Error

Target

Derivation

1. Split input into 3 regimes.

2. if b < -9.534865642779829e+39

   1. Initial program 40.2

      \[\frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]

   2. Applied taylor 10.5

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

   3. Taylor expanded around -inf 10.5

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

   4. Applied simplify 0.0

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

   5. Applied simplify 0.0

      \[\leadsto \color{blue}{\frac{c}{b}} - \frac{b}{a}\]

   if -9.534865642779829e+39 < b < 7.649843461055766e-75

   1. Initial program 13.5

      \[\frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
   2. Using strategy rm

   3. Applied div-inv 13.6

      \[\leadsto \color{blue}{\left(\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}\right) \cdot \frac{1}{2 \cdot a}}\]

   if 7.649843461055766e-75 < b

   1. Initial program 58.7

      \[\frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
   2. Using strategy rm

   3. Applied flip-+ 58.7

      \[\leadsto \frac{\color{blue}{\frac{{\left(-b\right)}^2 - {\left(\sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}\right)}^2}{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}}{2 \cdot a}\]

   4. Applied simplify 34.5

      \[\leadsto \frac{\frac{\color{blue}{a \cdot \left(4 \cdot c\right)}}{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}{2 \cdot a}\]
   5. Using strategy rm

   6. Applied *-un-lft-identity 34.5

      \[\leadsto \frac{\frac{a \cdot \left(4 \cdot c\right)}{\color{blue}{1 \cdot \left(\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}\right)}}}{2 \cdot a}\]

   7. Applied times-frac 33.9

      \[\leadsto \frac{\color{blue}{\frac{a}{1} \cdot \frac{4 \cdot c}{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}}{2 \cdot a}\]

   8. Applied taylor 14.6

      \[\leadsto \frac{\frac{a}{1} \cdot \frac{4 \cdot c}{\left(-b\right) - \left(b - 2 \cdot \frac{c \cdot a}{b}\right)}}{2 \cdot a}\]

   9. Taylor expanded around inf 14.6

      \[\leadsto \frac{\frac{a}{1} \cdot \frac{4 \cdot c}{\left(-b\right) - \color{blue}{\left(b - 2 \cdot \frac{c \cdot a}{b}\right)}}}{2 \cdot a}\]

   10. Applied simplify 14.5

       \[\leadsto \color{blue}{\frac{\frac{4 \cdot c}{a} \cdot \frac{a}{2}}{\frac{a + a}{\frac{b}{c}} + \left(\left(-b\right) - b\right)}}\]

   11. Applied simplify 3.8

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

Runtime

Time bar (total: 24.4s) Debug logProfile

Please include this information when filing a bug report:

herbie shell --seed '#(1065003094 2074156664 2352254222 753858891 3745550101 3374585842)'
(FPCore (a b c)
  :name "quadp (p42, positive)"

  :target
  (if (< b 0) (/ (+ (- b) (sqrt (- (sqr b) (* 4 (* a c))))) (* 2 a)) (/ c (* a (/ (- (- b) (sqrt (- (sqr b) (* 4 (* a c))))) (* 2 a)))))

  (/ (+ (- b) (sqrt (- (sqr b) (* 4 (* a c))))) (* 2 a)))