\[\frac{a \cdot c + b \cdot d}{{c}^2 + {d}^2}\]
Test:
Complex division, real part
Bits:
128 bits
Bits error versus a
Bits error versus b
Bits error versus c
Bits error versus d
Time: 6.4 s
Input Error: 25.1
Output Error: 25.3
Log: ⚲
Profile: 🕒
\(\left(a \cdot c + b \cdot d\right) \cdot \frac{1}{{c}^2 + {d}^2}\)
  1. Started with
    \[\frac{a \cdot c + b \cdot d}{{c}^2 + {d}^2}\]
    25.1
  2. Using strategy rm
    25.1
  3. Applied div-inv to get
    \[\color{red}{\frac{a \cdot c + b \cdot d}{{c}^2 + {d}^2}} \leadsto \color{blue}{\left(a \cdot c + b \cdot d\right) \cdot \frac{1}{{c}^2 + {d}^2}}\]
    25.3

Original test:


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