Average Error: 43.1 → 43.1
Time: 10.5s
Precision: 64
\[\Im(\left(\frac{\left(\left(e^{\left(xre + xim i\right)}\right) + \left(e^{\left(-\left(xre + xim i\right)\right)}\right)\right)}{\left(2 + 0.0 i\right)}\right))\]
↓
\[\Im(\left(\frac{\left(\left(e^{\left(xre + xim i\right)}\right) + \left(e^{\left(-\left(xre + xim i\right)\right)}\right)\right)}{\left(2 + 0.0 i\right)}\right))\]
\Im(\left(\frac{\left(\left(e^{\left(xre + xim i\right)}\right) + \left(e^{\left(-\left(xre + xim i\right)\right)}\right)\right)}{\left(2 + 0.0 i\right)}\right))
↓
\Im(\left(\frac{\left(\left(e^{\left(xre + xim i\right)}\right) + \left(e^{\left(-\left(xre + xim i\right)\right)}\right)\right)}{\left(2 + 0.0 i\right)}\right))
double f(double xre, double xim) {
        double r17180 = xre;
        double r17181 = xim;
        double r17182 = /* ERROR: no complex support in C */;
        double r17183 = exp(r17182);
        double r17184 = -r17182;
        double r17185 = exp(r17184);
        double r17186 = r17183 + r17185;
        double r17187 = 2.0;
        double r17188 = 0.0;
        double r17189 = /* ERROR: no complex support in C */;
        double r17190 = r17186 / r17189;
        double r17191 = /* ERROR: no complex support in C */;
        return r17191;
}
↓
double f(double xre, double xim) {
        double r17192 = xre;
        double r17193 = xim;
        double r17194 = /* ERROR: no complex support in C */;
        double r17195 = exp(r17194);
        double r17196 = -r17194;
        double r17197 = exp(r17196);
        double r17198 = r17195 + r17197;
        double r17199 = 2.0;
        double r17200 = 0.0;
        double r17201 = /* ERROR: no complex support in C */;
        double r17202 = r17198 / r17201;
        double r17203 = /* ERROR: no complex support in C */;
        return r17203;
}

Error

Bits error versus xre

Bits error versus xim

Derivation

  1. Initial program 43.1

    \[\Im(\left(\frac{\left(\left(e^{\left(xre + xim i\right)}\right) + \left(e^{\left(-\left(xre + xim i\right)\right)}\right)\right)}{\left(2 + 0.0 i\right)}\right))\]

  2. Final simplification43.1

    \[\leadsto \Im(\left(\frac{\left(\left(e^{\left(xre + xim i\right)}\right) + \left(e^{\left(-\left(xre + xim i\right)\right)}\right)\right)}{\left(2 + 0.0 i\right)}\right))\]

Reproduce

herbie shell --seed 2020020 
(FPCore (xre xim)
  :name "exp with complex power imaginary part (p55)"
  :precision binary64
  (im (/ (+ (exp (complex xre xim)) (exp (- (complex xre xim)))) (complex 2 0.0))))