Вычислить с точностью ε сумму и указать количество учтенных слагаемых

#include <iostream>
#include <stdint.h>
#include <math.h>
 
class KahanSummator {
  double sum;
  volatile double c;
 
public:
  KahanSummator()
      : sum(0.0)
      , c(0.0) {};
  void add(double x)
  {
    double y = x - c;
    double t = sum + y;
    c = (t - sum) - y;
    sum = t;
  };
  double result()
  {
    return sum;
  };
};
 
class Series {
  double a_k;
  double x;
  uint64_t k;
  KahanSummator sum;
 
public:
  Series(double x)
      : a_k(-1.0 * x * x / 9.0)
      , x(x)
      , k(0)
      , sum() {};
  double next()
  {
    ++k;
    a_k *= (-1.0) * (x * x * x * x) / (81.0 * ((2 * k) * (2 * k + 1)));
    sum.add(a_k);
    return a_k;
  };
  double result()
  {
    return sum.result();
  };
};
 
void task(double x, double epsilon)
{
  const uint64_t MAX_STEPS = 100LL;
  const uint64_t MIN_STEPS = 10LL;
  Series series(x);
 
  std::cout << "Starting with:" << std::endl;
  std::cout << "x = " << x << std::endl;
  std::cout << "ε = " << epsilon << std::endl;
  std::cout << "Working..." << std::endl;
 
  for (uint64_t k = 1; k <= MAX_STEPS; ++k) {
    double a_k = series.next();
    std::cout << "a_" << k << " =  " << a_k << std::endl;
    if ((k > MIN_STEPS) && (fabs(a_k) < epsilon)) {
      std::cout << "Results:" << std::endl;
      std::cout << "S = " << series.result() << std::endl;
      std::cout << "k = " << k << std::endl;
      std::cout << std::endl;
      return;
    }
  }
 
  std::cout << "ERROR: stop on k = " << MAX_STEPS << std::endl;
  std::cout << "ERROR: current S = " << series.result() << std::endl;
  std::cout << std::endl;
};
 
int main()
{
  task(0.1, 1e-10);
  task(1.1, 1e-100);
  task(1000.0, 1e-10);
  return 0;
};