\[\frac{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}{a}\]
Test:
NMSE problem 3.2.1, positive
Bits:
128 bits
Bits error versus a
Bits error versus b/2
Bits error versus c
Time: 7.4 s
Input Error: 33.5
Output Error: 33.6
Log: ⚲
Profile: 🕒
\(\frac{1}{a \cdot \frac{1}{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}}\)
  1. Started with
    \[\frac{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}{a}\]
    33.5
  2. Using strategy rm
    33.5
  3. Applied clear-num to get
    \[\color{red}{\frac{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}{a}} \leadsto \color{blue}{\frac{1}{\frac{a}{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}}}\]
    33.6
  4. Using strategy rm
    33.6
  5. Applied div-inv to get
    \[\frac{1}{\color{red}{\frac{a}{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}}} \leadsto \frac{1}{\color{blue}{a \cdot \frac{1}{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}}}\]
    33.6

Original test:


(lambda ((a default) (b/2 default) (c default))
  #:name "NMSE problem 3.2.1, positive"
  (/ (+ (- b/2) (sqrt (- (sqr b/2) (* a c)))) a))