Error

Derivation

1. Split input into 4 regimes.

2. if b/2 < -1.7321058520772784e+67

   1. Initial program 41.7

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

   2. Applied taylor 0

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

   3. Taylor expanded around -inf 0

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

   if -1.7321058520772784e+67 < b/2 < 1.922375846709798e-232

   1. Initial program 10.5

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

   3. Applied div-inv 10.6

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

   if 1.922375846709798e-232 < b/2 < 1438490.0801097094

   1. Initial program 30.1

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

   3. Applied flip-+ 30.2

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

   4. Applied simplify 19.2

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

   6. Applied div-inv 19.2

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

   if 1438490.0801097094 < b/2

   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-+ 58.3

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

   4. Applied simplify 31.6

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

   6. Applied add-cube-cbrt 31.8

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\frac{\frac{a \cdot c}{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}}{a}}\right)}^3}\]

   7. Applied simplify 28.3

      \[\leadsto {\color{blue}{\left(\sqrt[3]{\frac{c}{\left(-b/2\right) - \sqrt{b/2 \cdot b/2 - c \cdot a}}}\right)}}^3\]

   8. Applied taylor 8.2

      \[\leadsto {\left(\sqrt[3]{\frac{c}{\left(-b/2\right) - \left(b/2 - \frac{1}{2} \cdot \frac{c \cdot a}{b/2}\right)}}\right)}^3\]

   9. Taylor expanded around inf 8.2

      \[\leadsto {\left(\sqrt[3]{\frac{c}{\left(-b/2\right) - \color{blue}{\left(b/2 - \frac{1}{2} \cdot \frac{c \cdot a}{b/2}\right)}}}\right)}^3\]

   10. Applied simplify 2.5

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

Runtime

Total time: 31.5s Debug log

Please include this information when filing a bug report:

herbie --seed '#(4204583864 2636495485 3400033341 319004202 4134280227 1599347260)'
(FPCore (a b/2 c)
  :name "NMSE problem 3.2.1, positive"
  (/ (+ (- b/2) (sqrt (- (sqr b/2) (* a c)))) a))