\[\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}\]
Test:
Complex division, imag part
Bits:
128 bits
Bits error versus a
Bits error versus b
Bits error versus c
Bits error versus d
Time: 7.0 s
Input Error: 25.4
Output Error: 24.3
Log: ⚲
Profile: 🕒
\(\frac{b}{1} \cdot \frac{c}{{c}^2 + {d}^2} - \frac{a \cdot d}{{c}^2 + {d}^2}\)
  1. Started with
    \[\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}\]
    25.4
  2. Using strategy rm
    25.4
  3. Applied div-sub to get
    \[\color{red}{\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}} \leadsto \color{blue}{\frac{b \cdot c}{{c}^2 + {d}^2} - \frac{a \cdot d}{{c}^2 + {d}^2}}\]
    25.4
  4. Using strategy rm
    25.4
  5. Applied *-un-lft-identity to get
    \[\frac{b \cdot c}{\color{red}{{c}^2 + {d}^2}} - \frac{a \cdot d}{{c}^2 + {d}^2} \leadsto \frac{b \cdot c}{\color{blue}{1 \cdot \left({c}^2 + {d}^2\right)}} - \frac{a \cdot d}{{c}^2 + {d}^2}\]
    25.4
  6. Applied times-frac to get
    \[\color{red}{\frac{b \cdot c}{1 \cdot \left({c}^2 + {d}^2\right)}} - \frac{a \cdot d}{{c}^2 + {d}^2} \leadsto \color{blue}{\frac{b}{1} \cdot \frac{c}{{c}^2 + {d}^2}} - \frac{a \cdot d}{{c}^2 + {d}^2}\]
    24.3

Original test:


(lambda ((a default) (b default) (c default) (d default))
  #:name "Complex division, imag part"
  (/ (- (* b c) (* a d)) (+ (sqr c) (sqr d)))
  #:target
  (if (< (fabs d) (fabs c)) (/ (- b (* a (/ d c))) (+ c (* d (/ d c)))) (/ (+ (- a) (* b (/ c d))) (+ d (* c (/ c d))))))