\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
Test:
math.cos on complex, real part
Bits:
128 bits
Bits error versus re
Bits error versus im
Time: 11.3 s
Input Error: 0.0
Output Error: 0.0
Log: ⚲
Profile: 🕒
\(\left(\frac{\cos re}{e^{im}} + e^{im} \cdot \cos re\right) \cdot 0.5\)
  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 add-cube-cbrt to get
    \[\left(0.5 \cdot \cos re\right) \cdot \color{red}{\left(e^{-im} + e^{im}\right)} \leadsto \left(0.5 \cdot \cos re\right) \cdot \color{blue}{{\left(\sqrt[3]{e^{-im} + e^{im}}\right)}^3}\]
    1.8
  4. Applied taylor to get
    \[\left(0.5 \cdot \cos re\right) \cdot {\left(\sqrt[3]{e^{-im} + e^{im}}\right)}^3 \leadsto \left(0.5 \cdot \cos re\right) \cdot \left(e^{im} + e^{-im}\right)\]
    0.0
  5. Taylor expanded around 0 to get
    \[\left(0.5 \cdot \cos re\right) \cdot \color{red}{\left(e^{im} + e^{-im}\right)} \leadsto \left(0.5 \cdot \cos re\right) \cdot \color{blue}{\left(e^{im} + e^{-im}\right)}\]
    0.0
  6. Applied simplify to get
    \[\left(0.5 \cdot \cos re\right) \cdot \left(e^{im} + e^{-im}\right) \leadsto \left(\cos re \cdot 0.5\right) \cdot e^{im} + \frac{\cos re \cdot 0.5}{e^{im}}\]
    0.0
  7. Applied final simplification
  8. Applied simplify to get
    \[\color{red}{\left(\cos re \cdot 0.5\right) \cdot e^{im} + \frac{\cos re \cdot 0.5}{e^{im}}} \leadsto \color{blue}{\left(\frac{\cos re}{e^{im}} + e^{im} \cdot \cos re\right) \cdot 0.5}\]
    0.0
  9. Removed slow pow expressions

Original test:


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