\[\frac{a \cdot c + b \cdot d}{{c}^2 + {d}^2}\]
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: 6.9 s
Input Error: 12.4
Output Error: 12.6
Log: ⚲
Profile: 🕒
\(\frac{1}{\frac{1}{\frac{a \cdot c + b \cdot d}{{c}^2 + {d}^2}}}\)
  1. Started with
    \[\frac{a \cdot c + b \cdot d}{{c}^2 + {d}^2}\]
    12.4
  2. Using strategy rm
    12.4
  3. Applied clear-num to get
    \[\color{red}{\frac{a \cdot c + b \cdot d}{{c}^2 + {d}^2}} \leadsto \color{blue}{\frac{1}{\frac{{c}^2 + {d}^2}{a \cdot c + b \cdot d}}}\]
    12.6
  4. Using strategy rm
    12.6
  5. Applied clear-num to get
    \[\frac{1}{\color{red}{\frac{{c}^2 + {d}^2}{a \cdot c + b \cdot d}}} \leadsto \frac{1}{\color{blue}{\frac{1}{\frac{a \cdot c + b \cdot d}{{c}^2 + {d}^2}}}}\]
    12.6

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))))))