %
format_time_share(evt.cpu_time_total, self_cpu_time_total),
evt.cpu_time_total_str, # CPU total
evt.cpu_time_str, # CPU time avg
# CUDA time total %
format_time_share(evt.cuda_time_total, cuda_time_total),
evt.cuda_time_total_str,
evt.cuda_time_str, # Cuda time avg
evt.count, # Number of calls
]
if has_input_shapes:
row_values.append(str(evt.input_shapes)[:SHAPES_COLUMN_WIDTH])
append(row_format.format(*row_values))
append(header_sep)
append("Self CPU time total: {}".format(format_time(self_cpu_time_total)))
append("CUDA time total: {}".format(format_time(cuda_time_total)))
return ''.join(result)
