Error

Derivation

1. Initial program 0.0

   \[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]

2. Simplified0.0

   \[\leadsto \color{blue}{\left(\frac{0.5}{e^{im}} + e^{im} \cdot 0.5\right) \cdot \cos re}\]
3. Using strategy rm

4. Applied add-sqr-sqrt0.0

   \[\leadsto \left(\frac{\color{blue}{\sqrt{0.5} \cdot \sqrt{0.5}}}{e^{im}} + e^{im} \cdot 0.5\right) \cdot \cos re\]

5. Applied associate-/l*0.0

   \[\leadsto \left(\color{blue}{\frac{\sqrt{0.5}}{\frac{e^{im}}{\sqrt{0.5}}}} + e^{im} \cdot 0.5\right) \cdot \cos re\]

6. Final simplification0.0

   \[\leadsto \cos re \cdot \left(\frac{\sqrt{0.5}}{\frac{e^{im}}{\sqrt{0.5}}} + e^{im} \cdot 0.5\right)\]

Reproduce

herbie shell --seed 2019090 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))