\[\frac{x.im \cdot y.re - x.re \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\]
Test:
_divideComplex, imaginary part
Bits:
128 bits
Bits error versus x.re
Bits error versus x.im
Bits error versus y.re
Bits error versus y.im
Time: 9.7 s
Input Error: 12.4
Output Error: 12.4
Log: ⚲
Profile: 🕒
\(\frac{y.re \cdot x.im - y.im \cdot x.re}{{\left(\sqrt{(y.im * y.im + \left(y.re \cdot y.re\right))_*}\right)}^2}\)
  1. Started with
    \[\frac{x.im \cdot y.re - x.re \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\]
    12.4
  2. Applied simplify to get
    \[\color{red}{\frac{x.im \cdot y.re - x.re \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}} \leadsto \color{blue}{\frac{y.re \cdot x.im - y.im \cdot x.re}{(y.im * y.im + \left(y.re \cdot y.re\right))_*}}\]
    12.4
  3. Using strategy rm
    12.4
  4. Applied add-sqr-sqrt to get
    \[\frac{y.re \cdot x.im - y.im \cdot x.re}{\color{red}{(y.im * y.im + \left(y.re \cdot y.re\right))_*}} \leadsto \frac{y.re \cdot x.im - y.im \cdot x.re}{\color{blue}{{\left(\sqrt{(y.im * y.im + \left(y.re \cdot y.re\right))_*}\right)}^2}}\]
    12.4
  5. Removed slow pow expressions

Original test:


(lambda ((x.re default) (x.im default) (y.re default) (y.im default))
  #:name "_divideComplex, imaginary part"
  (/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im))))