Average Error: 0.0 → 0.0
Time: 12.4s
Precision: 64
\[\Re(\left(\frac{\left(\left(e^{\left(xre + xim i\right)}\right) + \left(e^{\left(-\left(xre + xim i\right)\right)}\right)\right)}{\left(2 + 0.0 i\right)}\right))\]
↓
\[\Re(\left(\frac{\left(\left(e^{\left(xre + xim i\right)}\right) + \left(e^{\left(-\left(xre + xim i\right)\right)}\right)\right)}{\left(2 + 0.0 i\right)}\right))\]
\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 r9116 = xre;
        double r9117 = xim;
        double r9118 = /* ERROR: no complex support in C */;
        double r9119 = exp(r9118);
        double r9120 = -r9118;
        double r9121 = exp(r9120);
        double r9122 = r9119 + r9121;
        double r9123 = 2.0;
        double r9124 = 0.0;
        double r9125 = /* ERROR: no complex support in C */;
        double r9126 = r9122 / r9125;
        double r9127 = /* ERROR: no complex support in C */;
        return r9127;
}
↓
double f(double xre, double xim) {
        double r9128 = xre;
        double r9129 = xim;
        double r9130 = /* ERROR: no complex support in C */;
        double r9131 = exp(r9130);
        double r9132 = -r9130;
        double r9133 = exp(r9132);
        double r9134 = r9131 + r9133;
        double r9135 = 2.0;
        double r9136 = 0.0;
        double r9137 = /* ERROR: no complex support in C */;
        double r9138 = r9134 / r9137;
        double r9139 = /* ERROR: no complex support in C */;
        return r9139;
}

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 2019195 +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))))