Average Error: 0.0 → 0.0
Time: 4.8s
Precision: 64
\[\Re(\left(\frac{\left(\left(e^{\left(xre + xim i\right)}\right) + \left(e^{\left(-\left(xre + xim i\right)\right)}\right)\right)}{\left(2 + 0.0 i\right)}\right))\]
↓
\[\Re(\left(\frac{\left(\left(e^{\left(xre + xim i\right)}\right) + \left(e^{\left(-\left(xre + xim i\right)\right)}\right)\right)}{\left(2 + 0.0 i\right)}\right))\]
\Re(\left(\frac{\left(\left(e^{\left(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(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 r11956 = xre;
        double r11957 = xim;
        double r11958 = /* ERROR: no complex support in C */;
        double r11959 = exp(r11958);
        double r11960 = -r11958;
        double r11961 = exp(r11960);
        double r11962 = r11959 + r11961;
        double r11963 = 2.0;
        double r11964 = 0.0;
        double r11965 = /* ERROR: no complex support in C */;
        double r11966 = r11962 / r11965;
        double r11967 = /* ERROR: no complex support in C */;
        return r11967;
}
↓
double f(double xre, double xim) {
        double r11968 = xre;
        double r11969 = xim;
        double r11970 = /* ERROR: no complex support in C */;
        double r11971 = exp(r11970);
        double r11972 = -r11970;
        double r11973 = exp(r11972);
        double r11974 = r11971 + r11973;
        double r11975 = 2.0;
        double r11976 = 0.0;
        double r11977 = /* ERROR: no complex support in C */;
        double r11978 = r11974 / r11977;
        double r11979 = /* ERROR: no complex support in C */;
        return r11979;
}

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

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

Reproduce

herbie shell --seed 2020089 
(FPCore (xre xim)
  :name "exp with complex power real part (p55)"
  :precision binary64
  (re (/ (+ (exp (complex xre xim)) (exp (- (complex xre xim)))) (complex 2 0.0))))