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Derivation

1. Split input into 3 regimes

2. if b < -6.358942485269841e+112

   1. Initial program 48.3

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]

   2. Taylor expanded around -inf 3.0

      \[\leadsto \color{blue}{\frac{c}{b} - \frac{b}{a}}\]

   if -6.358942485269841e+112 < b < 5.6739031961074284e-89

   1. Initial program 12.4

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]

   if 5.6739031961074284e-89 < b

   1. Initial program 52.2

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]

   2. Taylor expanded around inf 10.1

      \[\leadsto \color{blue}{-1 \cdot \frac{c}{b}}\]

   3. Simplified10.1

      \[\leadsto \color{blue}{\frac{-c}{b}}\]
3. Recombined 3 regimes into one program.

4. Final simplification10.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -6.358942485269841 \cdot 10^{+112}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \le 5.6739031961074284 \cdot 10^{-89}:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)}}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;-\frac{c}{b}\\ \end{array}\]

Runtime

Time bar (total: 40.7s)Debug logProfile

herbie shell --seed 2018256 
(FPCore (a b c)
  :name "Quadratic roots, full range"
  (/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a)))