Error

Derivation

1. Split input into 4 regimes

2. if b_2 < -1.748102583967223e+146

   1. Initial program 57.4

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

   3. Applied div-inv57.4

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

   4. Taylor expanded around -inf 11.3

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

   5. Applied simplify3.1

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

   if -1.748102583967223e+146 < b_2 < 1.2391911148819273e-284

   1. Initial program 8.5

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

   3. Applied div-inv8.7

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

   if 1.2391911148819273e-284 < b_2 < 7.7635612098687e+72

   1. Initial program 32.1

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

   3. Applied flip-+32.2

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

   4. Applied simplify17.1

      \[\leadsto \frac{\frac{\color{blue}{c \cdot a}}{\left(-b_2\right) - \sqrt{b_2 \cdot b_2 - a \cdot c}}}{a}\]
   5. Using strategy rm

   6. Applied clear-num17.3

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

   7. Applied simplify9.5

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

   if 7.7635612098687e+72 < b_2

   1. Initial program 57.5

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

   2. Taylor expanded around inf 41.1

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

   3. Applied simplify2.5

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

Runtime

Time bar (total: 1.4m)Debug logProfile

herbie shell --seed '#(1070991898 1055468627 4280279443 640792587 928206309 3646738750)' +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))