\[\frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
Test:
NMSE p42, positive
Bits:
128 bits
Bits error versus a
Bits error versus b
Bits error versus c
Time: 10.5 s
Input Error: 15.8
Output Error: 15.8
Log: ⚲
Profile: 🕒
\(\frac{1}{2} \cdot \frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{a}\)
  1. Started with
    \[\frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
    15.8
  2. Using strategy rm
    15.8
  3. Applied *-un-lft-identity to get
    \[\frac{\color{red}{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}{2 \cdot a} \leadsto \frac{\color{blue}{1 \cdot \left(\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}\right)}}{2 \cdot a}\]
    15.8
  4. Applied times-frac to get
    \[\color{red}{\frac{1 \cdot \left(\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}\right)}{2 \cdot a}} \leadsto \color{blue}{\frac{1}{2} \cdot \frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{a}}\]
    15.8

Original test:


(lambda ((a default) (b default) (c default))
  #:name "NMSE p42, positive"
  (/ (+ (- b) (sqrt (- (sqr b) (* 4 (* a c))))) (* 2 a))
  #:target
  (if (< b 0) (/ (+ (- b) (sqrt (- (sqr b) (* 4 (* a c))))) (* 2 a)) (/ c (* a (/ (- (- b) (sqrt (- (sqr b) (* 4 (* a c))))) (* 2 a))))))