Error

Derivation

1. Split input into 4 regimes.

2. if b/2 < -1.2104515124530692e+151

   1. Initial program 59.2

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

   3. Applied flip-+ 62.3

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

   4. Applied simplify 62.5

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

   6. Applied clear-num 62.5

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

   7. Applied simplify 62.4

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

   8. Applied taylor 0.0

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

   9. Taylor expanded around -inf 0.0

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

   if -1.2104515124530692e+151 < b/2 < 2.5179726424422933e-277

   1. Initial program 9.0

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

   3. Applied div-inv 9.2

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

   if 2.5179726424422933e-277 < b/2 < 2.3106113327966147e+121

   1. Initial program 33.9

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

   3. Applied flip-+ 34.0

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

   4. Applied simplify 16.0

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

   6. Applied clear-num 16.2

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

   7. Applied simplify 8.4

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

   if 2.3106113327966147e+121 < b/2

   1. Initial program 60.2

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

   3. Applied flip-+ 60.3

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

   4. Applied simplify 35.7

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

   6. Applied clear-num 35.9

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

   7. Applied simplify 34.4

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

   8. Applied taylor 9.1

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

   9. Taylor expanded around inf 9.1

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

   10. Applied simplify 1.1

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

Runtime

Time bar (total: 19.6s) Debug logProfile

Please include this information when filing a bug report:

herbie shell --seed '#(1067901057 3396600083 3715501224 3126139233 3908045574 1593683916)'
(FPCore (a b/2 c)
  :name "quad2p (problem 3.2.1, positive)"
  (/ (+ (- b/2) (sqrt (- (sqr b/2) (* a c)))) a))