\[\frac{x.im \cdot y.re - x.re \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\]
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: 12.5
Output Error: 12.7
Log: ⚲
Profile: 🕒
\(\frac{x.im \cdot y.re - x.re \cdot y.im}{{\left(\sqrt[3]{{y.re}^2 + y.im \cdot y.im}\right)}^3}\)
  1. Started with
    \[\frac{x.im \cdot y.re - x.re \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\]
    12.5
  2. Using strategy rm
    12.5
  3. Applied add-cube-cbrt to get
    \[\frac{x.im \cdot y.re - x.re \cdot y.im}{\color{red}{y.re \cdot y.re + y.im \cdot y.im}} \leadsto \frac{x.im \cdot y.re - x.re \cdot y.im}{\color{blue}{{\left(\sqrt[3]{y.re \cdot y.re + y.im \cdot y.im}\right)}^3}}\]
    12.7
  4. Applied simplify to get
    \[\frac{x.im \cdot y.re - x.re \cdot y.im}{{\color{red}{\left(\sqrt[3]{y.re \cdot y.re + y.im \cdot y.im}\right)}}^3} \leadsto \frac{x.im \cdot y.re - x.re \cdot y.im}{{\color{blue}{\left(\sqrt[3]{{y.re}^2 + y.im \cdot y.im}\right)}}^3}\]
    12.7

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))))