Error

Derivation

1. Split input into 4 regimes

2. if b_2 < -1.0145027623461143e+112

   1. Initial program 46.5

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

   2. Taylor expanded around -inf 3.6

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

   if -1.0145027623461143e+112 < b_2 < 1.830255897208847e-62

   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 div-inv12.9

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

   if 1.830255897208847e-62 < b_2 < 3.94495643515449e+97

   1. Initial program 43.2

      \[\frac{\left(-b_2\right) + \sqrt{b_2 \cdot b_2 - a \cdot c}}{a}\]
   2. Using strategy rm

   3. Applied flip-+43.3

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

   4. Applied simplify15.6

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

   if 3.94495643515449e+97 < b_2

   1. Initial program 58.6

      \[\frac{\left(-b_2\right) + \sqrt{b_2 \cdot b_2 - a \cdot c}}{a}\]
   2. Using strategy rm

   3. Applied flip-+58.6

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

   4. Applied simplify29.9

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

   5. Taylor expanded around inf 13.6

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

   6. Applied simplify2.9

      \[\leadsto \color{blue}{\frac{c}{\frac{\frac{1}{2} \cdot a}{\frac{b_2}{c}} - 2 \cdot b_2}}\]
3. Recombined 4 regimes into one program.

Runtime

Time bar (total: 1.2m)Debug logProfile

herbie shell --seed '#(1071246582 2318319007 2683472949 3810440501 3233274817 2724848749)' 
(FPCore (a b_2 c)
  :name "quad2p (problem 3.2.1, positive)"
  (/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a))