Check Machin-like formulas: Difference between revisions

<lang d>import std.stdio, std.regex, std.conv, std.string, std.typecons,

std.array, std.range;

import arithmetic_rational: Rational;

immutable equationText =

"pi/4 = arctan(1/2) + arctan(1/3)

pi/4 = 2*arctan(1/3) + arctan(1/7)

pi/4 = 4*arctan(1/5) - arctan(1/239)

pi/4 = 5*arctan(1/7) + 2*arctan(3/79)

pi/4 = 5*arctan(29/278) + 7*arctan(3/79)

pi/4 = arctan(1/2) + arctan(1/5) + arctan(1/8)

pi/4 = 4*arctan(1/5) - arctan(1/70) + arctan(1/99)

pi/4 = 5*arctan(1/7) + 4*arctan(1/53) + 2*arctan(1/4443)

pi/4 = 6*arctan(1/8) + 2*arctan(1/57) + arctan(1/239)

pi/4 = 8*arctan(1/10) - arctan(1/239) - 4*arctan(1/515)

pi/4 = 12*arctan(1/18) + 8*arctan(1/57) - 5*arctan(1/239)

pi/4 = 16*arctan(1/21) + 3*arctan(1/239) + 4*arctan(3/1042)

pi/4 = 22*arctan(1/28) + 2*arctan(1/443) - 5*arctan(1/1393) - 10*arctan(1/11018)

pi/4 = 22*arctan(1/38) + 17*arctan(7/601) + 10*arctan(7/8149)

pi/4 = 44*arctan(1/57) + 7*arctan(1/239) - 12*arctan(1/682) + 24*arctan(1/12943)

pi/4 = 88*arctan(1/172) + 51*arctan(1/239) + 32*arctan(1/682) + 44*arctan(1/5357) + 68*arctan(1/12943)

pi/4 = 88*arctan(1/172) + 51*arctan(1/239) + 32*arctan(1/682) + 44*arctan(1/5357) + 68*arctan(1/12944)";

alias Pair = Tuple!(int, Rational);

Pair[][] parseEquations(in string text) {

r"arctan\((?P<num>\d+)/(?P<denom>\d+)\)", "g");

foreach (const line; text.splitLines()) {

foreach (part; std.string.split(line, "=")[1].match(r)) {

immutable string mul = part["mul"];

immutable string num = part["num"];

immutable string denom = part["denom"];

(mul.empty ? 1 : to!int(mul)),

Rational(to!int(num),

denom.empty ? 1 : to!int(denom)));

/*const*/ auto a = tanEval(coef / 2, f);

/*const*/ auto b = tanEval(coef - coef / 2, f);

/*const*/ auto a = tans(xs[0 .. xs.length / 2]);

/*const*/ auto b = tans(xs[xs.length / 2 .. $]);

/*const*/ auto machins = parseEquations(equationText);

foreach (machin, eqn; zip(machins, equationText.splitLines())) {

/*const*/ auto ans = tans(machin);