Error

Derivation

1. Split input into 5 regimes.

2. if b/2 < -9.534865642779829e+39

   1. Initial program 58.2

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

   3. Applied flip-- 58.2

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

   4. Applied simplify 31.8

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

   6. Applied div-inv 31.8

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

   7. Applied taylor 14.6

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

   8. Taylor expanded around -inf 14.6

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

   9. Applied simplify 1.9

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

   if -9.534865642779829e+39 < b/2 < -3.6019808479897e-63

   1. Initial program 43.1

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

   3. Applied flip-- 43.1

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

   4. Applied simplify 15.1

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

   if -3.6019808479897e-63 < b/2 < -3.3498534903732907e-77

   1. Initial program 60.3

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

   3. Applied flip-- 60.3

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

   4. Applied simplify 49.9

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

   6. Applied div-inv 49.9

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

   7. Applied taylor 16.0

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

   8. Taylor expanded around -inf 16.0

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

   9. Applied simplify 10.2

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

   if -3.3498534903732907e-77 < b/2 < 2.479231526661392e+104

   1. Initial program 12.2

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

   3. Applied clear-num 12.4

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

   if 2.479231526661392e+104 < b/2

   1. Initial program 46.5

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

   2. Applied taylor 0

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

   3. Taylor expanded around inf 0

      \[\leadsto \color{blue}{-2 \cdot \frac{b/2}{a}}\]
3. Recombined 5 regimes into one program.
4. Removed slow pow expressions

Runtime

Time bar (total: 16.0s) Debug logProfile

Please include this information when filing a bug report:

herbie shell --seed '#(1065003094 2074156664 2352254222 753858891 3745550101 3374585842)'
(FPCore (a b/2 c)
  :name "quad2m (problem 3.2.1, negative)"
  (/ (- (- b/2) (sqrt (- (sqr b/2) (* a c)))) a))