# Flake Aware Culprit Finding

**Tim A. D. Henderson**, Bobby Dorward, Eric Nickell, Collin Johnston, and Avi Kondareddy.
*Flake Aware Culprit Finding*. ICST Industry Track 2023.

DOI.
PDF.
WEB.
Google Research Preprint.

#### Note

This is a conversion from a latex paper I wrote. If you want all formatting correct you should read the pdf version.

#### Abstract

When a change introduces a bug into a large software repository, there is
often a delay between when the change is committed and when bug is detected.
This is true even when the bug causes an existing test to fail! These delays
are caused by resource constraints which prevent the organization from running
all of the tests on every change. Due to the delay, a Continuous Integration
system needs to locate buggy commits. Locating them is complicated by flaky
tests that pass and fail non-deterministically. The flaky tests introduce
noise into the CI system requiring costly reruns to determine if a failure was
caused by a bad code change or caused by non-deterministic test behavior. This
paper presents an algorithm, *Flake Aware Culprit Finding*, that locates
buggy commits more accurately than a traditional bisection search. The
algorithm is based on Bayesian inference and noisy binary search, utilizing
prior information about which changes are most likely to contain the bug. A
large scale empirical study was conducted at Google on 13,000+ test breakages.
The study evaluates the accuracy and cost of the new algorithm versus a
traditional deflaked bisection search.

# Introduction

Fast, collaborative, large scale development is enabled by the use of
Continuous Integration in a *mono-repository* (monorepo)
environment where all of the source code is stored in a single shared
repository (Potvin and Levenberg
2016). In a monorepo, all developers share a single source of
truth for the state of the code and most builds are made from “head”
(the most recent commit to the repository) using the source code for all
libraries and dependencies rather than versioned pre-compiled archives.
This enables (among other things) unified versioning, atomic changes,
large scale refactorings, code re-use, cross team collaboration, and
flexible code ownership boundaries.

Very large scale monorepos (such as those at Google (Potvin and Levenberg
2016; Memon et al.
2017), Microsoft (Herzig and Nagappan 2015), and Facebook
(Machalica et al.
2019)) require advanced systems for ensuring changes
submitted to the repository are properly tested and validated.
*Continuous Integration* (CI) (Fowler 2006) is a system and practice of
automatically integrating changes into the code repository that serves
as the source of truth for the organization. In modern environments,
integration involves not only performing the textual merge required to
add the change but also verification tasks such as ensuring the software
compiles and the automated tests pass both on the new change before it
is integrated *and after* it has been incorporated into the main
development branch.

Due to resource constraints, tests are only run at specific versions
(called *milestones* at Google) and many tests may be skipped
because they were not affected by the intervening changes (as determined
by static build dependencies) (Gupta, Ivey, and Penix 2011). This
process is illustrated in Figure [fig:ci-timeline]. A test is
considered passing at a version \(b\)
if and only if it has a passing result at the most recent preceding
affecting version. Formally, if there exists a version \(a\) where the test is passing and \(a \le b\) and there does not exist an
intervening version \(c\), \(a < c \le b\), which affects the test
then the test is passing at version \(a\). A project’s status is considered
passing at a version \(b\) if all tests
are passing (using the above definition) at version \(b\).

If a test \(t\) is failing
(consistently) at a milestone version \(m\), it may not necessarily mean that
version \(m\) introduced a change which
broke test \(t\). As shown in Figure [fig:ci-timeline] one or more
changes between \(m\) and the previous
milestone at which test \(t\) was run
may have introduced a breaking change. Figuring out which version
introduced the *breakage* is called *culprit finding*.

Many companies now employ automated culprit finding systems. These systems typically implement a (possibly n-way) “bisect search” similar to the one built into the Git version control system (Couder 2008). Git’s bisect command runs a binary search on the versions between the first known breaking version and the last known passing version to identify the version which broke the test.

In the Google environment, there are two problems with a traditional
bisection algorithm (Couder 2008): (1)
it does not account for flaky (non-deterministic) tests, and (2) when
using \(k\)-reruns to deflake the
search accuracy plateaus while build cost continues to increase
linearly. **This paper proposes** a new method for culprit
finding which is both robust to non-deterministic (flaky) test behavior
and can identify the culprit with only logarithmic builds in the best
case by using prior information to accelerate the search.

## Contributions

A Flake Aware Culprit Finding (FACF) algorithm.

A mathematical model for culprit finding adjusting for non-deterministic test behavior.

A large scale empirical study of FACF on Google’s mono repository comparing its performance against the traditional bisect algorithm.

The study also evaluates the effectiveness: (a) optimizations for FACF, and (b) adding deflaking runs to Bisect.

# Background

At Google, the Test Automation Platform (TAP) runs most tests that
can run on a single machine (and do not use the network except for the
loopback interface)^{1} and can run in under 15 minutes.^{2} Figure [fig:ci-timeline] illustrates at a
high level of how TAP works. First, (not illustrated) tests are grouped
into logical projects by the teams that own them. Then, (for accounting
and quota allocation purposes) those projects are grouped into very high
level groupings called Quota Buckets. Each Quota Bucket is scheduled
independently when build resources are available. This means that TAP
does not run every test at every version. Instead it only runs tests
periodically at select versions called “Milestones” (Memon et al. 2017; Micco 2013; Leong et al.
2019).

When scheduling a Milestone, all the tests that are built and run
with the same command line flags to the build system^{3} are
grouped into a set. That set is filtered to remove tests that haven’t
been affected by a change to themselves or a build level dependency
(Gupta, Ivey, and Penix
2011; Micco 2013,
2012). This is
a very coarse grained form of static dependence-based test selection
(Binkley 1992; Horwitz and Reps 1992;
Tip 1995).
Google’s use of build dependence test selection has been influential and
it is now also used at a number of other corporations who have adopted
Bazel or similar tools (Ananthanarayanan
et al. 2019; Machalica et al. 2019). Finally, that
(potentially very large) set of “affected” tests is sent to the Build
System (Wang et al. 2020)
which batches them into efficiently sized groups and then builds and
runs them when there is capacity.

Since tests are only run periodically even with accurate build level
dependence analysis to drive test selection, there are usually multiple
changes which may have introduced a fault in the software or a bug in
the test. Finding these “bug inducing changes” – which we call
**culprits** – is the subject of this paper. The process of
finding these changes is aggravated by any non-deterministic behavior of
the tests and the build system running them.

## Flaky Tests

When a test behaves non-deterministically, we refer to it, using the
standard term, as a *flaky test*. A flaky test is one that passes
or fails non-deterministically with no changes to the code of either the
test or the system under test. At Google, we consider all tests to be at
least *slightly* flaky as the machines that tests are running on
could fail in ways that get classified as a test failure (such as
resource exhaustion due to a noisy neighbor resulting in a test
exceeding its time limit). We encourage everyone to adopt this
conservative view for the purposes of identifying culprits.

An important input to the culprit finding algorithm we are presenting is an estimate of how flaky a test might be, as represented by an estimated probability of the test failing due to a flaky failure. We will denote the estimated probability of failure due to a flake for a test \(t\) as \(\hat{f}_t\). The actual probability of failure due to a flake will be denoted \(f_t\) (it is impossible in practice to know \(f_t\)). At Google, we estimate \(\hat{f}_t\) based on the historical failure rate of the test. Apple and Facebook recently published on their work in on estimating flake rates (Kowalczyk et al. 2020; Machalica et al. 2020). One challenge with flake rate estimation is that a single change to the code can completely change the flakiness characteristics of a test in unpredictable ways. Making the flake rate estimation sensitive to recent changes is an ongoing challenge and one we partially solve in this work by doing live re-estimation of the flake rate during the culprit finding process itself.

## Culprit Finding

Informally, Culprit Finding is the problem of identifying a version \(c\) between two versions \(a\) and \(b\) such that \(a < c \le b\) where a given test \(t\) was passing at \(a\), failing at \(b\), and \(c\) is the version which introduced the fault. At Google we consider the passing status of a test to be 100% reliable and therefore version \(a\) cannot be a culprit but version \(b\) could be the culprit. For simplicity, this paper only considers searching for the culprit for a single test \(t\) (which failed at \(b\)) but in principle it can be extended to a set of tests \(T\).

Google’s version control system, Piper (Potvin and Levenberg 2016), stores the
mainline history as a linear list of versions. Each version gets a
monotonically, *but not sequentially*, increasing number as its
version number called the *Changelist Number* or CL number for
short. Thus, our implementation and experiments do not consider branches
and merges as would be necessary for a Distributed Version Control
System (DVCS) such as git. However, only trivial changes to the
mathematics are needed to apply our approach to such an environment
(Couder 2008).

Thus, the versions larger than \(a\)
and smaller or equal to \(b\) are an
ordered list of items we will call the *search range* and denote
as \(S =
\left\{s_1, ..., s_{n-1}, s_n\right\}\) where \(s_n = b\). During the search, test
executions will be run (and may be run in parallel) at various versions.
The unordered set of executions at version \(s_i\) will be denoted \(X_i\).

For the purposes of culprit finding, based on the status of failure
detected, the build/test execution statuses are mapped to one of 2
possible states: `PASS`

or `FAIL`

. We denote (for
version \(s_i\)): the number of
statuses that map to `PASS`

as \(\texttt{\small PASSES}(X_i)\) and the
number of statuses that map to `FAIL`

as \(\texttt{\small FAILS}(X_i)\).

## Bisection

The Bisect algorithm is a specialized form of binary search. It runs
tests (or more generally any operation on the code that can return PASS
or FAIL) to attempt to identify which commit introduced a bug. Algorithm
[alg:bisect] gives the psuedo-code for
this procedure. Bisect is now commonly implemented in most version
control systems (see `git bisect`

and `hg bisect`

as common examples). In the case of Distributed Version Control Systems
(DVCS) systems such as ‘git‘ and ‘hg‘ the implementation of bisect is
somewhat more complex as they model version history as a directed
acyclic graph (Couder 2008).

The algorithm presented in Alg [alg:bisect]
has two important changes from the standard binary search. First, it
takes into account that a test can fail and pass at the same version and
the `firstFail`

function specifically looks for a failure
after the `lastPass`

. Second, it takes a parameter \(k\) which allows the user to specify that
each test execution be run \(k\) times.
This allows the user to “deflake” the test executions by rerunning
failures. Our empirical evaluation (Section 5)
examines both the cost and effectiveness of this simple modification.
While this simple modification to bisect may be reasonably effective for
moderately flaky tests, it does not explicitly model the effect of
non-deterministic failures on the likelihood of a suspect to be the
culprit.

## Guessing Games and Noisy Searches

One can view the culprit finding scenario as a kind of guessing game. The questioner guesses the test always fails at a given suspect version. A test execution at that suspect acts as a kind of “responder” or “oracle” which answers. The test execution is an unreliable oracle which may answer FAIL when it should have answered PASS. But, the oracle never answers PASS when it should have answered FAIL – note the asymmetry.

This kind of guessing game is a Rényi-Ulam game, which has been well
characterized by the community (Pelc
2002). The main differences from the “classical” games
presented by Rényi and separately by Ulam is (a) the format of the
questions and (b) the limitations placed on the oracle responding
incorrectly. In a common formulation of the Rényi-Ulam game, the
questioner is trying to “guess the number” between (for instance) 1 and
1,000,000. Each question is allowed to be any subset of numbers in the
search range. The responder or oracle is allowed to lie at most a fixed
number of times (for instance once or twice). This formulation has
allowed the community to find analytic solutions to determine the number
of questions in the optimal strategy. We refer the reader to the survey
from Pelc for an overview of the field and its connection with error
correcting codes (Pelc 2002). The
culprit finding scenario is “noisy binary search” scenario where the
oracle only lies for one type of response. Rivest *et al.* (Rivest, Meyer, and Kleitman 1978)
provide a theoretical treatment of this “half-lie” variant (as well as
the usual variation).

## Bayesian Binary Search

Ben Or and Hassidim (Ben-Or and Hassidim 2008) noted the connection between these “Noisy Binary Search” problems and Bayesian inference. Our work builds off of their formulation and applies it to the culprit finding setting. In the Bayesian setting, consider the probability each suspect is the culprit and the probability there is no culprit (i.e. the original failure was caused by a flake). These probabilities together form a distribution: \[(\textrm{Pr}\left[{\text{there is no culprit}}\right]) + \sum_{i=1}^{n} \textrm{Pr}\left[{s_i \text{ is the culprit}}\right] = 1\]

We represent this distribution with \(\textrm{Pr}\left[{C_i}\right]\) with \(i=1..(n+1)\) where \[\begin{aligned} \begin{split} \textrm{Pr}\left[{C_i}\right] &= \textrm{Pr}\left[{s_i \text{ is the culprit}}\right], \; \forall \; i \in [1, n] \\ \textrm{Pr}\left[{C_{n+1}}\right] &= \textrm{Pr}\left[{\text{there is no culprit}}\right] \\ \end{split}\end{aligned}\]

Initially when the original failure is first detected at \(s_n\) and the search range is created, the
probability distribution is uniform: \(\textrm{Pr}\left[{C_i}\right] =
\frac{1}{(n+1)}\) for all \(i \in [1,
n+1]\). Now consider new evidence \(E\) arriving. In the Bayesian model, this
would *update* our probability given this new evidence: \[\begin{aligned}
\textrm{Pr}\left[{C_i | E}\right] = \frac{\textrm{Pr}\left[{E |
C_i}\right] \cdot
\textrm{Pr}\left[{C_i}\right]}{\textrm{Pr}\left[{E}\right]}
\label{eq:bayes}\end{aligned}\]

In the above equation, the \(\textrm{Pr}\left[{C_i}\right]\) is the
*prior* probability and the probability \(\textrm{Pr}\left[{C_i | E}\right]\) is the
*posterior* probability. In the culprit finding context, the new
evidence is typically newly observed test executions. However, there is
no reason we cannot take into account other information as well.

In the Bayesian framework, new evidence is applied iteratively. In each iteration, the prior probability is the posterior probability of the previous iteration. Since multiplication is commutative, multiple pieces of evidence can be applied in any order to arrive at the same posterior probability: \[\begin{aligned} \begin{split} \textrm{Pr}\left[{C_i | E_1, E_2}\right] &= \frac{\textrm{Pr}\left[{E_2 | C_i}\right]}{\textrm{Pr}\left[{E_2}\right]} \frac{\textrm{Pr}\left[{E_1 | C_i}\right]}{\textrm{Pr}\left[{E_1}\right]} \textrm{Pr}\left[{Ci}\right] \\ &= \frac{\textrm{Pr}\left[{E_1 | C_i}\right]}{\textrm{Pr}\left[{E_1}\right]} \frac{\textrm{Pr}\left[{E_2 | C_i}\right]}{\textrm{Pr}\left[{E_2}\right]} \textrm{Pr}\left[{Ci}\right] \end{split}\end{aligned}\]

After the current posterior probability has been calculated, it is used to select the next suspect to execute a test at. In the traditional Bayes approach, the suspect to examine is the one with the maximum posterior probability. However, in the context of a noisy binary search, the suspects are ordered so a PASS at suspect \(s_i\) indicates a PASS at all suspects prior to \(s_i\). Following Ben Or and Hassidim (Ben-Or and Hassidim 2008), we convert the posterior distribution to a cumulative probability distribution and select the first suspect with a cumulative probability \(\geq 0.5\).

# Flake Aware Culprit Finding

Now we introduce our algorithm, Flake Aware Culprit Finding (FACF), in the Bayesian framework of Ben Or and Hassidim (Ben-Or and Hassidim 2008). As above, let \(\textrm{Pr}\left[{C_i}\right]\) be the probability that suspect \(s_i\) is the culprit and \(\textrm{Pr}\left[{C_{n+1}}\right]\) be the probability there is no culprit. These probabilities are initialized to some suitable initial distribution such as the uniform distribution.

To update the distribution with new evidence \(E\) in the form of a pass or fail for some suspect \(k\), apply Bayes rule (Equation [eq:bayes]). Note that \(\textrm{Pr}\left[{E}\right]\) can be rewritten by Bayes rule in terms of a sum by marginalizing over the likelihood that each suspect \(j\) could be the culprit: \[\begin{aligned} \textrm{Pr}\left[{E}\right] = \sum_{j=1}^{n} \textrm{Pr}\left[{E | C_j}\right] \textrm{Pr}\left[{C_j}\right]\end{aligned}\]

There are two types of evidence: test executions with state
`PASS`

or `FAIL`

at suspect \(i\). We indicate these as the events \(P_i\) and \(F_i\) respectively. The marginalized
probability of a `PASS`

at \(i\) given there is a culprit at \(j\) is: \[\begin{aligned}
\textrm{Pr}\left[{P_i | C_j}\right] =
\begin{cases}
1 - \hat{f}_t & \text{if } i < j \\
0 & \text{otherwise}
\end{cases}
\label{eq:pass}\end{aligned}\]

The marginalized probability of a `FAIL`

at \(i\) given there is a culprit at \(j\) is: \[\begin{aligned}
\textrm{Pr}\left[{F_i | C_j}\right] =
\begin{cases}
\hat{f}_t & \text{if } i < j \\
1 & \text{otherwise}
\end{cases}
\label{eq:fail}\end{aligned}\]

With Equation [eq:pass], we write a Bayesian update for
`PASS`

at suspect \(k\) as
the following. Given \[\begin{aligned}
\textrm{Pr}\left[{C_i | P_k}\right] = \frac{\textrm{Pr}\left[{P_k |
C_i}\right] \textrm{Pr}\left[{C_i}\right]}{
\textrm{Pr}\left[{P_k}\right]
}\end{aligned}\]

let \[\begin{aligned} \begin{split} \textrm{Pr}\left[{P_k}\right] &= \sum_{j=1}^{n} \textrm{Pr}\left[{P_k | C_j}\right] \textrm{Pr}\left[{C_j}\right] \\ &= \sum_{j=k+1}^{n} (1 - \hat{f}_t) \textrm{Pr}\left[{C_j}\right] \end{split}\end{aligned}\]

cdf = cumulativeDistribution(dist) thresholds = \(\left\{ \frac{i}{(k+1)} \; | \; i=1..k \right\}\) tidx = 0 runs = list() runs

then \[\begin{aligned} \textrm{Pr}\left[{C_i | P_k}\right] = \begin{cases} \frac{(1 - \hat{f}_t) \textrm{Pr}\left[{C_i}\right]}{\textrm{Pr}\left[{P_k}\right]} & \text{if } k < i \\ 0 & \text{otherwise} \\ \end{cases}\end{aligned}\]

The update using Equation [eq:fail] for
`FAIL`

at suspect \(k\) is
similar. Given \[\begin{aligned}
\textrm{Pr}\left[{C_i | F_k}\right] = \frac{\textrm{Pr}\left[{F_k |
C_i}\right] \textrm{Pr}\left[{C_i}\right]}{
\sum_{j=1}^{n} \textrm{Pr}\left[{F_k | C_j}\right]
\textrm{Pr}\left[{C_j}\right]
}\end{aligned}\]

let \[\begin{aligned} \begin{split} \textrm{Pr}\left[{F_k}\right] &= \sum_{j=1}^{n} \textrm{Pr}\left[{F_k | C_j}\right] \textrm{Pr}\left[{C_j}\right] \\ &= \sum_{j=1}^{k} \textrm{Pr}\left[{C_j}\right] + \sum_{j=k+1}^{n} \hat{f}_t \textrm{Pr}\left[{C_j}\right] \end{split}\end{aligned}\]

then \[\begin{aligned} \textrm{Pr}\left[{C_i | F_k}\right] = \begin{cases} \frac{\hat{f}_t \textrm{Pr}\left[{C_i}\right]}{\textrm{Pr}\left[{F_k}\right]} & \text{if } k < i \\ \frac{\textrm{Pr}\left[{C_i}\right]}{\textrm{Pr}\left[{F_k}\right]} & \text{otherwise} \\ \end{cases}\end{aligned}\]

## The FACF Algorithm

Algorithm [alg:facf] presents the pseudo code for a
culprit finding algorithm based on the above Bayesian formulation. It
takes a prior distribution (the uniform distribution can be used), an
estimated flake rate \(\hat{f}_t\), and
the suspects. It returns the most likely culprit or `NONE`

(in the case that it is most likely there is no culprit). The FACF
algorithm builds a set of evidence \(X\) containing the observed passes and
failures so far. At each step, that evidence is converted to a
distribution using the math presented above. Then, FACF calls Algorithm
[alg:nextRuns] `NextRuns`

to compute the next suspect to run.

`NextRuns`

converts the probability distribution into a
cumulative distribution. It then selects the suspects with cumulative
probability over a set of thresholds and returns them. The version of
`NextRuns`

we present here has been generalized to allow for
\(k\) parallel runs and also contains a
minor optimization on lines 10-11. If the suspect \(s_{i-1}\) prior to the selected suspect
\(s_i\) hasn’t been selected to run and
its cumulative probability is above \(0\) then the prior suspect \(s_{i-1}\) is selected in favor of \(s_i\). This optimization ensures that we
look for the passing run preceding the most likely culprit before
looking for a failing run at the culprit.

## Choosing the Thresholds in NextRuns

Another optimization can be made to NextRuns by changing the thresholds used to select suspects. Instead of simply dividing the probability space up evenly it uses the observation that the information gain from a PASS is more than the gain from a FAIL. Modeling that as \(I(P_i) = 1\) and \(I(F_i) = 1 - \hat{f}_t\), we can compute the expected information gain for new evidence at suspect \(s_i\) as \(\textrm{E}\left[{I(s_i)}\right] = I(P_i)P_i + I(F_i)F_i\). Expanding from the marginalized equations [eq:pass] and [eq:fail] gives \[\begin{aligned} \textrm{E}\left[{I(s_i)}\right] = (1 - \hat{f}_t)(n + i \hat{f}_t - 1)\end{aligned}\]

Computing the cumulative expectation over \(\{ \textrm{E}\left[{I(s_1)}\right], ..., \textrm{E}\left[{I(s_{n+1})}\right] \}\) and normalizing allows us to select the suspect that maximizes the information gain. The empirical evaluation (Section 5) examines the effect of this optimization. The importance of the supplied flake rate estimate (\(\hat{f}_t\)) is also examined in Section 5.

## Prior Probabilities for FACF

The prior distribution supplied to Algorithm [alg:facf] does not have to be a uniform distribution. Instead, it can be informed by any other data the culprit finding system might find useful. At Google, we are exploring many such sources of data, but so far are only using two primary sources in production.

First, we have always used the static build dependence graph to filter out non-affecting suspects before culprit finding (Gupta, Ivey, and Penix 2011). In FACF, we take that a step further and, using a stale snapshot for scalability, we compute the minimum distance in the build graph between the files changed in each suspect and the test being culprit-found (Memon et al. 2017). Using these distances, we form a probability distribution where the suspects with files closer to the test have a higher probability of being the culprit (Ziftci and Ramavajjala 2013; Ziftci and Reardon 2017). Second, we look at the historical likelihood of a true breakage (versus a flaky one) to determine the probability that there is no culprit. Combining that distribution with the one from the minimum build distance forms a prior distribution we use for culprit finding.

Using this scheme, flaky tests tend to get reruns at the \(s_n\) (the suspect where the failure was detected) as their first test executions during culprit finding. This is intentional as a large fraction of the search ranges we culprit find tend to be flaky and this reduces the cost of proving that. In the empirical evaluation (Section 5), we examine the effect of the prior distribution on both cost and accuracy.

# Culprit Verification for Accuracy Evaluation

The previous sections detailed our culprit finding algorithm (FACF) and the baseline algorithm we compare against (deflaked bisection). In order to evaluate the accuracy of a culprit finding system for a particular dataset, we need to know which commits are the actual culprit commits. If the actual culprit commits are known, then we can compute the usual measures (True Positive Rate, False Positive Rate, Accuracy, Precision, Recall, etc...) (Tharwat 2021). Previous work in culprit finding, test case selection, fault localization and related research areas have often used curated datasets (e.g. Defects4J (Just, Jalali, and Ernst 2014)), bug databases (Bhattacharya and Neamtiu 2010; Herzig et al. 2015; Najafi, Rigby, and Shang 2019), and synthetic benchmarks with injected bugs (Henderson and Podgurski 2018; Henderson, Podgurski, and Kucuk 2019). But our primary interest is in the accuracy of the algorithms in the Google environment, not the accuracy on open source bug databases, curated datasets, or synthetic bugs.

At Google, we do not have a comprehensive database of developer investigations of every continuous integration test failure – indeed there are far too many failures per day for developers to examine and evaluate every single one. We also didn’t want to completely rely on human feedback to tell us when our culprit finding systems have identified the wrong culprit – as had been previously done (Ziftci and Reardon 2017).

Instead, we wanted to be able to verify whether or not an identified culprit for a particular test and search range is correct or not. The verification needs to be automated such that the we can operationally monitor the accuracy of the deployed system and catch any performance regressions in the culprit finder. Continuous monitoring ensures a high quality user experience by alerting our team to accuracy degradations.

## Culprit Finding Conclusions

A culprit finder may draw one of two conclusions:

**FI**:`FLAKE_IDENTIFIED`

*the culprit finder determined the status transition was caused by non-deterministic behavior.***CVI**:`CULPRIT_VERSION_IDENTIFIED(version)`

*the culprit finder determined a specific*.`version`

was identified as the culprit

The verification system will label each conclusion examined with
either `CORRECT`

or `INCORRECT`

from which we can
define the standard counts for True and False Positives and Negatives.
Accuracy, Precision, and Recall can then be directly computed.

## When is a Culprit Incorrect?

For ease of discussion, we will use the notation introduced in Section 2.2 for the search range \(S\) with \(s_0\) indicating the previous passing version, \(s_n\) indicating the version where the failure was first detected, and \(s_k\) indicating the identified culprit. Now, consider the two cases

`FLAKE_IDENTIFIED`

these are incorrect if no subsequent runs pass at the version where the original failure was detected (no flaky behavior can be reproduced).`CULPRIT_VERSION_IDENTIFIED(version)`

these are incorrect if we can prove any of the following:A pass at \(s_n\) indicates the failure was a flake.

A pass at the culprit \(s_k\) indicates that the culprit was incorrectly identified.

No passes detected at the version prior to the culprit, \(s_{k-1}\), indicates that the culprit was incorrectly identified.

Additionally the following conditions indicate the culprit may have been misidentified due to a test dependency on either time or some unknown external factor:

No passes are identified at \(s_0\), indicating the test failure may be time or environment dependent (and the conclusion cannot be trusted).

No pass at \(s_0\) is detected prior (in the time dimension) to a failure at \(s_n\).

No failure at \(s_n\) is detected prior (in the time dimension) to a pass at \(s_0\).

No pass at \(s_{k-1}\) is detected prior (in the time dimension) to a failure at \(s_k\).

No failure at \(s_k\) is detected prior (in the time dimension) to a pass at \(s_{k-1}\).

Verification is not reproducible 17 hours later.

^{4}

Thus, our approach for determining whether or not a culprit is correct is to do extensive reruns for a particular conclusion.

## How Many Reruns to Conduct to Verify a Conclusion

A test run \(x\) times fails every time with the rate \(\hat{f}_t^x\). If we want to achieve confidence level \(C\) (ex. \(C = .99999999\)) of verifier correctness, we can compute the number of reruns to conduct for each check with \(x = \left\lceil{\frac{\,\textrm{log}\!\!\left({1 - C}\right)}{\,\textrm{log}\!\!\left({\hat{f}_t}\right)}}\right\rceil\).

## Sampling Strategy

While it would be ideal to verify every single culprit for every single test, the expense, in practice, of such an operation is too high. We conduct verification with a very high confidence level (\(C = 0.99999999\)) and a minimum on the estimated flakiness rate of \(0.1\) to ensure a minimum of 8 reruns for each check even for targets that have not been historically flaky. With such an expensive configuration, we can only afford the following sampling strategy.

Randomly sample at \(1\%\) of culprit finding conclusions.

Sample the first conclusion for each unique culprit version.

We tag which sampling strategy was used to sample a particular conclusion allowing us to compute statistics for each sampling frame independently.

## The Verified Culprits Dataset

Using our production culprit finders based on the FACF algorithm and a verifier implementing the above verification strategy, we have produced an internal dataset with 144,130 verified conclusions in the last 60 days, which we use in Section 5 to evaluate the performance of the algorithms presented in this paper. Note, because the evaluation of an algorithm is also expensive, we only conduct the evaluation on a subset of the whole dataset.

While we are unable to make the dataset public, we encourage others to use our verification approach on their own culprit finding systems and when possible share these datasets with the external community for use in future studies. Such datasets are not only useful for culprit finding research but also for fault localization, test prioritization, test selection, automatic program repair, and other topics.

# Empirical Evaluation

We empirically evaluated the behavior of the probabilistic Flake Aware Culprit Finding (FACF) algorithm, compared it to the traditional Bisect algorithm (Couder 2008), evaluated the effectiveness of adding deflaking runs to Bisect, and evaluated the effectiveness of two optimizations for FACF.

## Research Questions

The following research questions were considered. All questions were considered with respect to the Google environment (see Section 5.5 for more details about the dataset used).

Which algorithm (FACF or Bisect) was more accurate in identifying culprit commits?

What difference do algorithmic tweaks (such as adding deflaking runs to Bisect) make to accuracy.

How efficient is each algorithm as measured in number of test executions?

What difference do algorithmic tweaks (such as adding deflaking runs to Bisect) make to efficiency.

Does flakiness affect culprit finding accuracy and cost?

## Measuring Culprit Finding Accuracy

To measure the accuracy of the culprit finders we produce a binary
variable (“correct”) which is true if the culprit finder identified
version matched the culprit in the dataset. Accuracy is then defined as
the sample proportion: \(\textbf{ACC} =
\frac{\text{\# correct}}{\text{Total}}\). Culprit finder “A” is
judged more accurate than culprit finder “B” if A’s **ACC**
value is higher than B’s and a statistical test (described in Section 5.4) determines the difference is
significant.

## Measuring Culprit Finding Cost

We measure cost as the number of test executions performed by the algorithm. Culprit finder “A” is judged lower cost than culprit finder “B” if the mean number of test executions is less than “B” and a statistical test (described in Section 5.4) determines the difference is significant.

## On Our Usage of Statistical Tests

For answering RQ1 and RQ2, we observe the distribution per culprit-finding algorithm of whether or not the algorithm identified the culprit (0 or 1). For answering RQ3 and RQ4, we observe the distribution per culprit-finding algorithm of the number of test executions required to complete culprit finding.

We follow the recommendations of McCrum-Gardner (McCrum-Gardner
2008) as well as Walpole *et al.* (Walpole 2007) as to the proper test
statistics for our analysis. Since data points for a specific culprit
range have a correspondence across algorithms, we perform paired
statistical tests when feasible. The analysis is complicated by the
observation that neither the dichotomous distribution of correctness nor
the numerical distribution of number of test executions are normally
distributed. Following McCrum-Gardner we opt to use non-parametric
tests. Additionally different tests are used for accuracy (dichotomous
nominal variable) and number of executions (numerical variable)
respectively.

As we have more than 2 groups to consider (10 algorithms), we initially perform omnibus tests over all algorithms to justify the existence of statistical significance over all algorithms. In response to the multiple comparisons problem (Walpole 2007), we compute the corrected significance bound using the formula for the family-wise error rate. Our experimental design has us first conduct the ANOVA significance test to determine if any of the algorithms differed in performance. Then we conduct post-hoc testing to determine which algorithm’s performance differed. For each considered question we conduct \(\binom{10}{2} + 1\) significance tests. We have \(6\) considered questions which we use significance testing to answer, giving us a total \(r = 6\left(\binom{10}{2} + 1\right) = 276\) tests.

Solving for the \(\alpha\) in the experiment-wise error rate formula from Walpole (pg. 529 (Walpole 2007)) with \(p\) standing for the probability of a false rejection of at least one hypothesis in the experiment gives: \(\alpha = 1 - (1 - p)^{\frac{1}{r}}\). Given \(r = 276\) tests and an intended experiment-wise error rate of \(p = 0.001\), we conservatively arrive at \(\alpha = 10^{-6}\) after rounding down to control for family-wise error rate. We use \(\alpha\) as our significance level in all tests.

Cochran’s Q Test is used for significance testing of the accuracy distributions and Friedman’s \(\chi^{2}\) Test for number of executions. Post-hoc testing was conducted with McNemar’s test and Wilcoxon Signed Rank Test respectively.

## Evaluation Dataset

For the study we used a subset of the dataset produced by the production Culprit Verifier (described in Section 4). The evaluation dataset consists of 13600 test breakages with their required build flags, search range of versions, and the verified culprit. The verified culprit may be an indicator that there was no culprit and detected transition was caused by a flake. Approximately 60% of the items had a culprit version and 40% did not (as these were caused by a flaky failure).

Multiple tests may be broken by the same version. When looking at unique search ranges, we actually see approximately twice as many flaky ranges as non-flaky ones. This hints towards having tighter bounds on which ranges are worth culprit finding as all of the runs for two-thirds of ranges would have been better utilized on more deflaking runs if these two categories are accurately discernable.

We therefore examine the overall dataset for discrepancies between the two categories. For example, flaky ranges have, on average, 8 tests failing while non-flaky ranges have 224. For the objective of finding unique real culprits, we are interested in the minimum flake rate over targets in a range for flaky and non-flaky ranges, respectively. Fig [fig:min-flake-rate] shows us that, in fact, 99% of real culprit ranges have targets below a flake rate of 75%.

## Results

### RQ1: Which algorithm (FACF or Bisect) was more accurate in identifying culprit commits?

All versions of FACF were more accurate overall than all versions of Bisect (Figure 2). The difference was significant with a p-value \(< 10^{-12}\), below the adjusted \(10^{-6}\) significance level required.

### RQ2: What difference do algorithmic tweaks (such as adding deflaking runs to Bisect) make to accuracy?

The production version of FACF, FACF(all), was most accurate and significantly different than all other algorithms (Figure 2). This was followed by FACF(fr=.1) which set the floor of 10% on the estimated flake rate for tests. The other FACF variants were equally accurate.

### RQ3: How efficient is each algorithm as measured in number of test executions?

Figure 2 shows the most efficient algorithm was unsurprisingly Bisect(1) which does not attempt to do any extra executions to deflake test failures. The next most efficient algorithm was FACF(all) which was also the most accurate. As can be seen in the boxplot in Figure 2, the FACF variants tend to have many more extreme outliers in their cost distribution than the Bisect variants. This is because they account for the prior flake rate. An organization may control their cost by not culprit finding tests which are more than (for instance) 50% flaky. No such upper bound was established for this experiment.

### RQ4: What difference do algorithmic tweaks (such as adding deflaking runs to Bisect) make to efficiency?

First, both FACF(all) and FACF(priors) had less cost than the standard FACF. This indicates that while FACF(priors) does not improve accuracy it does improve efficiency of the algorithm. In particular many more culprits were found with just two builds.

Second, FACF(heur-thresholds) had no significant effect on cost nor did it show any improvement accuracy. We conclude that although the mathematical motivation may be sound, in the Google environment, we cannot validate a benefit to this optimization at this time.

### RQ5: Does flakiness affect culprit finding accuracy and cost?

Figures 3 and 4 show the accuracy and cost of culprit finding flaky and non-flaky culprits. For search ranges without a culprit, FACF(all) clearly dominates Bisect in accuracy and even has a small advantage in cost over Bisect(1).

When there is a culprit, the FACF variants are all more accurate than the Bisect variants according to the statistical tests. However, the difference is much less pronounced with Bisect(1) accuracy \(\sim\)96.1% and FACF(all) accuracy \(\sim\)97.5%. In terms of cost, Bisect(1) and Bisect(2) are the most efficient followed by the FACF variants.

We will note, a production culprit finder cannot know a priori if a breakage was caused by a flake. It would need to do deflaking runs to establish that, costing approximately \(\left\lceil{\frac{\,\textrm{log}\!\!\left({p}\right)}{\,\textrm{log}\!\!\left({\hat{f}_t}\right)}}\right\rceil\) where \(p\) is your desired confidence level. For \(p=10^{-4}\) and \(\hat{f} = .2\), this amounts to 6 extra runs, which would significantly increase the cost of bisection. However, as noted in Section 5.5, prior flakiness rates could be used to prune out a significant portion of flaky ranges (lowering cost) with a minimal hit to accuracy.

# Related Work

## Culprit Finding

Despite its industrial importance, culprit finding has been relatively less studied in the literature in comparison to topics such as Fault Localization (Agarwal and Agrawal 2014; Wong et al. 2016) (coverage based (J. a. Jones, Harrold, and Stasko 2002; J. A. Jones and Harrold 2005; Lucia et al. 2014; Henderson and Podgurski 2018; Henderson, Podgurski, and Kucuk 2019; Kucuk, Henderson, and Podgurski 2021), information retrieval based (J. Zhou, Zhang, and Lo 2012; Youm et al. 2015; Ciborowska and Damevski 2022), or slicing based (Podgurski and Clarke 1990; Horwitz and Reps 1992; Ren et al. 2004)), Bug Prediction (Lewis et al. 2013; Punitha and Chitra 2013; Osman et al. 2017), Test Selection (Engström, Runeson, and Skoglund 2010; Pan et al. 2022), Test Prioritization (de S. Campos Junior et al. 2017; Pan et al. 2022) and the SZZ algorithm for identifying bug inducing commits in the context of research studies (Śliwerski, Zimmermann, and Zeller 2005; Rodríguez-Pérez, Robles, and González-Barahona 2018; Borg et al. 2019; Wen et al. 2019). This is perhaps understandable as the problem only emerges in environments were it becomes to costly to run every test at every code submission.

The idea of using a binary search to locate the culprit is common,
but it is not completely clear who invented it first. The Christian
Couder of `git bisect`

wrote a comprehensive paper on its
implementation (Couder 2008) but
indicates there are other similar tools: “So what are the tools used to
fight regressions? [...] The only specific tools are test suites and
tools similar to `git bisect`

.” The first version of the
`git bisect`

command appears to have been written by Linus
Torvalds in 2005.^{5} Torvald’s commit message simply
states “This is useful for doing binary searching for problems.” The
source code for the mercurial bisect command `hg bisect`

states that it was inspired by the git command.^{6} The
Subversion (SVN) command, `svn bisect`

, also cites the git
command as inspiration.^{7} Therefore, as far as the authors can
tell bisection for finding culprits appears to have been invented by
Torvalds.

The Couder paper (Couder 2008)
cites a GitHub repository for a program called “BBChop,” which is
lightly documented and appears not entirely completed by a user
enigmatically named Ealdwulf Wuffinga (likely a pseudonym, as that was a
name of the King of East Anglia from 664-713).^{8}
This program claims to have also implemented a Bayesian search for
culprits. We gladly cede the throne for first invention of applying
Bayes rule to culprit finding to Ealdwulf and note that our invention
was independent of the work in BBChop.

More recently, work has been emerging on the industrial practice of Culprit Finding. In 2013, Ziftci and Ramavajjala gave a public talk at the Google Test Automation Conference in on Culprit Finding at Google (Ziftci and Ramavajjala 2013). They note, that by 2013 Google has already been using \(m\)-ary bisection based culprit finding for “small” and “medium” tests. They then give a preview of an approach elaborated on in Ziftci and Reardon’s 2017 paper (Ziftci and Reardon 2017) for culprit finding integration tests where test executions take a long time to run. The authors propose a suspiciousness metric based on the minimum build dependence distance and conduct a case study on the efficacy of using such a metric to surface potential culprits to developers. We utilize a similar build dependence distance as input to construct a prior probability (see Section 3.3) in this work but do not directly surface the metric to our end users. Finally, for ground truth they rely on the developers to report what the culprit version is. In contrast, the empirical evaluation we present in this new work is fully automated and does not rely on developers.

In 2017, Saha and Gligoric (Saha and Gligoric 2017) proposed accelerating the traditional bisect algorithm via Test Selection techniques. They use Coverage Based Test Selection (Z. Q. Zhou 2010; Musa et al. 2015) to choose which commits are most likely to affect the test results at the failing commit. This technique can be viewed as fine grained, dynamic version of the static build dependence selection strategy we employ at Google.

In 2019, Najafi *et al.* (Najafi, Rigby, and Shang 2019) looked at
a similar problem to the traditional culprit finding problem we examine
here. In their scenario, there is a submission queue that queues up
commits to integrate into the main development branch. It batches these
waiting commits and tests them together. If a test fails, they need to
culprit find to determine the culprit commit. The authors evaluate using
a ML-driven risk based batching approach. In 2022, the same research
group re-evaluated the 2019 paper on an open source dataset in
Beheshtian *et al.*’s 2022 paper (Beheshtian, Bavand, and Rigby 2022).
They found that in the new environment the risk based batching didn’t do
as well as a new and improved combinatorics based batching scheme for
identifying the culprit commits.

James Keenan gave a presentation in 2019 at the Perl Conference in
which he presented a concept, *multisection*, for dealing with
multiple bugs in the same search range (Keenan 2019). Ideally, industrial
culprit finders would automatically detect that there are multiple
distinct bug inducing commits.

In 2021, two papers looked at using coverage based data for
accelerating bug localization. An and Yoo (An and
Yoo 2021) used coverage data to accelerate both bisection and
SZZ (Śliwerski, Zimmermann,
and Zeller 2005) and found significant speedups. Wen *et
al.* (Wen et al. 2021)
combined traditional Coverage Based Statistical Fault Localization (J. a. Jones, Harrold, and Stasko 2002)
with historical information to create a new suspiciousness score (Sun and Podgurski 2016). This fault
localization method could be used in a culprit finding context by using
the line rankings to rank the commits.

Finally, in 2022 Frolin Ocariza (Ocariza 2022) published a paper on bisecting performance regressions. There are strong connections between a flaky test and a performance regression as a performance regression may not happen 100% of the time. Furthermore, the “baseline” version may randomly have poor performance due to environmental or other factors. Ocariza also arrives at a probabilistic approach, using a Bayesian model to determine whether a run at a particular version is exhibiting the performance regression or not. While mathematically related to our work here and complementary, the approach is distinct. The authors note that their technique can be combined with a Noisy Binary Search citing Karp (Karp and Kleinberg 2007) or with a multisection search citing Keenan (Keenan 2019).

## Noisy Binary Search

There is a vast literature on Rényi-Ulam games and Noisy Searching
problems (doubly so when considering their connection to error
correcting codes)! We direct readers to the Pelc survey (Pelc 2002) as a starting point. We will
highlight a few articles here. First and foremost, the Ben Or and
Hassidim paper (Ben-Or and Hassidim
2008) from 2008 most clearly explains the problem in terms of
a Bayesian inference, which is the formulation we use here. Second,
Waeber *et al.* in 2013 (Waeber, Frazier, and Henderson 2013)
discuss the theoretical foundations of these *probabilistic bisection
algorithms*. Finally, according to Waeber, Horstein first described
this algorithm in the context of error correcting codes in 1963 (Horstein 1963).

# Conclusion

Flake Aware Culprit Finding (FACF) is both accurate, efficient, and able to flexibly incorporate prior information on the location of a culprit. A large scale empirical study on real test and build breakages found FACF to be significantly more effective than a traditional bisection search while not increasing cost over a deflaked bisection.

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In practice the restriction on network usage on TAP is somewhat loose. There are legacy tests that have been tagged to allow them to utilize the network and there is an on going effort to fully eliminate network usage on TAP.↩︎

Other CI platforms exist for integration tests that span multiple machines, use large amounts of RAM, or take a very long time to run. The algorithm presented in this paper has also been implemented for one of those CI systems but we will not present an empirical evaluation of its performance in that environment in this paper. In general, Culprit Finding is much more difficult in such environments as tests may use a mixture of code from different versions and network resources may be shared across tests.↩︎

An internal version of Bazel https://bazel.build/.↩︎

The exact number of hours isn’t so important. The main thing is to repeat the verification at a suitable interval from the original attempt.↩︎

https://github.com/git/git/commit/8b3a1e056f2107deedfdada86046971c9ad7bb87↩︎

https://www.mercurial-scm.org/repo/hg/file/52464a20add0/mercurial/hbisect.py, https://www.mercurial-scm.org/repo/hg/rev/a7678cbd7c28↩︎

https://metacpan.org/release/INFINOID/App-SVN-Bisect-1.1/source/README↩︎