Benchmark
Benchmark harness.
Usage
var bench = require( '@stdlib/bench/harness' );
bench( name[, options][, benchmark] )
Queues a benchmark
to be run during a subsequent turn of the event loop. After running the benchmark
, the function outputs benchmark results as Test Anything Protocol (TAP) output.
bench( 'Math.sin', function benchmark( b ) {
var x;
var i;
b.tic();
for ( i = 0; i < b.iterations; i++ ) {
x = Math.sin( Math.random() );
if ( x !== x ) {
b.fail( 'should not return NaN' );
}
}
b.toc();
if ( x !== x ) {
b.fail( 'should not return NaN' );
}
b.pass( 'benchmark finished' );
b.end();
});
A benchmark
function has the following signature:
function benchmark( b ) {
// Benchmark code...
}
where b
is a Benchmark
instance. Synchronous benchmarks should, at minimum, have the following structure:
function benchmark( b ) {
var x;
var i;
// [1] Start timing:
b.tic();
// [2] Loop containing code to time...
for ( i = 0; i < b.iterations; i++ ) {
// [3] Code to time...
// [4] A conditional verifying results to prevent certain compiler optimizations:
if ( x !== x ) {
b.fail( 'something went wrong!' );
}
}
// [5] Stop timing:
b.toc();
// [6] Another conditional verifying results to prevent certain compiler optimizations:
if ( x !== x ) {
b.fail( 'something went wrong!' );
}
// [7] End the benchmark:
b.end();
}
Asynchronous benchmarks should have a structure similar to the following:
function benchmark( b ) {
var i = 0;
// [1] Start timing:
b.tic();
// [2] Asynchronous code to time:
return next();
function next( error ) {
if ( error ) {
return b.fail( error.message );
}
i += 1;
// [3] Exit condition:
if ( i <= b.iterations ) {
// Asynchronous task...
return;
}
// [4] Stop timing:
b.toc();
// [5] End the benchmark:
b.end();
}
}
For both synchronous and asynchronous benchmarks, calling b.end()
is mandatory, as failing to do so will cause the harness to hang. For example, the following benchmark will never complete.
function benchmark( b ) {
var i;
b.tic();
for ( i = 0; i < b.iterations; i++ ) {
// Synchronous task...
}
b.toc();
}
Avoid making assertions within timed code, as doing so will significantly affect raw performance numbers. For example, avoid the following:
function benchmark( b ) {
var x;
var i;
b.tic();
for ( i = 0; i < b.iterations; i++ ) {
x = Math.sin( Math.random() );
b.equal( x, x, 'does not return NaN' ); // Avoid doing this!
}
b.toc();
b.equal( x, x, 'does not return NaN' ); // This is fine.
b.end();
}
Additionally, ensure that all setup code executes before calling b.tic()
and that all cleanup code executes after calling b.toc()
. For example, avoid the following:
function benchmark( b ) {
var x;
var y;
var i;
// Start timing:
b.tic();
// Setup code:
x = new Array( b.iterations ); // Should be before b.tic()!
for ( i = 0; i < b.iterations; i++ ) {
x[ i ] = Math.random();
}
// Code to be timed...
for ( i = 0; i < b.iterations; i++ ) {
y = Math.sin( x[ i ] );
if ( y !== y ) {
b.fail( 'should not return NaN' );
}
}
// Verify results:
b.equal( x, x, 'does not return NaN' ); // Should be after b.toc()!
// Stop timing:
b.toc();
b.end();
}
The function accepts the following options
:
- iterations: number of iterations. If
null
, the number of iterations is determined by trying successive powers of10
until the total time is at least0.1
seconds. Default:null
. - repeats: number of repeats. Default:
3
. - timeout: number of milliseconds before a benchmark is considered failed. Exceeding a timeout does not, however, end the benchmark. Ending a long running benchmark requires manual intervention. Default:
300000
(5 minutes). - skip:
boolean
indicating whether to skip a benchmark.
By default, the harness will automatically determine an iteration number for each benchmark such that a benchmark runs for a length of time sufficient to accurately compute benchmark results. To require a specific number of iterations, set the iterations
option.
var opts = {
'iterations': 1e6
};
bench( 'require a specific number of iterations', opts, function benchmark( b ) {
var i;
b.tic();
for ( i = 0; i < b.iterations; i++ ) {
// Code to be benchmarked...
}
b.toc();
b.end();
});
To ensure that benchmark results are reproducible, the harness runs each benchmark function multiple times. To specify a repetition number, set the repeats
option.
var opts = {
'repeats': 5
};
bench( 'repeat a benchmark multiple times', opts, function benchmark( b ) {
var i;
b.tic();
for ( i = 0; i < b.iterations; i++ ) {
// Code to be benchmarked...
}
b.toc();
b.end();
});
To skip a benchmark, set the skip
option.
var opts = {
'skip': true
};
bench( 'skipped benchmark', opts, function benchmark( b ) {
var i;
b.tic();
for ( i = 0; i < b.iterations; i++ ) {
// Code to be benchmarked...
}
b.toc();
b.end();
});
To fail benchmarks which take longer than a specified amount of time to complete, set a timeout
option (in milliseconds).
var opts = {
'timeout': 5000 // 5 seconds
};
bench( 'async benchmark', opts, function benchmark( b ) {
var i = 0;
b.tic();
return next();
function next( error ) {
if ( error ) {
return b.fail( error.message );
}
i += 1;
if ( i <= b.iterations ) {
// Asynchronous task...
return;
}
b.toc();
b.end();
}
});
bench.onFinish( clbk )
Sets a listener which is invoked once the harness finishes running all benchmarks.
function onFinish() {
console.log( 'Done!' );
}
bench.onFinish( onFinish );
bench.createStream( [options] )
Returns a results stream.
var stdout = require( '@stdlib/streams/node/stdout' );
var stream = bench.createStream();
// Direct all results to `stdout`:
stream.pipe( stdout );
var opts = {
'iterations': 1,
'repeats': 1
};
bench( 'beep', opts, function benchmark( b ) {
var i;
b.tic();
for ( i = 0; i < b.iterations; i++ ) {
b.equal( 3.14, 3.14, 'should be equal' );
}
b.toc();
b.end();
});
TAP version 13
# beep
ok 1 should be equal
---
iterations: 1
elapsed: 0.002985193
rate: 334.98671610177297
...
#
1..1
# total 1
# pass 1
#
# ok
The results stream can be combined with any Writable
stream (e.g., network connection, file, stdout
, etc).
The function accepts the same options
as @stdlib/streams/node/transform. For example, by default, the method returns a stream which produces TAP output as text. To return an object stream,
var opts = {
'objectMode': true
};
var stream = bench.createStream( opts );
stream.on( 'data', onRow );
function onRow( row ) {
console.log( JSON.stringify( row ) );
}
opts = {
'iterations': 1,
'repeats': 1
};
bench( 'beep', opts, function benchmark( b ) {
var i;
b.tic();
for ( i = 0; i < b.iterations; i++ ) {
b.equal( 3.14, 3.14, 'should be equal' );
}
b.toc();
b.end();
});
{"type":"benchmark","name":"beep","id":0}
{"id":0,"ok":true,"name":"should be equal","operator":"equal","actual":3.14,"expected":3.14,"benchmark":0,"type":"assert"}
{"ok":true,"operator":"result","iterations":1,"elapsed":0.00283753,"rate":352.41918147120913,"benchmark":0,"type":"result"}
{"benchmark":0,"type":"end"}
bench.createHarness( [options][, clbk] )
Creates a benchmark harness with a new pending stack and state.
var harness = bench.createHarness();
harness( 'beep', function benchmark( b ) {
var i;
b.tic();
for ( i = 0; i < b.iterations; i++ ) {
// Synchronous task...
}
b.toc();
b.end();
});
To trigger an action when a harness finishes running all benchmarks, provide a callback function
.
var harness = bench.createHarness( onFinish );
function onFinish() {
harness.close();
}
harness( 'beep', function benchmark( b ) {
var i;
b.tic();
for ( i = 0; i < b.iterations; i++ ) {
// Synchronous task...
}
b.toc();
b.end();
});
The method accepts the following options
:
- autoclose:
boolean
indicating whether to automatically close a harness after running all benchmarks.
By default, a harness
does not automatically close. To automatically close a harness once a harness finishes running all benchmarks, set the autoclose
option to true
.
var harness = bench.createHarness({
'autoclose': true
});
harness( 'beep', function benchmark( b ) {
var i;
b.tic();
for ( i = 0; i < b.iterations; i++ ) {
// Synchronous task...
}
b.toc();
b.end();
});
Harness
A harness
has the following properties and methods...
harness.createStream( [options] )
Returns a results stream.
var stdout = require( '@stdlib/streams/node/stdout' );
var harness = bench.createHarness();
var stream = harness.createStream();
// Direct all results to `stdout`:
stream.pipe( stdout );
var opts = {
'iterations': 1,
'repeats': 1
};
harness( 'beep', opts, function benchmark( b ) {
var i;
b.tic();
for ( i = 0; i < b.iterations; i++ ) {
b.equal( 'beep', 'beep', 'should be equal' );
}
b.toc();
b.end();
});
TAP version 13
# beep
ok 1 should be equal
---
iterations: 1
elapsed: 0.00166768
rate: 599.6354216636286
...
#
1..1
# total 1
# pass 1
#
# ok
The method accepts the same options
as @stdlib/streams/node/transform.
Note: benchmarks will not run until a destination stream has been created.
harness.close()
Closes a benchmark harness. Any pending benchmarks are cleared from the harness stack.
var stdout = require( '@stdlib/streams/node/stdout' );
var harness = bench.createHarness();
var stream = harness.createStream();
stream.pipe( stdout );
var opts = {
'iterations': 5,
'repeats': 5
};
harness( 'early close', opts, function benchmark( b ) {
var i = 0;
b.tic();
setTimeout( next, 0 );
function next() {
i += 1;
if ( i <= b.iterations ) {
b.ok( true, 'should be truthy' );
return setTimeout( next, 10 );
}
b.toc();
b.end();
}
});
// Early close:
setTimeout( onTimeout, 50 );
function onTimeout() {
harness.close();
}
TAP version 13
# early close
ok 1 should be truthy
ok 2 should be truthy
# WARNING: harness closed before completion.
ok 3 should be truthy
ok 4 should be truthy
ok 5 should be truthy
---
iterations: 5
elapsed: 0.05940291
rate: 84.17096064822414
...
Warning: a running benchmark may finish after closing a harness.
harness.exit()
Forcefully exits a benchmark harness. All pending benchmarks will generate failing assertions.
var stdout = require( '@stdlib/streams/node/stdout' );
var harness = bench.createHarness();
var stream = harness.createStream();
stream.pipe( stdout );
var opts = {
'iterations': 5
};
harness( 'force exit', opts, function benchmark( b ) {
var i = 0;
b.tic();
return next();
function next() {
i += 1;
if ( i <= b.iterations ) {
b.ok( true, 'should be truthy' );
return setTimeout( next, 10 );
}
b.toc();
b.end();
}
});
// Forcefully exit:
setTimeout( onTimeout, 20 );
function onTimeout() {
harness.exit();
}
TAP version 13
# force exit
ok 1 should be truthy
not ok 2 benchmark exited without ending
---
operator: fail
TODO: include stack
...
not ok 3 benchmark exited without ending
---
operator: fail
TODO: include stack
...
ok 4 should be truthy
ok 5 should be truthy
ok 6 should be truthy
ok 7 should be truthy
---
iterations: 5
elapsed: 0.061504862
rate: 81.29438612511642
...
Warning: a running benchmark may finish after exiting a harness.
harness.exitCode
Read-only property whose value is the harness exit code. If all benchmarks run successfully (i.e., no failing assertions), the exit code is 0
; otherwise, the exit code is 1
.
var harness = bench.createHarness();
// Benchmarks only start running when results have a destination:
var stream = harness.createStream();
function onFinish() {
console.log( harness.exitCode );
// => 1
}
var opts = {
'iterations': 1,
'repeats': 1
};
harness( 'exit code', opts, function benchmark( b ) {
var i;
b.tic();
for ( i = 0; i < b.iterations; i++ ) {
b.fail( 'failing assertion' );
}
b.toc();
b.end();
});
Benchmark
A Benchmark
instance has the following properties and methods...
b.name
Read-only property whose value is the benchmark name
.
var str = b.name;
// returns <string>
b.iterations
Read-only property whose value is the number of iterations.
var iter = b.iterations;
// returns <number>
b.tic()
Starts a benchmark timer. In order to benchmark code, this method must always be called within a benchmark
function.
function benchmark( b ) {
var x;
var i;
// Start a timer:
b.tic();
for ( i = 0; i < b.iterations; i++ ) {
x = Math.sin( Math.random() );
if ( x !== x ) {
b.fail( 'should not return NaN' );
}
}
b.toc();
if ( x !== x ) {
b.fail( 'should not return NaN' );
}
b.end();
}
b.toc()
Stops a benchmark timer. In order to benchmark code, this method must always be called within a benchmark
function.
function benchmark( b ) {
var x;
var i;
b.tic();
for ( i = 0; i < b.iterations; i++ ) {
x = Math.sin( Math.random() );
if ( x !== x ) {
b.fail( 'should not return NaN' );
}
}
// Stop a timer:
b.toc();
if ( x !== x ) {
b.fail( 'should not return NaN' );
}
b.end();
}
b.end()
Explicitly ends a benchmark. In order to benchmark code, this method must always be called within a benchmark
function.
function benchmark( b ) {
var x;
var i;
b.tic();
for ( i = 0; i < b.iterations; i++ ) {
x = Math.sin( Math.random() );
if ( x !== x ) {
b.fail( 'should not return NaN' );
}
}
b.toc();
if ( x !== x ) {
b.fail( 'should not return NaN' );
}
// Explicitly end the benchmark:
b.end();
}
Warning: no assertions should follow a call to b.end()
. Including assertions after b.end()
may result in interleaved TAP output or an output stream closing before a benchmark executes pending assertions.
b.comment( msg )
Writes a message without breaking TAP output.
b.comment( 'This is a comment.' );
# This is a comment.
To prevent confusing results parsers, avoid using comments. Comments are frequently used for demarcating the beginning of a new benchmark run and/or providing diagnostic information. Both of the aforementioned use cases typically fall under the domain of the harness, not the user.
b.skip( value, msg )
Generates an assertion which will be skipped.
b.skip( false, 'This is skipped.' );
b.skip( true, 'This is skipped.' );
ok 1 This is skipped. # SKIP
ok 2 This is skipped. # SKIP
b.todo( value, msg )
Generates an assertion which should be implemented.
b.todo( false, 'This is a todo.' );
b.todo( true, 'This is a todo.' );
not ok 3 This is a todo. # TODO
---
operator: todo
TODO: include stack
...
ok 4 This is a todo. # TODO
While b.todo()
assertions typically fail, they do not contribute to the failed assertion count. If a benchmark includes b.todo()
assertions and no other failing assertions, the benchmark is considered successful.
b.fail( msg )
Generates a failing assertion.
b.fail( 'This is a failing assertion.' );
not ok 5 This is a failing assertion.
---
operator: fail
TODO: include stack
...
b.pass( msg )
Generates a passing assertion.
b.pass( 'This is a passing assertion.' );
ok 6 This is a passing assertion.
b.ok( value[, msg] )
Asserts that a value
is truthy.
b.ok( [] );
ok 7 should be truthy
To override the default message, provide a msg
argument.
b.ok( true, 'This asserts a value is truthy.' );
b.ok( false, 'This asserts a value is truthy.' );
ok 8 This asserts a value is truthy.
not ok 9 This asserts a value is truthy.
---
operator: ok
TODO: include stack
...
b.notOk( value[, msg] )
Asserts that a value
is falsy.
b.notOk( null );
ok 10 should be falsy
To override the default message, provide a msg
argument.
b.notOk( false, 'This asserts a value is falsy.' );
b.notOk( true, 'This asserts a value is falsy.' );
ok 11 This asserts a value is falsy.
not ok 12 This asserts a value is falsy.
---
operator: notOk
TODO: include stack
...
b.equal( actual, expected[, msg] )
Asserts that actual
is strictly equal to expected
.
var expected = [];
var actual = expected;
b.equal( actual, expected );
ok 13 should be equal
To override the default message, provide a msg
argument.
var expected = [];
var actual = expected;
b.equal( actual, expected, 'This asserts two values are strictly equal.' );
b.equal( 1.0, 2.0, 'This asserts two values are strictly equal.' );
ok 14 This asserts two values are strictly equal.
not ok 15 This asserts two values are strictly equal.
---
operator: equal
TODO: include stack
...
b.notEqual( actual, expected[, msg] )
Asserts that actual
is not strictly equal to expected
.
var expected = [];
var actual = [];
b.notEqual( actual, expected );
ok 16 should not be equal
To override the default message, provide a msg
argument.
var expected = [];
var actual = [];
b.notEqual( 1.0, 2.0, 'This asserts two values are not equal.' );
b.notEqual( actual, expected, 'This asserts two values are not equal.' );
ok 17 This asserts two values are not equal.
not ok 18 This asserts two values are not equal.
---
operator: notEqual
TODO: include stack
...
b.deepEqual( actual, expected[, msg] )
Asserts that actual
is deeply equal to expected
.
var expected = {
'a': 'b'
};
var actual = {
'a': 'b'
};
b.deepEqual( actual, expected );
ok 19 should be deeply equal
To override the default message, provide a msg
argument.
var expected = {
'a': 'b'
};
var actual = {
'a': 'b'
};
b.deepEqual( actual, expected, 'This asserts two values are deeply equal.' );
actual.a = 'c';
b.deepEqual( actual, expected, 'This asserts two values are deeply equal.' );
TODO
b.notDeepEqual( actual, expected[, msg] )
Asserts that actual
is not deeply equal to expected
.
var expected = {
'a': 'b'
};
var actual = {
'a': 'c'
};
b.notDeepEqual( actual, expected );
ok 22 should not be deeply equal
To override the default message, provide a msg
argument.
var expected = {
'a': 'b'
};
var actual = {
'a': 'c'
};
b.notDeepEqual( actual, expected, 'This asserts two values are not deeply equal.' );
actual.a = 'b';
b.notDeepEqual( actual, expected, 'This asserts two values are not deeply equal.' );
TODO
Notes
- All benchmark functions execute serially in separate turns of the event loop.
- All benchmark functions should be added during the same turn of the event loop. Otherwise, you will likely encounter race conditions where a benchmark executes and finishes causing a harness to close before subsequent benchmarks register.
- Similarly, create results streams before adding benchmarks to the harness. Otherwise, you will likely miss benchmark results.
- If a harness is invoked without providing a
benchmark
function, the benchmark is considered atodo
andopts.repeat
is ignored. - All benchmarks are pretested. If a benchmark generates failing assertions or fails to call
b.tic()
and/orb.toc()
during pretests (even if due to an intermittent failure), a benchmark is only run once (i.e.,options.repeats
is ignored). Similarly, ifoptions.iterations
isnull
and a benchmark fails during iteration number determination, a benchmark is only run once and for one iteration. Accordingly, if a benchmark does not run an expected number of repetitions and/or iterations, this behavior is likely attributable to a benchmark failure during pretesting. - All benchmarks must have a
name
. If aname
is not provided, the harness will throw anError
. - While not required, all benchmarks should have a unique
name
. Unique names ensure easier identification and assignment of benchmark results. - Uncaught exceptions in benchmark functions are not intercepted and will cause the harness to error.
- If any one of
b.tic()
,b.toc()
, orb.end()
is called more than once within a benchmark, the benchmark will fail. - Always verify results. Doing so prevents the compiler from performing dead code elimination and other optimization techniques, which would render timing results meaningless.
- While many benchmark frameworks calculate various statistics over raw timing results (e.g., mean and standard deviation), do not do this. Instead, consider the fastest time an approximate lower bound for how fast an environment can execute benchmark code. Slower times are more likely attributable to other processes interfering with timing accuracy rather than attributable to variability in JavaScript's speed. In which case, the minimum time is most likely the only result of interest. When considering all raw timing results, apply common sense rather than statistics.
TAP
Results are output in accordance with the Test Anything Protocol (TAP) version 13.
Example TAP output:
TAP version 13 # Math.hypot --- iterations: 1000000 elapsed: 0.457849215 rate: 2184125.181911691 ... ok 1 benchmark finished # Math.hypot --- iterations: 1000000 elapsed: 0.454676639 rate: 2199365.250432407 ... ok 2 benchmark finished # Math.hypot --- iterations: 1000000 elapsed: 0.472378014 rate: 2116948.652059831 ... ok 3 benchmark finished # hypot --- iterations: 1000000 elapsed: 0.13120811 rate: 7621480.105155086 ... ok 4 benchmark finished # hypot --- iterations: 1000000 elapsed: 0.129308984 rate: 7733414.717727579 ... ok 5 benchmark finished # hypot --- iterations: 1000000 elapsed: 0.12404053 rate: 8061881.064197323 ... ok 6 benchmark finished # 1..6 # total 6 # pass 6 # # ok
For each failing assertion, the harness outputs diagnostic information as YAML blocks.
TODO
Timing results are output as YAML blocks. The fields are as follows:
- iterations: number of iterations.
- elapsed: total elapsed time beginning with
b.tic()
and ending withb.toc()
(in seconds). - rate: number of operations per second.
Examples
var randu = require( '@stdlib/random/base/randu' );
var isnan = require( '@stdlib/math/base/assert/is-nan' );
var sin = require( '@stdlib/math/base/special/sin' );
var bench = require( '@stdlib/bench/harness' );
var opts = {
'iterations': 1e6,
'repeats': 3
};
bench( 'Math.sin', opts, function benchmark( b ) {
var x;
var y;
var i;
b.tic();
for ( i = 0; i < b.iterations; i++ ) {
x = (randu()*100.0) - 50.0;
y = Math.sin( x );
if ( y < -1.0 || y > 1.0 ) {
b.fail( 'something went wrong!' );
}
}
b.toc();
if ( isnan( y ) ) {
b.fail( 'something went wrong!' );
}
b.pass( 'benchmark finished' );
b.end();
});
bench( 'sin', opts, function benchmark( b ) {
var x;
var y;
var i;
b.tic();
for ( i = 0; i < b.iterations; i++ ) {
x = (randu()*100.0) - 50.0;
y = sin( x );
if ( y < -1.0 || y > 1.0 ) {
b.fail( 'something went wrong!' );
}
}
b.toc();
if ( isnan( y ) ) {
b.fail( 'something went wrong!' );
}
b.pass( 'benchmark finished' );
b.end();
});
CLI
Usage
Usage: bench [options] <glob> ...
Options:
-h, --help Print this message.
-V, --version Print the package version.
-r, --require module Load module before running benchmarks.
Notes
Running benchmark files does not require using the command-line interface. For example, to run a single file containing benchmarks,
$ node /path/to/benchmark.js
To load one or more modules before running benchmarks, set the
-r
flag one or more times. For example,$ bench -r foo -r bar 'benchmark/*.js'
the modules
foo
andbar
will both be loaded before any benchmarks matching the globbenchmark/*.js
. The-r
flag behaves exactly likerequire
, and modules are resolved relative to the current working directory. To load local modules, use relative paths.$ bench -r ./foo/bar.js -r ./beep/boop/bap 'benchmark/*.js'
Note that
-r
modules are loaded before running benchmarks regardless of order. Hence,$ bench -r foo -r bar 'benchmark/*.js'
and
$ bench -r foo 'benchmark/*.js' -r bar
behave the same.
Depending on the preloaded module, a module may support parameterization via environment variables, command-line options, and/or configuration files.
To perform shell expansion on systems supporting globbing, do not quote provided globs.
$ bench benchmark/*.js
Beware, however, that globbing via shell expansion may result in shell argument lists which exceed length limits. To prevent shell expansion, wrap globs in quotes.
$ bench 'benchmark/*.js' $ bench "benchmark/*.js"
Examples
$ bench ./examples/index.js
will generate TAP output similar to the following
TAP version 13
# Math.sin
---
iterations: 1000000
elapsed: 0.107631765
rate: 9290937.484858675
...
ok 1 benchmark finished
# Math.sin
---
iterations: 1000000
elapsed: 0.100319363
rate: 9968165.368035682
...
ok 2 benchmark finished
# Math.sin
---
iterations: 1000000
elapsed: 0.095116262
rate: 10513449.31952856
...
ok 3 benchmark finished
# sin
---
iterations: 1000000
elapsed: 0.173696195
rate: 5757178.503536016
...
ok 4 benchmark finished
# sin
---
iterations: 1000000
elapsed: 0.158544701
rate: 6307369.42762912
...
ok 5 benchmark finished
# sin
---
iterations: 1000000
elapsed: 0.157709895
rate: 6340756.234730865
...
ok 6 benchmark finished
#
1..6
# total 6
# pass 6
#
# ok
References
- Chen, Jiahao, and Jarrett Revels. 2016. "Robust benchmarking in noisy environments." CoRR abs/1608.04295 (August). http://arxiv.org/abs/1608.04295.