Error

Derivation

1. Split input into 4 regimes.

2. if b2 < -4.930770214232589e+18

   1. Initial program 57.2

      \[\frac{\left(-b2\right) - \sqrt{b2 \cdot b2 - a \cdot c}}{a}\]
   2. Using strategy rm

   3. Applied flip-- 57.2

      \[\leadsto \frac{\color{blue}{\frac{{\left(-b2\right)}^2 - {\left(\sqrt{b2 \cdot b2 - a \cdot c}\right)}^2}{\left(-b2\right) + \sqrt{b2 \cdot b2 - a \cdot c}}}}{a}\]

   4. Applied simplify 29.1

      \[\leadsto \frac{\frac{\color{blue}{c \cdot a}}{\left(-b2\right) + \sqrt{b2 \cdot b2 - a \cdot c}}}{a}\]
   5. Using strategy rm

   6. Applied add-sqr-sqrt 29.2

      \[\leadsto \frac{\frac{c \cdot a}{\color{blue}{{\left(\sqrt{\left(-b2\right) + \sqrt{b2 \cdot b2 - a \cdot c}}\right)}^2}}}{a}\]

   7. Applied taylor 13.6

      \[\leadsto \frac{\frac{c \cdot a}{{\left(\sqrt{\left(-b2\right) + \left(\frac{1}{2} \cdot \frac{c \cdot a}{b2} - b2\right)}\right)}^2}}{a}\]

   8. Taylor expanded around -inf 13.6

      \[\leadsto \frac{\frac{c \cdot a}{{\left(\sqrt{\left(-b2\right) + \color{blue}{\left(\frac{1}{2} \cdot \frac{c \cdot a}{b2} - b2\right)}}\right)}^2}}{a}\]

   9. Applied simplify 1.3

      \[\leadsto \color{blue}{\frac{c}{\left(\frac{1}{2} \cdot c\right) \cdot \frac{a}{b2} - \left(b2 - \left(-b2\right)\right)}}\]

   if -4.930770214232589e+18 < b2 < -4.4891519221511533e-128

   1. Initial program 38.3

      \[\frac{\left(-b2\right) - \sqrt{b2 \cdot b2 - a \cdot c}}{a}\]
   2. Using strategy rm

   3. Applied flip-- 38.4

      \[\leadsto \frac{\color{blue}{\frac{{\left(-b2\right)}^2 - {\left(\sqrt{b2 \cdot b2 - a \cdot c}\right)}^2}{\left(-b2\right) + \sqrt{b2 \cdot b2 - a \cdot c}}}}{a}\]

   4. Applied simplify 17.3

      \[\leadsto \frac{\frac{\color{blue}{c \cdot a}}{\left(-b2\right) + \sqrt{b2 \cdot b2 - a \cdot c}}}{a}\]
   5. Using strategy rm

   6. Applied add-sqr-sqrt 17.5

      \[\leadsto \frac{\frac{c \cdot a}{\color{blue}{{\left(\sqrt{\left(-b2\right) + \sqrt{b2 \cdot b2 - a \cdot c}}\right)}^2}}}{a}\]

   if -4.4891519221511533e-128 < b2 < 4.983767219933664e+51

   1. Initial program 11.5

      \[\frac{\left(-b2\right) - \sqrt{b2 \cdot b2 - a \cdot c}}{a}\]

   if 4.983767219933664e+51 < b2

   1. Initial program 39.7

      \[\frac{\left(-b2\right) - \sqrt{b2 \cdot b2 - a \cdot c}}{a}\]

   2. Applied taylor 0

      \[\leadsto -2 \cdot \frac{b2}{a}\]

   3. Taylor expanded around inf 0

      \[\leadsto \color{blue}{-2 \cdot \frac{b2}{a}}\]
3. Recombined 4 regimes into one program.
4. Removed slow pow expressions

Runtime

Time bar (total: 25.7s) Debug log

Please include this information when filing a bug report:

herbie shell --seed '#(3052192724 3812927732 3686175817 630908657 2373248591 511094450)'
(FPCore (a b2 c)
  :name "NMSE problem 3.2.1, negative"
  :pre (and (>= (* b2 b2) (* a c)) (!= a 0))
  (/ (- (- b2) (sqrt (- (* b2 b2) (* a c)))) a))