Error

Derivation

1. Split input into 4 regimes

2. if b/2 < -1.0015408820196246e+67

   1. Initial program 38.9

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

   3. Applied div-inv39.0

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

   4. Taylor expanded around -inf 4.8

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

   if -1.0015408820196246e+67 < b/2 < 5.905604736002757e-181

   1. Initial program 11.2

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

   3. Applied div-inv11.3

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

   if 5.905604736002757e-181 < b/2 < 5.667357913699899e+71

   1. Initial program 35.9

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

   3. Applied flip-+36.0

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

   4. Applied simplify16.4

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

   if 5.667357913699899e+71 < b/2

   1. Initial program 57.1

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

   3. Applied flip-+57.2

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

   4. Applied simplify29.4

      \[\leadsto \frac{\frac{\color{blue}{c \cdot a}}{\left(-b/2\right) - \sqrt{b/2 \cdot b/2 - a \cdot c}}}{a}\]
   5. Using strategy rm

   6. Applied add-exp-log30.3

      \[\leadsto \frac{\frac{c \cdot a}{\left(-b/2\right) - \color{blue}{e^{\log \left(\sqrt{b/2 \cdot b/2 - a \cdot c}\right)}}}}{a}\]

   7. Taylor expanded around inf 16.7

      \[\leadsto \frac{\frac{c \cdot a}{\left(-b/2\right) - e^{\log \color{blue}{\left(b/2 - \frac{1}{2} \cdot \frac{c \cdot a}{b/2}\right)}}}}{a}\]

   8. Applied simplify3.0

      \[\leadsto \color{blue}{\frac{c}{\left(\left(-b/2\right) - b/2\right) + \frac{a}{b/2} \cdot \left(\frac{1}{2} \cdot c\right)}}\]
3. Recombined 4 regimes into one program.
4. Removed slow pow expressions.

Runtime

Time bar (total: 1.9m)Debug logProfile

herbie shell --seed '#(1063154770 1824007522 645063331 41291047 494775821 1237684644)' 
(FPCore (a b/2 c)
  :name "quad2p (problem 3.2.1, positive)"
  (/ (+ (- b/2) (sqrt (- (* b/2 b/2) (* a c)))) a))