Profiling in Sage

This page lists several methods available in Sage to measure and analyze the performances of a piece of code. For more general information on profiling, see Wikipedia article Profiling_(computer_programming).

How long does it take? %time and %timeit

The two IPython magics %time and %timeit measure the time it takes to run a command:

sage: %time p=random_prime(2**300)
CPU times: user 152 ms, sys: 0 ns, total: 152 ms
Wall time: 150 ms

sage: %timeit p=random_prime(2**300)
10 loops, best of 3: 62.2 ms per loop

Note that while %time only runs the command once, %timeit tries to return a more meaningful value over several runs.

For more information see %timeit? or this page.

Note that Sage provides a timeit function which also runs in the Sage notebook.

Python-level function calls: %prun

With %prun, you can obtain the list of all Python functions involved in a computation, as well as the time spent on each of them:

sage: %prun  _=random_prime(2**500)
      468 function calls in 0.439 seconds

Ordered by: internal time

ncalls  tottime  percall  cumtime  percall filename:lineno(function)
    32    0.438    0.014    0.438    0.014 {method 'is_prime' of 'sage.rings.integer.Integer' objects}
    32    0.001    0.000    0.439    0.014
    32    0.000    0.000    0.001    0.000
    32    0.000    0.000    0.000    0.000

The most time-consuming functions should appear on the top. A description of the different columns is available here.


You may want to sort this list differently, e.g: use %prun -s cumulative for decreasing cumulative time.

Alternatively, you can “save” this data to a Stats object for further inspection:

sage: %prun -r random_prime(2**500)
sage: stats_object = _
sage: stats_object.total_calls

For more information see %prun? or this page.

Visualize the statistics: you can obtain a more graphical output with RunSnake and Sage’s function runsnake():

sage: runsnake('random_prime(2**500)')

Python-level line-by-line profiling: %lprun

With line_profiler and its %lprun magic, you can find out which lines of one (or many) functions are the most time-consuming. The syntax is the following:

%lprun -f function1 -f function2 code_to_run

This will display the line-by-line analysis of function1 and function2 when code_to_run is executed:

sage: %lprun -f random_prime random_prime(2**500)
Line #      Hits         Time  Per Hit   % Time  Line Contents
1193                                           def random_prime(n, proof=None, lbound=2):
...                                                ...
1251                                               # since we don't want current_randstate to get
1252                                               # pulled when you say "from sage.arith.all import *".
1253         1           11     11.0      0.0      from sage.misc.randstate import current_randstate
1254         1            7      7.0      0.0      from sage.structure.proof.proof import get_flag
1255         1            6      6.0      0.0      proof = get_flag(proof, "arithmetic")
1256         1           17     17.0      0.0      n = ZZ(n)

In order to install line_profiler you must first run the following command:

[user@localhost ~] sage -pip install "line_profiler"

C-level function calls: %crun

With %crun, you can obtain the list of all C functions involved in a computation, as well as the time spent on each of them. You will need to have the Google performance analysis tools installed on your system:

sage: %crun p=random_prime(2**500)
PROFILE: interrupts/evictions/bytes = 45/0/18344
Total: 45 samples
       0   0.0%   0.0%       35  77.8% PyEval_EvalCode
       0   0.0%   0.0%       35  77.8% PyEval_EvalCodeEx
       0   0.0%   0.0%       35  77.8% PyEval_EvalFrameEx
       0   0.0%   0.0%       35  77.8% PyObject_Call
       0   0.0%   0.0%       35  77.8% PyRun_StringFlags
       0   0.0%   0.0%       35  77.8% __Pyx_PyObject_Call.constprop.73

For more information on %crun, see sage.misc.gperftools.

C-level line-by-line profiling: perf (Linux only)

If your code is written in C or in Cython, you can find out line-by-line which are the most costly using perf (included in the Ubuntu package linux-tools).

The easiest way to use it is to run some (very long) computation in Sage, and to type in a console:

[user@localhost ~] sudo perf top

Select the entry that interests you, and press Enter. The annotate command will show you:

  • the CPU instructions
  • the source code
  • the associated time
      │     *         cdef unsigned long word = (<unsigned long>1) << (v & self.radix_mod_mask)
      │     *         return (self.edges[place] & word) >> (v & self.radix_mod_mask)             # <<<<<<<<<<<<<<
      │     *
      │     *     cpdef bint has_arc(self, int u, int v) except -1:
      │     */
      │      __pyx_r = (((__pyx_v_self->edges[__pyx_v_place]) & __pyx_v_word) >> (__pyx_v_v & __pyx_v_self->radix_mod_mask));
10.88 │      movslq %esi,%rsi
 6.52 │      and    (%rdi,%rsi,8),%rax
12.84 │      shr    %cl,%rax


  • press s to toggle source code view
  • press H to cycle through hottest instructions
  • press h for help

Alternatively, or if you have no sudo privileges, you can record the statistics of a specific process into a file from its PID. Then, visualize the result using perf report:

[user@localhost ~] perf record -p PID
[user@localhost ~] perf report --vmlinux vmlinux