#include <cmath>
#include <cstdint>
#include <optional>

struct Rates { double fps; double normalizedFrames; };

// Standalone illustration of the measurement formula, not a rendering runner.
std::optional<Rates> MakeRates(std::uint64_t frames,
                              double elapsedMs,
                              double nominalMs) {
    if (!std::isfinite(elapsedMs) || elapsedMs <= 0 ||
        !std::isfinite(nominalMs) || nominalMs <= 0) {
        return std::nullopt;
    }
    const double fps = static_cast<double>(frames) * 1000.0 / elapsedMs;
    const double score = static_cast<double>(frames) * nominalMs / elapsedMs;
    return Rates{fps, score};
}