\[\frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
Test:
The quadratic formula (r1)
Bits:
128 bits
Bits error versus a
Bits error versus b
Bits error versus c
Time: 11.9 s
Input Error: 15.8
Output Error: 15.8
Log: ⚲
Profile: 🕒
\(\frac{1}{2} \cdot \frac{(1 * \left(-b\right) + \left(\sqrt{{b}^2 - 4 \cdot \left(c \cdot a\right)}\right))_*}{a}\)
  1. Started with
    \[\frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
    15.8
  2. Using strategy rm
    15.8
  3. Applied *-un-lft-identity to get
    \[\frac{\color{red}{\left(-b\right)} + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} \leadsto \frac{\color{blue}{1 \cdot \left(-b\right)} + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
    15.8
  4. Applied fma-def to get
    \[\frac{\color{red}{1 \cdot \left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a} \leadsto \frac{\color{blue}{(1 * \left(-b\right) + \left(\sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right))_*}}{2 \cdot a}\]
    15.8
  5. Applied taylor to get
    \[\frac{(1 * \left(-b\right) + \left(\sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right))_*}{2 \cdot a} \leadsto \frac{1}{2} \cdot \frac{(1 * \left(-b\right) + \left(\sqrt{{b}^2 - 4 \cdot \left(c \cdot a\right)}\right))_*}{a}\]
    15.8
  6. Taylor expanded around 0 to get
    \[\color{red}{\frac{1}{2} \cdot \frac{(1 * \left(-b\right) + \left(\sqrt{{b}^2 - 4 \cdot \left(c \cdot a\right)}\right))_*}{a}} \leadsto \color{blue}{\frac{1}{2} \cdot \frac{(1 * \left(-b\right) + \left(\sqrt{{b}^2 - 4 \cdot \left(c \cdot a\right)}\right))_*}{a}}\]
    15.8

Original test:


(lambda ((a default) (b default) (c default))
  #:name "The quadratic formula (r1)"
  (/ (+ (- 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))))))