Average Error: 0.0 → 0.0
Time: 15.4s
Precision: 64
\[\Re(\left(\frac{\left(\left(e^{\left(xre + xim i\right)}\right) + \left(e^{\left(-\left(xre + xim i\right)\right)}\right)\right)}{\left(2 + 0.0 i\right)}\right))\]
↓
\[\Re(\left(\frac{\left(\left(e^{\left(-\left(xre + xim i\right)\right)}\right) + \left(e^{\left(xre + xim i\right)}\right)\right)}{\left(2 + 0.0 i\right)}\right))\]
\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 + 0.0 i\right)}\right))
↓
\Re(\left(\frac{\left(\left(e^{\left(-\left(xre + xim i\right)\right)}\right) + \left(e^{\left(xre + xim i\right)}\right)\right)}{\left(2 + 0.0 i\right)}\right))
double f(double xre, double xim) {
        double r10298 = xre;
        double r10299 = xim;
        double r10300 = /* ERROR: no complex support in C */;
        double r10301 = exp(r10300);
        double r10302 = -r10300;
        double r10303 = exp(r10302);
        double r10304 = r10301 + r10303;
        double r10305 = 2.0;
        double r10306 = 0.0;
        double r10307 = /* ERROR: no complex support in C */;
        double r10308 = r10304 / r10307;
        double r10309 = /* ERROR: no complex support in C */;
        return r10309;
}
↓
double f(double xre, double xim) {
        double r10310 = xre;
        double r10311 = xim;
        double r10312 = /* ERROR: no complex support in C */;
        double r10313 = -r10312;
        double r10314 = exp(r10313);
        double r10315 = exp(r10312);
        double r10316 = r10314 + r10315;
        double r10317 = 2.0;
        double r10318 = 0.0;
        double r10319 = /* ERROR: no complex support in C */;
        double r10320 = r10316 / r10319;
        double r10321 = /* ERROR: no complex support in C */;
        return r10321;
}

Error

Bits error versus xre

Bits error versus xim

Derivation

  1. Initial program 0.0

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

  2. Final simplification0.0

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

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (xre xim)
  :name "exp with complex power real part (p55)"
  (re (/ (+ (exp (complex xre xim)) (exp (- (complex xre xim)))) (complex 2.0 0.0))))