Error

Try it out

Derivation

1. Split input into 3 regimes

2. if b < -9.466382232385927e+88

   1. Initial program 41.8

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

   2. Initial simplification41.8

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

   3. Taylor expanded around -inf 4.4

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

   if -9.466382232385927e+88 < b < 1.0293007663908137e-45

   1. Initial program 14.2

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

   2. Initial simplification14.2

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

   if 1.0293007663908137e-45 < b

   1. Initial program 54.0

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

   2. Initial simplification53.9

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

   3. Taylor expanded around inf 7.4

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

   4. Simplified7.4

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

4. Final simplification10.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -9.466382232385927 \cdot 10^{+88}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \le 1.0293007663908137 \cdot 10^{-45}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;-\frac{c}{b}\\ \end{array}\]

Runtime

Time bar (total: 24.4s)Debug logProfile

herbie shell --seed 2018297 
(FPCore (a b c)
  :name "Quadratic roots, full range"
  (/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a)))