### 6.1 Statistical Sampling Error

The run-time figures that `gprof`

gives you are based on a sampling
process, so they are subject to statistical inaccuracy. If a function runs
only a small amount of time, so that on the average the sampling process
ought to catch that function in the act only once, there is a pretty good
chance it will actually find that function zero times, or twice.

By contrast, the number-of-calls and basic-block figures are derived by counting, not sampling. They are completely accurate and will not vary from run to run if your program is deterministic.

The sampling period that is printed at the beginning of the flat profile says how often samples are taken. The rule of thumb is that a run-time figure is accurate if it is considerably bigger than the sampling period.

The actual amount of error can be predicted.
For `n` samples, the *expected* error
is the square-root of `n`. For example,
if the sampling period is 0.01 seconds and `foo`

's run-time is 1 second,
`n` is 100 samples (1 second/0.01 seconds), sqrt(`n`) is 10 samples, so
the expected error in `foo`

's run-time is 0.1 seconds (10*0.01 seconds),
or ten percent of the observed value.
Again, if the sampling period is 0.01 seconds and `bar`

's run-time is
100 seconds, `n` is 10000 samples, sqrt(`n`) is 100 samples, so
the expected error in `bar`

's run-time is 1 second,
or one percent of the observed value.
It is likely to
vary this much *on the average* from one profiling run to the next.
(*Sometimes* it will vary more.)

This does not mean that a small run-time figure is devoid of information.
If the program's *total* run-time is large, a small run-time for one
function does tell you that that function used an insignificant fraction of
the whole program's time. Usually this means it is not worth optimizing.

One way to get more accuracy is to give your program more (but similar)
input data so it will take longer. Another way is to combine the data from
several runs, using the -s option of `gprof`

. Here is how:

- Run your program once.
- Issue the command mv gmon.out gmon.sum.
- Run your program again, the same as before.
- Merge the new data in gmon.out into gmon.sum with this command:
gprof -s

`executable-file`gmon.out gmon.sum - Repeat the last two steps as often as you wish.
- Analyze the cumulative data using this command:
gprof

`executable-file`gmon.sum >`output-file`