\[\Re(\left(\frac{e^{xre + xim i} + e^{-\left(xre + xim i\right)}}{2 + 0 i}\right))\]

↓

\[\Re(\left(\frac{e^{-\left(xre + xim i\right)} + e^{xre + xim i}}{2 + 0 i}\right))\]

double f(double xre, double xim) {
        double r12073 = xre;
        double r12074 = xim;
        double r12075 = /* ERROR: no complex support in C */;
        double r12076 = exp(r12075);
        double r12077 = -r12075;
        double r12078 = exp(r12077);
        double r12079 = r12076 + r12078;
        double r12080 = 2.0;
        double r12081 = 0.0;
        double r12082 = /* ERROR: no complex support in C */;
        double r12083 = r12079 / r12082;
        double r12084 = /* ERROR: no complex support in C */;
        return r12084;
}

↓

double f(double xre, double xim) {
        double r12085 = xre;
        double r12086 = xim;
        double r12087 = /* ERROR: no complex support in C */;
        double r12088 = -r12087;
        double r12089 = exp(r12088);
        double r12090 = exp(r12087);
        double r12091 = r12089 + r12090;
        double r12092 = 2.0;
        double r12093 = 0.0;
        double r12094 = /* ERROR: no complex support in C */;
        double r12095 = r12091 / r12094;
        double r12096 = /* ERROR: no complex support in C */;
        return r12096;
}

\Re(\left(\frac{e^{xre + xim i} + e^{-\left(xre + xim i\right)}}{2 + 0 i}\right))

↓

\Re(\left(\frac{e^{-\left(xre + xim i\right)} + e^{xre + xim i}}{2 + 0 i}\right))

Derivation

Initial program 0.0
\[\Re(\left(\frac{\left(\left(e^{\left(xre + xim i\right)}\right) + \left(e^{\left(-\left(xre + xim i\right)\right)}\right)\right)}{\left(2 + 0 i\right)}\right))\]
Final simplification0.0
\[\leadsto \Re(\left(\frac{e^{-\left(xre + xim i\right)} + e^{xre + xim i}}{2 + 0 i}\right))\]

Reproduce

herbie shell --seed 2019101 
(FPCore (xre xim)
  :name "exp with complex power real part (p55)"
  (re (/.c (+.c (exp.c (complex xre xim)) (exp.c (neg.c (complex xre xim)))) (complex 2 0))))

Error

Derivation

Reproduce