#include <cmath>

static const double INV_PI = 0.318309886183790671537768;

static const double c0 = +1.0;
static const double c1 = -1.6449340668482264364724e-0; // pi^2/3!
static const double c2 = +8.1174242528335364363700e-1; // pi^4/5!
static const double c3 = -1.9075182412208421369647e-1; // pi^6/7!
static const double c4 = +2.6147847817654800504653e-2; // pi^8/9!
static const double c5 = -2.3460810354558236375089e-3; // pi^10/11!

/*
 * Let's compute x + c0.x^3 + c1.x^5 + c2.x^7 + c3.x^9 + c4.x^11 + c5.x^13
 */

double sin1(double x)
{
    double absx = fabs(x * INV_PI);
    double x2 = absx * absx;

    /* 5 multiplications */
    double taylor = ((((c5 * x2 + c4) * x2 + c3) * x2 + c2) * x2 + c1) * x2 + c0;
    /* */

    return x * taylor;
}

double sin2(double x)
{
    double absx = fabs(x * INV_PI);
    double x2 = absx * absx;

    /* 6 multiplications */
    double x4 = x2 * x2;
    double sub1 = (c4 * x4 + c2) * x4 + c0;
    double sub2 = (c5 * x4 + c3) * x4 + c1;
    double taylor = sub2 * x2 + sub1;
    /* */

    return x * taylor;
}

double sin3(double x)
{
    double absx = fabs(x * INV_PI);
    double x2 = absx * absx;

    /* 7 multiplications */
    double x4 = x2 * x2;
    double x6 = x4 * x2;
    double sub1 = (c2 * x2 + c1) * x2 + c0;
    double sub2 = (c5 * x2 + c4) * x2 + c3;
    double taylor = sub2 * x6 + sub1;
    /* */

    return x * taylor;
}