\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
Test:
math.sin on complex, real part
Bits:
128 bits
Bits error versus re
Bits error versus im
Time: 6.5 s
Input Error: 14.8
Output Error: 3.0
Log: ⚲
Profile: 🕒
\((\frac{1}{12} * \left({im}^{4}\right) + \left((im * im + 2)_*\right))_* \cdot \left(\sin re \cdot 0.5\right)\)
  1. Started with
    \[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
    14.8
  2. Applied taylor to get
    \[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right) \leadsto \left(0.5 \cdot \sin re\right) \cdot \left(2 + \left({im}^2 + \frac{1}{12} \cdot {im}^{4}\right)\right)\]
    3.0
  3. Taylor expanded around 0 to get
    \[\left(0.5 \cdot \sin re\right) \cdot \color{red}{\left(2 + \left({im}^2 + \frac{1}{12} \cdot {im}^{4}\right)\right)} \leadsto \left(0.5 \cdot \sin re\right) \cdot \color{blue}{\left(2 + \left({im}^2 + \frac{1}{12} \cdot {im}^{4}\right)\right)}\]
    3.0
  4. Applied simplify to get
    \[\color{red}{\left(0.5 \cdot \sin re\right) \cdot \left(2 + \left({im}^2 + \frac{1}{12} \cdot {im}^{4}\right)\right)} \leadsto \color{blue}{(\frac{1}{12} * \left({im}^{4}\right) + \left((im * im + 2)_*\right))_* \cdot \left(\sin re \cdot 0.5\right)}\]
    3.0

Original test:


(lambda ((re default) (im default))
  #:name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))