1 #ifndef STAN_MATH_FWD_SCAL_FUN_PHI_APPROX_HPP
2 #define STAN_MATH_FWD_SCAL_FUN_PHI_APPROX_HPP
3 
4 #include <stan/math/fwd/core.hpp>
5 #include <stan/math/prim/scal/fun/inv_logit.hpp>
6 #include <cmath>
7 
8 namespace stan {
9 namespace math {
10 
11 /**
12  * Return an approximation of the unit normal cumulative
13  * distribution function (CDF).
14  *
15  * @tparam T scalar type of forward-mode autodiff variable
16  * argument.
17  * @param x argument
18  * @return approximate probability random sample is less than or
19  * equal to argument
20  */
21 template <typename T>
Phi_approx(const fvar<T> & x)22 inline fvar<T> Phi_approx(const fvar<T>& x) {
23   using std::pow;
24   return inv_logit(0.07056 * pow(x, 3.0) + 1.5976 * x);
25 }
26 
27 }  // namespace math
28 }  // namespace stan
29 #endif
30