Added the ability for microbenchmarks to print the probability of the result. (#101154)

dev/benchmarks/microbenchmarks/lib/common.dart

@@ -3,6 +3,50 @@
 // found in the LICENSE file.
 
 import 'dart:convert' show json;
+import 'dart:math' as math;
+
+double _doNormal(
+    {required double mean, required double stddev, required double x}) {
+  return (1.0 / (stddev * math.sqrt(2.0 * math.pi))) *
+      math.pow(math.e, -0.5 * math.pow((x - mean) / stddev, 2.0));
+}
+
+double _doMean(List<double> values) =>
+    values.reduce((double x, double y) => x + y) / values.length;
+
+double _doStddev(List<double> values, double mean) {
+  double stddev = 0.0;
+  for (final double value in values) {
+    stddev += (value - mean) * (value - mean);
+  }
+  return math.sqrt(stddev / values.length);
+}
+
+double _doIntegral({
+  required double Function(double) func,
+  required double start,
+  required double stop,
+  required double resolution,
+}) {
+  double result = 0.0;
+  while (start < stop) {
+    final double value = func(start);
+    result += resolution * value;
+    start += resolution;
+  }
+  return result;
+}
+
+/// Probability is defined as the probability that the mean is within the
+/// [margin] of the true value.
+double _doProbability({required double mean, required double stddev, required double margin}) {
+  return _doIntegral(
+    func: (double x) => _doNormal(mean: mean, stddev: stddev, x: x),
+    start: (1.0 - margin) * mean,
+    stop: (1.0 + margin) * mean,
+    resolution: 0.001,
+  );
+}
 
 /// This class knows how to format benchmark results for machine and human
 /// consumption.
@@ -33,6 +77,28 @@ class BenchmarkResultPrinter {
     _results.add(_BenchmarkResult(description, value, unit, name));
   }
 
+  /// Adds a benchmark result to the list of results and a probability of that
+  /// result.
+  ///
+  /// The probability is calculated as the probability that the mean is +- 5% of
+  /// the true value.
+  ///
+  /// See also [addResult].
+  void addResultStatistics({
+    required String description,
+    required List<double> values,
+    required String unit,
+    required String name,
+  }) {
+    final double mean = _doMean(values);
+    final double stddev = _doStddev(values, mean);
+    const double margin = 0.05;
+    final double probability = _doProbability(mean: mean, stddev: stddev, margin: margin);
+    _results.add(_BenchmarkResult(description, mean, unit, name));
+    _results.add(_BenchmarkResult('$description - probability margin of error $margin', probability,
+        'percent', '${name}_probability_5pct'));
+  }
+
   /// Prints the results added via [addResult] to standard output, once as JSON
   /// for computer consumption and once formatted as plain text for humans.
   void printToStdout() {

dev/benchmarks/microbenchmarks/lib/stocks/build_bench.dart

@@ -21,6 +21,7 @@ Future<void> main() async {
 
   final Stopwatch watch = Stopwatch();
   int iterations = 0;
+  final List<double> values = <double>[];
 
   await benchmarkWidgets((WidgetTester tester) async {
     stocks.main();
@@ -33,8 +34,10 @@ Future<void> main() async {
     final Element appState = tester.element(find.byType(stocks.StocksApp));
     binding.framePolicy = LiveTestWidgetsFlutterBindingFramePolicy.benchmark;
 
+    Duration elapsed = Duration.zero;
+    while (elapsed < kBenchmarkTime) {
+      watch.reset();
       watch.start();
-    while (watch.elapsed < kBenchmarkTime) {
       appState.markNeedsBuild();
       // We don't use tester.pump() because we're trying to drive it in an
       // artificially high load to find out how much CPU each frame takes.
@@ -43,15 +46,17 @@ Future<void> main() async {
       // We use Timer.run to ensure there's a microtask flush in between
       // the two calls below.
       await tester.pumpBenchmark(Duration(milliseconds: iterations * 16));
+      watch.stop();
       iterations += 1;
+      elapsed += Duration(microseconds: watch.elapsedMicroseconds);
+      values.add(watch.elapsedMicroseconds.toDouble());
     }
-    watch.stop();
   });
 
   final BenchmarkResultPrinter printer = BenchmarkResultPrinter();
-  printer.addResult(
+  printer.addResultStatistics(
     description: 'Stock build',
-    value: watch.elapsedMicroseconds / iterations,
+    values: values,
     unit: 'µs per iteration',
     name: 'stock_build_iteration',
   );