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

⬇

\[\begin{array}{l} \mathbf{if}\;b/2 \le -5.224339320607286 \cdot 10^{+142}:\\ \;\;\;\;-2 \cdot \frac{b/2}{a}\\ \mathbf{if}\;b/2 \le 5.922881749075492 \cdot 10^{-58}:\\ \;\;\;\;\frac{1}{\frac{a}{\left(-b/2\right) + \sqrt{b/2 \cdot b/2 - a \cdot c}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b/2} \cdot \frac{-1}{2}\\ \end{array}\]

Derivation

Split input into 3 regimes.
if b/2 < -5.224339320607286e+142
1. Initial program 57.7
  \[\frac{\left(-b/2\right) + \sqrt{b/2 \cdot b/2 - a \cdot c}}{a}\]
2. Applied taylor 0
  \[\leadsto -2 \cdot \frac{b/2}{a}\]
3. Taylor expanded around -inf 0
  
  \[\leadsto \color{blue}{-2 \cdot \frac{b/2}{a}}\]
if -5.224339320607286e+142 < b/2 < 5.922881749075492e-58
1. Initial program 12.7
  \[\frac{\left(-b/2\right) + \sqrt{b/2 \cdot b/2 - a \cdot c}}{a}\]
2. Using strategy rm
3. Applied clear-num 12.8
  \[\leadsto \color{blue}{\frac{1}{\frac{a}{\left(-b/2\right) + \sqrt{b/2 \cdot b/2 - a \cdot c}}}}\]
if 5.922881749075492e-58 < b/2
1. Initial program 58.9
  \[\frac{\left(-b/2\right) + \sqrt{b/2 \cdot b/2 - a \cdot c}}{a}\]
2. Applied taylor 14.6
  \[\leadsto \frac{\frac{-1}{2} \cdot \frac{c \cdot a}{b/2}}{a}\]
3. Taylor expanded around inf 14.6
  
  \[\leadsto \frac{\color{blue}{\frac{-1}{2} \cdot \frac{c \cdot a}{b/2}}}{a}\]
4. Applied simplify 0.0
  \[\leadsto \color{blue}{\frac{c}{b/2} \cdot \frac{-1}{2}}\]
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 "quad2p (problem 3.2.1, positive)"
  (/ (+ (- b/2) (sqrt (- (* b/2 b/2) (* a c)))) a))

Error

Derivation

`if b/2 < -5.224339320607286e+142`

`if -5.224339320607286e+142 < b/2 < 5.922881749075492e-58`

`if 5.922881749075492e-58 < b/2`

Runtime