Average Error: 0.0 → 0.0
Time: 13.3s
Precision: 64
\[\Re(\left(\frac{\left(\left(e^{\left(xre + xim i\right)}\right) + \left(e^{\left(-\left(xre + xim i\right)\right)}\right)\right)}{\left(2 + 0 i\right)}\right))\]
↓
\[\Re(\left(\frac{e^{-\left(xre + xim i\right)} + e^{xre + xim i}}{2 + 0 i}\right))\]
\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))
↓
\Re(\left(\frac{e^{-\left(xre + xim i\right)} + e^{xre + xim i}}{2 + 0 i}\right))
double f(double xre, double xim) {
        double r10239 = xre;
        double r10240 = xim;
        double r10241 = /* ERROR: no complex support in C */;
        double r10242 = exp(r10241);
        double r10243 = -r10241;
        double r10244 = exp(r10243);
        double r10245 = r10242 + r10244;
        double r10246 = 2.0;
        double r10247 = 0.0;
        double r10248 = /* ERROR: no complex support in C */;
        double r10249 = r10245 / r10248;
        double r10250 = /* ERROR: no complex support in C */;
        return r10250;
}
↓
double f(double xre, double xim) {
        double r10251 = xre;
        double r10252 = xim;
        double r10253 = /* ERROR: no complex support in C */;
        double r10254 = -r10253;
        double r10255 = exp(r10254);
        double r10256 = exp(r10253);
        double r10257 = r10255 + r10256;
        double r10258 = 2.0;
        double r10259 = 0.0;
        double r10260 = /* ERROR: no complex support in C */;
        double r10261 = r10257 / r10260;
        double r10262 = /* ERROR: no complex support in C */;
        return r10262;
}

Error

Bits error versus xre

Bits error versus xim

Derivation

  1. Initial program 0.0

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

  2. 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 2019165 
(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))))