text: #include <stan/math/mix/scal.hpp>
  #include <gtest/gtest.h>
  #include <boost/math/special_functions/cbrt.hpp>
  #include <test/unit/math/rev/scal/fun/util.hpp>
  #include <test/unit/math/mix/scal/fun/nan_util.hpp>
  
  TEST(AgradFwdCbrt, FvarVar_1stDeriv) {
    using stan::math::cbrt;
    using stan::math::fvar;
    using stan::math::var;
  
    fvar<var> x(1.5, 1.3);
    fvar<var> a = cbrt(x);
  
    EXPECT_FLOAT_EQ(cbrt(1.5), a.val_.val());
    EXPECT_FLOAT_EQ(1.3 / (3 * cbrt(1.5) * cbrt(1.5)), a.d_.val());
  
    AVEC y = createAVEC(x.val_);
    VEC g;
    a.val_.grad(y, g);
    EXPECT_FLOAT_EQ(1.0 / (3.0 * cbrt(1.5) * cbrt(1.5)), g[0]);
  }
  
  TEST(AgradFwdCbrt, FvarVar_2ndDeriv) {
    using stan::math::cbrt;
    using stan::math::fvar;
    using stan::math::var;
  
    fvar<var> x(1.5, 1.3);
    fvar<var> a = cbrt(x);
  
    AVEC y = createAVEC(x.val_);
    VEC g;
    a.d_.grad(y, g);
    EXPECT_FLOAT_EQ(-2.0 * 1.3 / 3.0 / (3.0 * cbrt(1.5) * cbrt(1.5) * 1.5), g[0]);
  }
  
  TEST(AgradFwdCbrt, FvarFvarVar_1stDeriv) {
    using stan::math::cbrt;
    using stan::math::fvar;
    using stan::math::var;
  
    fvar<fvar<var> > x;
    x.val_.val_ = 1.5;
    x.val_.d_ = 2.0;
  
    fvar<fvar<var> > a = cbrt(x);
  
    EXPECT_FLOAT_EQ(cbrt(1.5), a.val_.val_.val());
    EXPECT_FLOAT_EQ(2.0 / (3.0 * cbrt(1.5) * cbrt(1.5)), a.val_.d_.val());
    EXPECT_FLOAT_EQ(0, a.d_.val_.val());
    EXPECT_FLOAT_EQ(0, a.d_.d_.val());
  
    AVEC p = createAVEC(x.val_.val_);
    VEC g;
    a.val_.val_.grad(p, g);
    EXPECT_FLOAT_EQ(1.0 / (3.0 * cbrt(1.5) * cbrt(1.5)), g[0]);
  
    fvar<fvar<var> > y;
    y.val_.val_ = 1.5;
    y.d_.val_ = 2.0;
  
    fvar<fvar<var> > b = cbrt(y);
    EXPECT_FLOAT_EQ(cbrt(1.5), b.val_.val_.val());
    EXPECT_FLOAT_EQ(0, b.val_.d_.val());
    EXPECT_FLOAT_EQ(2.0 / (3.0 * cbrt(1.5) * cbrt(1.5)), b.d_.val_.val());
    EXPECT_FLOAT_EQ(0, b.d_.d_.val());
  
    AVEC q = createAVEC(y.val_.val_);
    VEC r;
    b.val_.val_.grad(q, r);
    EXPECT_FLOAT_EQ(1.0 / (3.0 * cbrt(1.5) * cbrt(1.5)), r[0]);
  }
  
  TEST(AgradFwdCbrt, FvarFvarVar_2ndDeriv) {
    using stan::math::cbrt;
    using stan::math::fvar;
    using stan::math::var;
  
    fvar<fvar<var> > x;
    x.val_.val_ = 1.5;
    x.val_.d_ = 2.0;
  
    fvar<fvar<var> > a = cbrt(x);
  
    AVEC p = createAVEC(x.val_.val_);
    VEC g;
    a.val_.d_.grad(p, g);
    EXPECT_FLOAT_EQ(2.0 * -2.0 / 3.0 / (3.0 * cbrt(1.5) * cbrt(1.5) * 1.5), g[0]);
  
    fvar<fvar<var> > y;
    y.val_.val_ = 1.5;
    y.d_.val_ = 2.0;
  
    fvar<fvar<var> > b = cbrt(y);
  
    AVEC q = createAVEC(y.val_.val_);
    VEC r;
    b.d_.val_.grad(q, r);
    EXPECT_FLOAT_EQ(2.0 * -2.0 / 3.0 / (3.0 * cbrt(1.5) * cbrt(1.5) * 1.5), r[0]);
  }
  TEST(AgradFwdCbrt, FvarFvarVar_3rdDeriv) {
    using stan::math::cbrt;
    using stan::math::fvar;
    using stan::math::var;
  
    fvar<fvar<var> > x;
    x.val_.val_ = 1.5;
    x.val_.d_ = 1.0;
    x.d_.val_ = 1.0;
  
    fvar<fvar<var> > a = cbrt(x);
  
    AVEC p = createAVEC(x.val_.val_);
    VEC g;
    a.d_.d_.grad(p, g);
    EXPECT_FLOAT_EQ(0.12562021866154533528757664877253, g[0]);
  }
  
  struct cbrt_fun {
    template <typename T0>
    inline T0 operator()(const T0& arg1) const {
      return cbrt(arg1);
    }
  };
  
  TEST(AgradFwdCbrt, cbrt_NaN) {
    cbrt_fun cbrt_;
    test_nan_mix(cbrt_, false);
  }
  