The aim of the kata is to try to show how difficult it can be to calculate decimals of an irrational number with a certain precision. We have chosen to get a few decimals of the number "pi" using
the following infinite series (Leibniz 1646–1716): 

PI / 4 = 1 - 1/3 + 1/5 - 1/7 + ... which gives an approximation of PI / 4.

http://en.wikipedia.org/wiki/Leibniz_formula_for_%CF%80

To have a measure of the difficulty we will count how many iterations are needed to calculate PI with a given precision. 

There are several ways to determine the precision of the calculus but to keep things easy we will calculate to within epsilon of your language Math::PI constant. In other words we will stop  the iterative process when the absolute value of the difference between our calculation and the Math::PI constant of the given language is less than epsilon.

Your function returns an array or an arrayList or a string or a tuple depending on the language (See sample tests) where your approximation of PI has 10 decimals 

In Haskell you can use the function "trunc10Dble" (see "Your solution"); in Clojure you can use the function "round" (see "Your solution");in OCaml or Rust the function "rnd10" (see "Your solution") in order to avoid discussions about the result.

Example :
```
your function calculates 1000 iterations and 3.140592653839794 but returns:
iter_pi(0.001) --> [1000, 3.1405926538]
```

Unfortunately, this series converges too slowly to be useful, 
as it takes over 300 terms to obtain a 2 decimal place precision. 
To obtain 100 decimal places of PI, it was calculated that
one would need to use at least 10^50 terms of this expansion!

About PI : http://www.geom.uiuc.edu/~huberty/math5337/groupe/expresspi.html

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

def _disabled_input(*args, **kwargs):
    raise RuntimeError("input() is disabled in callable mode")
builtins.input = _disabled_input

ns = {"__name__": "__judge__"}  # prevent if __name__ == "__main__" blocks
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'import math\ndef iter_pi(epsilon):\n    pi,k = 0,0\n    while abs(pi-math.pi/4) > epsilon/4:\n        pi += (-1)**k * 1/(2*k + 1)\n        k += 1\n    pi *=4\n\n    return [k , round(pi, 10)]'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'iter_pi'
if _fn_name:
    if "Solution" in ns:
        try:
            _obj = ns["Solution"]()
            if hasattr(_obj, _fn_name):
                _target = getattr(_obj, _fn_name)
        except Exception:
            _target = None
    if _target is None and _fn_name in ns and callable(ns[_fn_name]):
        _target = ns[_fn_name]
# Fallback: if there's exactly one user-defined function, use it
if _target is None:
    _cands = [v for k, v in ns.items() if callable(v) and getattr(v, "__module__", "") in ("__judge__", "__main__")]
    _user_funcs = [c for c in _cands if getattr(c, "__name__", "").startswith("_") is False]
    if len(_user_funcs) == 1:
        _target = _user_funcs[0]
if _target is None:
    raise RuntimeError(f"Could not resolve callable '{_fn_name}'")

_raw = sys.stdin.read().strip()
if _raw:
    _parsed = json.loads(_raw)
    if isinstance(_parsed, dict):
        _kwargs = _parsed.get("kwargs", {})
        _args = _parsed.get("args", [])
    else:
        _args, _kwargs = _parsed, {}
else:
    _args, _kwargs = [], {}
if not isinstance(_args, (list, tuple)):
    _args = [_args]
_res = _target(*_args, **_kwargs)
try:
    sys.stdout.write(repr(_res) + "\n")
except Exception:
    pass

```

Measured memory_bytes: 5664