Error

Derivation

if b/2 < -3.2138303248745144e+50

1. Initial program 40.1

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

2. Applied taylor 11.0

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

3. Taylor expanded around -inf 11.0

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

4. Applied simplify 0.1

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

if -3.2138303248745144e+50 < b/2 < -3.147839144939969e-238

1. Initial program 8.5

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

if -3.147839144939969e-238 < b/2 < 1.5588782102575123e+76

1. Initial program 27.6

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

3. Applied flip-+ 27.7

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

4. Applied simplify 15.7

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

6. Applied *-un-lft-identity 15.7

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

7. Applied times-frac 13.5

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

if 1.5588782102575123e+76 < 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-+ 58.2

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

4. Applied simplify 32.4

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

5. Applied taylor 16.0

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

6. Taylor expanded around inf 16.0

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

7. Applied simplify 1.5

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

Runtime

Total time: 32.5s Debug log

Please report a bug with the following info:

herbie --seed '#(3998637471 2327741461 3535618413 852106778 676758467 1297175556)'
(FPCore (a b/2 c)
  :name "NMSE problem 3.2.1, positive"
  (/ (+ (- b/2) (sqrt (- (sqr b/2) (* a c)))) a))