Error

Derivation

1. Split input into 3 regimes.

2. if b/2 < -4.531827883994214e-14

   1. Initial program 58.3

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

   3. Applied flip-- 58.4

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

   4. Applied simplify 32.6

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

   6. Applied div-inv 32.7

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

   7. Applied taylor 15.5

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

   8. Taylor expanded around -inf 15.5

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

   9. Applied simplify 2.6

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

   if -4.531827883994214e-14 < b/2 < 1438490.0801097094

   1. Initial program 18.1

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

   3. Applied div-inv 18.2

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

   if 1438490.0801097094 < b/2

   1. Initial program 37.8

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

   2. Applied taylor 10.0

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

   3. Taylor expanded around inf 10.0

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

   4. Applied simplify 0.2

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

Runtime

Total time: 37.4s Debug log

Please include this information when filing a bug report:

herbie --seed '#(1313658220 317547239 628843654 2904764784 1390587098 3025944073)'
(FPCore (a b/2 c)
  :name "NMSE problem 3.2.1, negative"
  (/ (- (- b/2) (sqrt (- (sqr b/2) (* a c)))) a))