\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
Test:
math.cos on complex, real part
Bits:
128 bits
Bits error versus re
Bits error versus im
Time: 8.8 s
Input Error: 0.0
Output Error: 0.1
Log: ⚲
Profile: 🕒
\(\frac{0.5}{\frac{e^{im}}{\cos re}} + \left(0.5 \cdot \cos re\right) \cdot e^{im}\)
  1. Started with
    \[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
    0.0
  2. Using strategy rm
    0.0
  3. Applied distribute-lft-in to get
    \[\color{red}{\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)} \leadsto \color{blue}{\left(0.5 \cdot \cos re\right) \cdot e^{-im} + \left(0.5 \cdot \cos re\right) \cdot e^{im}}\]
    0.0
  4. Applied simplify to get
    \[\color{red}{\left(0.5 \cdot \cos re\right) \cdot e^{-im}} + \left(0.5 \cdot \cos re\right) \cdot e^{im} \leadsto \color{blue}{\frac{0.5}{\frac{e^{im}}{\cos re}}} + \left(0.5 \cdot \cos re\right) \cdot e^{im}\]
    0.1

Original test:


(lambda ((re default) (im default))
  #:name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))