Average Error: 0.0 → 0.0
Time: 27.9s
Precision: 64
\[\Re(\left(\frac{e^{x} + e^{-x}}{2} \cdot \cos y + \frac{e^{x} - e^{-x}}{2} \cdot \sin y i\right))\]
↓
\[\Re(\left(\frac{e^{x} + e^{-x}}{2} \cdot \cos y + \frac{e^{x} - e^{-x}}{2} \cdot \sin y i\right))\]
\Re(\left(\frac{e^{x} + e^{-x}}{2} \cdot \cos y + \frac{e^{x} - e^{-x}}{2} \cdot \sin y i\right))
↓
\Re(\left(\frac{e^{x} + e^{-x}}{2} \cdot \cos y + \frac{e^{x} - e^{-x}}{2} \cdot \sin y i\right))
double f(double x, double y) {
        double r1161351 = x;
        double r1161352 = exp(r1161351);
        double r1161353 = -r1161351;
        double r1161354 = exp(r1161353);
        double r1161355 = r1161352 + r1161354;
        double r1161356 = 2.0;
        double r1161357 = r1161355 / r1161356;
        double r1161358 = y;
        double r1161359 = cos(r1161358);
        double r1161360 = r1161357 * r1161359;
        double r1161361 = r1161352 - r1161354;
        double r1161362 = r1161361 / r1161356;
        double r1161363 = sin(r1161358);
        double r1161364 = r1161362 * r1161363;
        double r1161365 = /* ERROR: no complex support in C */;
        double r1161366 = /* ERROR: no complex support in C */;
        return r1161366;
}
↓
double f(double x, double y) {
        double r1161367 = x;
        double r1161368 = exp(r1161367);
        double r1161369 = -r1161367;
        double r1161370 = exp(r1161369);
        double r1161371 = r1161368 + r1161370;
        double r1161372 = 2.0;
        double r1161373 = r1161371 / r1161372;
        double r1161374 = y;
        double r1161375 = cos(r1161374);
        double r1161376 = r1161373 * r1161375;
        double r1161377 = r1161368 - r1161370;
        double r1161378 = r1161377 / r1161372;
        double r1161379 = sin(r1161374);
        double r1161380 = r1161378 * r1161379;
        double r1161381 = /* ERROR: no complex support in C */;
        double r1161382 = /* ERROR: no complex support in C */;
        return r1161382;
}

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0.0

    \[\Re(\left(\frac{e^{x} + e^{-x}}{2} \cdot \cos y + \frac{e^{x} - e^{-x}}{2} \cdot \sin y i\right))\]

  2. Final simplification0.0

    \[\leadsto \Re(\left(\frac{e^{x} + e^{-x}}{2} \cdot \cos y + \frac{e^{x} - e^{-x}}{2} \cdot \sin y i\right))\]

Reproduce

herbie shell --seed 2019128 
(FPCore (x y)
  :name "Euler formula real part (p55)"
  (re (complex (* (/ (+ (exp x) (exp (- x))) 2) (cos y)) (* (/ (- (exp x) (exp (- x))) 2) (sin y)))))