Error

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. Simplified0.0

   \[\leadsto \color{blue}{\frac{\frac{\cos y}{e^{x}} + \cos y \cdot e^{x}}{2}}\]
3. Using strategy rm

4. Applied div-inv0.0

   \[\leadsto \frac{\color{blue}{\cos y \cdot \frac{1}{e^{x}}} + \cos y \cdot e^{x}}{2}\]

5. Applied distribute-lft-out0.0

   \[\leadsto \frac{\color{blue}{\cos y \cdot \left(\frac{1}{e^{x}} + e^{x}\right)}}{2}\]

6. Final simplification0.0

   \[\leadsto \frac{\left(\frac{1}{e^{x}} + e^{x}\right) \cdot \cos y}{2}\]

Reproduce

herbie shell --seed 2019093 
(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)))))