int main(int argc, char *argv[]) { SymEngine::print_stack_on_segfault(); RCP<const Basic> e = sin(integer(1)); double r, r_exact; for (int i = 0; i < 10000; i++) e = pow(add(mul(add(e, pow(integer(2), integer(-3))), integer(3)), integer(1)), div(integer(2), integer(3))); // Too long: // std::cout << "Evaluating: " << *e << std::endl; auto t1 = std::chrono::high_resolution_clock::now(); for (int i = 0; i < 500; i++) r = eval_double(*e); auto t2 = std::chrono::high_resolution_clock::now(); std::cout << std::chrono::duration_cast<std::chrono::milliseconds>(t2 - t1) .count() / 500. << "ms" << std::endl; /* In SymPy for few iterations: In [7]: sympify("(1 + 3*(1/8 + (1 + 3*(1/8 + (1 + 3*(1/8 + (1 + 3*(1/8 + (1 + 3*(1/8 + sin(1)))^(2/3)))^(2/3)))^(2/3)))^(2/3)))^(2/3)").n(20) Out[7]: 8.0152751504518535013 // r_exact = 8.0152751504518535013; Here is code to use SymPy for more iterations: In [5]: e = sin(1) In [6]: for i in range(10): ...: e = ((e+2**(-S(3)))*3 + 1)**(S(2)/3) ...: In [7]: e.n(20) Out[7]: 9.6473976427977306146 But unfortunately SymPy can't do more than perhaps 10 or 20 iterations, while we need to test ~10000. However, the numbers seem to converge to 9.85647... */ r_exact = 9.8564741713701043569; std::cout << "r (double) = " << r << std::endl; std::cout << "r (exact) = " << r_exact << std::endl; std::cout << "error = " << std::abs(r - r_exact) << std::endl; return 0; }
double S2() { RCP<const Basic> x = symbol("x"); RCP<const Basic> y = symbol("y"); RCP<const Basic> z = symbol("z"); RCP<const Basic> e; RCP<const Basic> f; e = pow(add(pow(x, sin(x)), add(pow(y, cos(y)), pow(z, add(x, y)))), integer(100)); auto t1 = std::chrono::high_resolution_clock::now(); f = expand(e); auto t2 = std::chrono::high_resolution_clock::now(); return std::chrono::duration_cast<std::chrono::nanoseconds>(t2-t1).count()/1000000000.0; }
using SymEngine::E; using SymEngine::EulerGamma; using SymEngine::loggamma; using SymEngine::gamma; using SymEngine::vec_basic; using SymEngine::rational_class; using SymEngine::max; using SymEngine::min; using SymEngine::min; using SymEngine::NotImplementedError; using SymEngine::SymEngineException; TEST_CASE("eval_double: eval_double", "[eval_double]") { RCP<const Basic> r1, r2, r3, r4, r5; r1 = sin(integer(1)); r2 = sin(div(integer(1), integer(2))); r3 = div(one, integer(5)); r4 = integer(5); #ifdef HAVE_SYMENGINE_MPFR SymEngine::mpfr_class a(100); SymEngine::eval_mpfr(a.get_mpfr_t(), *r1, MPFR_RNDN); r5 = SymEngine::real_mpfr(std::move(a)); #else r5 = SymEngine::real_double(SymEngine::eval_double(*r1)); #endif std::vector<std::pair<RCP<const Basic>, double>> vec = { {r1, 0.841470984808}, {r2, 0.479425538604},
REQUIRE(unified_eq(gens, rgens)); // 2**(2*x + 1) -> (2**x) basic = pow(i2, add(mul(i2, x), one)); gens = _find_gens_poly(basic); rgens = {{twopx, one}}; REQUIRE(unified_eq(gens, rgens)); // 2**(x**(x+1))-> (2**(x**(x+1))) basic = pow(i2, pow(x, add(x, one))); gens = _find_gens_poly(basic); rgens = {{basic, one}}; REQUIRE(unified_eq(gens, rgens)); // sin(x)*sin(y) + sin(x)**2 + sin(y) -> (sin(x), sin(y)) basic = add(mul(sin(x), sin(y)), add(pow(sin(x), i2), sin(y))); gens = _find_gens_poly(basic); rgens = {{sin(x), one}, {sin(y), one}}; REQUIRE(unified_eq(gens, rgens)); // 2**x + 2**(x+y) -> (2**x, 2**y) basic = add(twopx, pow(i2, add(x, y))); gens = _find_gens_poly(basic); rgens = {{pow(i2, y), one}, {twopx, one}}; REQUIRE(unified_eq(gens, rgens)); // x**x + x**(x/2) + x**(x/3) -> (x**(x/6)) basic = add(pow(x, x), add(pow(x, div(x, i2)), pow(x, div(x, i3)))); gens = _find_gens_poly(basic); rgens = {{pow(x, x), rcp_static_cast<const Number>(div(one, i6))}}; REQUIRE(unified_eq(gens, rgens));
using SymEngine::cosh; using SymEngine::tanh; using SymEngine::coth; using SymEngine::asinh; using SymEngine::acosh; using SymEngine::atanh; using SymEngine::acoth; using SymEngine::log; using SymEngine::pi; using SymEngine::E; using SymEngine::vec_basic; TEST_CASE("eval_double: eval_double", "[eval_double]") { RCP<const Basic> r1, r2, r3, r4; r1 = sin(integer(1)); r2 = sin(div(integer(1), integer(2))); r3 = div(one, integer(5)); r4 = integer(5); std::vector<std::pair<RCP<const Basic>, double>> vec = { { r1, 0.841470984808 }, { r2, 0.479425538604 }, { add(r1, r2), 1.320896523412 }, { mul(r1, r2), 0.403422680111 }, { pow(r1, r2), 0.920580670898 }, { tan(pow(r1, r2)), 1.314847038576 }, { add(sin(r3), add(cos(r4), add(tan(r3), add(sec(integer(6)), add(csc(r4), cot(r4)))))), 0.387875350057 }, { add(asin(r3), add(acos(r3), add(atan(r3), add(asec(integer(6)), add(acsc(r4), acot(r4)))))), 3.570293614860 }, { add(sinh(one), add(cosh(one), add(tanh(one), coth(one)))), 4.792911269914 }, { add(asinh(r4), add(acosh(r4), add(atanh(r3), acoth(r4)))), 5.010335118942 },