\[\frac{\left(-b/2\right) - \sqrt{b/2 \cdot b/2 - a \cdot c}}{a}\]

⬇

\[\begin{array}{l} \mathbf{if}\;b/2 \le -1.978699881745306 \cdot 10^{-162}:\\ \;\;\;\;\frac{c}{b/2} \cdot \frac{-1}{2}\\ \mathbf{if}\;b/2 \le 2.4225703873767033 \cdot 10^{+115}:\\ \;\;\;\;\frac{1}{\frac{a}{\left(-b/2\right) - \sqrt{b/2 \cdot b/2 - a \cdot c}}}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{b/2}{a}\\ \end{array}\]

Derivation

Split input into 3 regimes.
if b/2 < -1.978699881745306e-162
1. Initial program 59.2
  \[\frac{\left(-b/2\right) - \sqrt{b/2 \cdot b/2 - a \cdot c}}{a}\]
2. Applied taylor 16.2
  \[\leadsto \frac{\frac{-1}{2} \cdot \frac{c \cdot a}{b/2}}{a}\]
3. Taylor expanded around -inf 16.2
  
  \[\leadsto \frac{\color{blue}{\frac{-1}{2} \cdot \frac{c \cdot a}{b/2}}}{a}\]
4. Applied simplify 0.0
  \[\leadsto \color{blue}{\frac{c}{b/2} \cdot \frac{-1}{2}}\]
if -1.978699881745306e-162 < b/2 < 2.4225703873767033e+115
1. Initial program 10.9
  \[\frac{\left(-b/2\right) - \sqrt{b/2 \cdot b/2 - a \cdot c}}{a}\]
2. Using strategy rm
3. Applied clear-num 11.1
  \[\leadsto \color{blue}{\frac{1}{\frac{a}{\left(-b/2\right) - \sqrt{b/2 \cdot b/2 - a \cdot c}}}}\]
if 2.4225703873767033e+115 < b/2
1. Initial program 50.2
  \[\frac{\left(-b/2\right) - \sqrt{b/2 \cdot b/2 - a \cdot c}}{a}\]
2. Applied taylor 0
  \[\leadsto -2 \cdot \frac{b/2}{a}\]
3. Taylor expanded around inf 0
  
  \[\leadsto \color{blue}{-2 \cdot \frac{b/2}{a}}\]
Recombined 3 regimes into one program.
Removed slow pow expressions

Runtime

Please include this information when filing a bug report:

herbie shell --seed '#(1068028399 4028058041 2917032441 2563479541 765645300 1132738916)'
(FPCore (a b/2 c)
  :name "quad2m (problem 3.2.1, negative)"
  (/ (- (- b/2) (sqrt (- (* b/2 b/2) (* a c)))) a))

Error

Derivation

`if b/2 < -1.978699881745306e-162`

`if -1.978699881745306e-162 < b/2 < 2.4225703873767033e+115`

`if 2.4225703873767033e+115 < b/2`

Runtime