\[\frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
Test:
NMSE p42, positive
Bits:
128 bits
Bits error versus a
Bits error versus b
Bits error versus c
Time: 16.7 s
Input Error: 33.5
Output Error: 33.5
Log: ⚲
Profile: 🕒
\(\frac{\left(-\sqrt{{b}^2 - a \cdot \left(4 \cdot c\right)}\right) + b}{-2 \cdot a}\)
  1. Started with
    \[\frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
    33.5
  2. Using strategy rm
    33.5
  3. Applied frac-2neg to get
    \[\color{red}{\frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}} \leadsto \color{blue}{\frac{-\left(\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}\right)}{-2 \cdot a}}\]
    33.5
  4. Applied simplify to get
    \[\frac{\color{red}{-\left(\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}\right)}}{-2 \cdot a} \leadsto \frac{\color{blue}{\left(-\sqrt{{b}^2 - a \cdot \left(4 \cdot c\right)}\right) + b}}{-2 \cdot a}\]
    33.5

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))))))