Leibiz formula for pi

leibnizAndE.ts

import { isArray, isString, isFunction } from "lodash";

const { performance } = require("perf_hooks");

type Parameters<Fn> = Fn extends (...args: infer T) => any ? T : never;

const trampoline = <Fn extends (...args: any[]) => any>(
  fn: Fn,
  ...args: Parameters<Fn>
) => {
  let result = fn(...args);
  let i: number = 0;
  while (result instanceof Function) {
    result = result();
  }
  return result as ReturnType<Fn>;
};

const piOver4 = (precision: number) => {
  const _piOver4 = (precision: number, current = 0, iteration = 0): number => {
    const sign = iteration % 2 ? -1 : 1;
    const nextApproximation = current + sign / (1 + 2 * iteration);
    return Math.abs(current - nextApproximation) <= precision / 4
      ? (nextApproximation as any)
      : ((() => _piOver4(precision, nextApproximation, iteration + 1)) as any);
  };
  return trampoline(_piOver4, precision);
};

const pi = (precision: number) => 4 * piOver4(precision);

const funcTimer = <Fn extends (...args: any[]) => any>(
  fn: Fn,
  ...args: Parameters<Fn>
) => {
  let result: ReturnType<Fn>;
  const start = performance.now();
  result = fn(...args);
  const end = performance.now();
  console.log({
    time: (end - start).toFixed(3) + "ms",
    result
  });
  return result;
};

const pi_while = (precision: number) => {
  let approximation;
  let nextApproximation = 0;
  let iteration: number = 0;
  do {
    approximation = nextApproximation;
    const sign = iteration % 2 ? -1 : 1;
    const summand = sign / (1 + 2 * iteration);
    nextApproximation = nextApproximation + summand;
    iteration++;
  } while (Math.abs(nextApproximation - approximation) > precision / 4);
  return 4 * nextApproximation;
};

const factorial = (n: number): number => (n === 0 ? 1 : n * factorial(n - 1));

const e_while = (precision: number) => {
  let approximation: number;
  let nextApproximation: number = 0;
  let iteration = 0;
  do {
    approximation = nextApproximation;
    const summand = 1 / factorial(iteration);
    nextApproximation += summand;
    iteration++;
  } while (Math.abs(nextApproximation - approximation) > precision);
  return nextApproximation;
};

const timedPi = (precision: number) => funcTimer(pi, precision);
const timedPi_while = (precision: number) => funcTimer(pi_while, precision);
const timedE_while = (precision: number) => funcTimer(e_while, precision);

[
  0.1,
  0.01,
  0.001,
  0.0001,
  0.00001,
  0.000001,
  0.0000001,
  0.00000001,
  0.000000001,
  0.0000000001,
  0.00000000001,
  0.000000000001,
  0.0000000000001,
  0.00000000000001,
  0.000000000000001,
  0.0000000000000001,
  0.00000000000000001
].forEach(timedE_while);

The while version had these times

{ time: '0.189ms', result: 3.189184782277596 }
{ time: '0.019ms', result: 3.1465677471829556 }
{ time: '0.177ms', result: 3.1420924036835256 }
{ time: '2.920ms', result: 3.1416426510898874 }
{ time: '1.324ms', result: 3.141597653564762 }
{ time: '5.234ms', result: 3.1415931535894743 }
{ time: '56.545ms', result: 3.1415927035898146 }
{ time: '532.923ms', result: 3.1415926485894077 }
{ time: '5139.991ms', result: 3.141592653088077 }

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

{ time: '0.277ms', result: 3.189184782277596 }
{ time: '0.041ms', result: 3.1465677471829556 }
{ time: '0.983ms', result: 3.1420924036835256 }
{ time: '5.079ms', result: 3.1416426510898874 }
{ time: '7.329ms', result: 3.141597653564762 }
{ time: '63.287ms', result: 3.1415931535894743 }
{ time: '566.173ms', result: 3.1415927035898146 }
{ time: '5674.105ms', result: 3.1415926485894077 }
{ time: '58817.543ms', result: 3.141592653088077 }

e

{ time: '0.160ms', result: 2.708333333333333 }
{ time: '0.007ms', result: 2.7166666666666663 }
{ time: '0.004ms', result: 2.7182539682539684 }
{ time: '0.004ms', result: 2.71827876984127 }
{ time: '0.004ms', result: 2.7182815255731922 }
{ time: '0.004ms', result: 2.7182818011463845 }
{ time: '0.005ms', result: 2.718281826198493 }
{ time: '0.005ms', result: 2.7182818282861687 }
{ time: '0.006ms', result: 2.7182818284467594 }
{ time: '0.007ms', result: 2.71828182845823 }
{ time: '0.007ms', result: 2.718281828458995 }
{ time: '0.006ms', result: 2.718281828458995 }
{ time: '0.007ms', result: 2.718281828459043 }
{ time: '0.008ms', result: 2.7182818284590455 }
{ time: '0.008ms', result: 2.7182818284590455 }
{ time: '0.008ms', result: 2.7182818284590455 }
{ time: '0.008ms', result: 2.7182818284590455 }