Error

Derivation

1. Split input into 3 regimes

2. if b_2 < -1.2802147447265656e+121

   1. Initial program 50.3

      \[\frac{\left(-b_2\right) + \sqrt{b_2 \cdot b_2 - a \cdot c}}{a}\]

   2. Initial simplification50.3

      \[\leadsto \frac{\sqrt{b_2 \cdot b_2 - a \cdot c} - b_2}{a}\]

   3. Taylor expanded around -inf 50.3

      \[\leadsto \frac{\sqrt{\color{blue}{{b_2}^{2} - a \cdot c}} - b_2}{a}\]
   4. Using strategy rm

   5. Applied div-inv50.3

      \[\leadsto \color{blue}{\left(\sqrt{{b_2}^{2} - a \cdot c} - b_2\right) \cdot \frac{1}{a}}\]

   6. Taylor expanded around -inf 3.2

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{c}{b_2} - 2 \cdot \frac{b_2}{a}}\]

   7. Simplified3.2

      \[\leadsto \color{blue}{(-2 \cdot \left(\frac{b_2}{a}\right) + \left(\frac{c}{\frac{b_2}{\frac{1}{2}}}\right))_*}\]

   if -1.2802147447265656e+121 < b_2 < 2.7131217300870123e-130

   1. Initial program 10.9

      \[\frac{\left(-b_2\right) + \sqrt{b_2 \cdot b_2 - a \cdot c}}{a}\]

   2. Initial simplification10.9

      \[\leadsto \frac{\sqrt{b_2 \cdot b_2 - a \cdot c} - b_2}{a}\]

   3. Taylor expanded around -inf 10.9

      \[\leadsto \frac{\sqrt{\color{blue}{{b_2}^{2} - a \cdot c}} - b_2}{a}\]

   if 2.7131217300870123e-130 < b_2

   1. Initial program 50.2

      \[\frac{\left(-b_2\right) + \sqrt{b_2 \cdot b_2 - a \cdot c}}{a}\]

   2. Initial simplification50.2

      \[\leadsto \frac{\sqrt{b_2 \cdot b_2 - a \cdot c} - b_2}{a}\]

   3. Taylor expanded around -inf 50.2

      \[\leadsto \frac{\sqrt{\color{blue}{{b_2}^{2} - a \cdot c}} - b_2}{a}\]

   4. Taylor expanded around inf 12.1

      \[\leadsto \color{blue}{\frac{-1}{2} \cdot \frac{c}{b_2}}\]
3. Recombined 3 regimes into one program.

4. Final simplification10.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;b_2 \le -1.2802147447265656 \cdot 10^{+121}:\\ \;\;\;\;(-2 \cdot \left(\frac{b_2}{a}\right) + \left(\frac{c}{\frac{b_2}{\frac{1}{2}}}\right))_*\\ \mathbf{elif}\;b_2 \le 2.7131217300870123 \cdot 10^{-130}:\\ \;\;\;\;\frac{\sqrt{{b_2}^{2} - c \cdot a} - b_2}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{2} \cdot \frac{c}{b_2}\\ \end{array}\]

Runtime

Time bar (total: 21.9s)Debug logProfile

herbie shell --seed 2018290 +o rules:numerics
(FPCore (a b_2 c)
  :name "quad2p (problem 3.2.1, positive)"
  (/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a))