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You debug it against a written contract that states how wrong the program may be, for which inputs, and how often. Without that contract, “it’s allowed to be wrong” becomes an excuse for defects you cannot explain. With it, debugging becomes a measurement problem: check observed behavior against the tolerance, add runtime checks where failures matter in service, and use a debugger to find out why a violation happens.
Passing a handful of test cases, or finding a plausible local fix, does not show that a probabilistic or approximate program meets its target. The rest of this article explains how to build that contract and what to do when the program falls outside it.
Start with the question Adrian Sampson asks
Adrian Sampson’s 2016 essay “Probably Correct” frames the problem directly: how do you know whether a program is good enough if it is allowed to be wrong some of the time? He calls the underlying idea statistical correctness, meaning an evaluation of whether a program is good enough even when it is not always correct (Sampson, “Probably Correct,” 15 June 2016). The essay is useful because it refuses to define “good” in advance. As Sampson puts it:
The word good is intentionally vague: it might mean something about the output f writes to a file, or about how fast f runs, or whether f violated some security policy.
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That vagueness is the real starting point. A program that renders approximate images, ranks search results, or runs a sensor model can be “wrong” in several different ways, and each way needs its own tolerance. Debugging begins once you have chosen which way matters.
Step one: write the contract before you touch the code
A usable contract has four parts. Each one answers a question that a debugger cannot answer for you.
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| Contract element | Question it answers | Hypothetical entry for an image-compression step |
|---|---|---|
| Quality measure | What counts as a correct output? | A perceptual similarity score against a reference render |
| Input population | Which inputs must the guarantee cover? | Photos up to 4000 × 3000 pixels from the production upload queue |
| Tolerance | How wrong may an output be, and how often? | Score below the agreed threshold in no more than a rate the team has chosen and written down |
| Hard limits | Which failures are never acceptable? | Leaking metadata from a private upload, regardless of image quality |
The table is hypothetical; Sampson’s essay does not supply any of these values, and the numbers in a real contract come from the application’s requirements and risk. Two points deserve emphasis.
Name the quality measure explicitly
“Good enough” is not a metric. Pick something you can compute for each output, whether that is an accuracy score, a latency bound, a comparison against a reference, or a policy check. If the output is a file, measure the file. If the concern is speed, measure time. Sampson’s point is that the measure follows from what the program is meant to do.
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Separate tolerated errors from unacceptable failures
Some errors are a matter of degree: a slightly blurrier image or a ranking that swaps two near-equal results. Others are binary: exposing private data, violating a security policy, or corrupting a stored record. Put the second category in its own list with a zero-tolerance rule. Mixing the two produces the common mistake of treating a security violation as a quality issue that a good average can offset.
Why a few passing examples cannot settle the question
Once a tolerance exists, the evidence has to match it. If the claim is about a population of inputs, a set of successful examples is evidence only about those examples. Statistical correctness shifts the question from “did this input work?” to “what fraction of inputs in this population meet the criterion, and where do the failures cluster?”
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This has practical consequences:
- Record every observation with its input, output, and a pass or fail judgment against the contract, not just the failures you noticed.
- Include deliberately hard inputs, such as unusual sizes, extreme values, or edge conditions you already suspect, so that weak spots are not hidden by an easy sample.
- Report the rate along with the cases behind it. A rate without a breakdown by input type can conceal a region where the program fails badly.
- Do not infer a population-wide claim from a small sample without addressing sampling and uncertainty. Sampson’s framing supports the statistical view but does not prescribe a sample size, so choose one that fits the stakes and say how you chose it.
Testing and runtime checks answer different questions
Sampson describes two ways to enforce statistical correctness. The first is a testing analogy: evaluate behavior on selected cases and treat the results as evidence about the program’s correctness. The second is runtime checking: move the check into execution so that the program’s behavior is evaluated as it runs. The article describes the runtime approach as giving a stronger guarantee.
| Comparison axis | Testing analogy | Runtime checking |
|---|---|---|
| When the check runs | Before release or in a test harness | During execution, in service |
| Which inputs it observes | The cases you chose | The inputs the program actually receives |
| Kind of guarantee | Evidence from chosen cases | A runtime guarantee, which Sampson describes as stronger |
| Runtime cost and operational complexity | Not quantified in Sampson’s essay; depends on the application | Not quantified in Sampson’s essay; depends on the application |
In practice you usually need both. Tests tell you whether the program is likely to meet its target before you ship it. Runtime checks tell you whether it is meeting the target on real traffic, and they make violations visible when the test population turns out to differ from production.
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When observed behavior violates the contract: debugging with GDB
A violation tells you that the program is outside its tolerance. It does not tell you why. For that, a conventional debugger is still the right tool. The GNU Debugger (GDB) manual, maintained as living documentation at Debugging with GDB, describes starting a program, stopping on conditions, examining state, and experimenting with changes. Those capabilities help you locate the cause of a violation. Deciding whether the resulting behavior is acceptable remains the job of the contract.
A diagnostic sequence
- Reproduce the violation. Save the input that produced the failing output. If the failure is intermittent, log enough state to replay the same input later.
- Start the program under GDB. Run
gdb ./your-program, thenrunwith the saved input as arguments or via a file redirect. - Stop at the relevant location or condition. Use
break file.c:42for a line, or add a condition such asbreak score_output if score < 0.8so the program pauses only when the suspect situation occurs. - Inspect state. Use
print variableto examine values andbacktraceto see how execution reached that point. - Experiment with a correction. Use
set var variable = valueto test whether changing a value at that point restores acceptable behavior, thencontinueto see the downstream effect. - Make the change in source code and rebuild. A value tweak in the debugger proves only that the variable matters; the fix still has to be written and measured.
The GDB command names above are standard, but exact behavior can vary with compiler flags and debugger version. The manual is the authoritative reference for the commands in your environment.
Re-run the statistical check after every change
A fix for one failing case can move error elsewhere. Tightening a threshold may reduce one kind of error while increasing another, and a change that speeds the program may lower output quality on hard inputs. After any change, rerun the same measurement against the same input population and compare rates by category, not only the headline number.
Keep ordinary deterministic tests too. They catch regressions in code paths that have nothing to do with approximation, such as crashes, malformed output, or broken interfaces. The statistical check does not replace them; it sits beside them as the release criterion for the behavior the contract covers.
Troubleshooting: when the numbers do not behave
- The overall rate meets the target, but one input group fails. Break the measurement down by input type. A passing average can hide a population the contract is supposed to cover; either fix that group or narrow the contract explicitly.
- The failures seem random. Log seeds, input hashes, and relevant state so the failing case can be replayed. Random-looking behavior is often deterministic once inputs are recorded.
- A hard-limit violation appears. Treat it as a defect, not a tolerance question. Stop the release, reproduce it, and fix it before measuring quality again.
- Runtime checks are expensive. Sample a fraction of production traffic, check the most sensitive outputs first, and record the cost so the trade-off is visible rather than assumed.
What the contract cannot tell you
Sampson’s essay establishes the framing, not the numbers. It does not give a universal error threshold, a sample size, or a domain-specific safety policy. Those must come from the application’s requirements, its users, and the consequences of a miss. If the contract is vague, the debugging will be vague too, no matter how good the tools are.
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