Error

Target

Derivation

1. Split input into 4 regimes.

2. if b < -9.612559777483023e+27

   1. Initial program 58.1

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

   3. Applied flip-- 58.2

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

   4. Applied simplify 31.5

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

   6. Applied *-un-lft-identity 31.5

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

   7. Applied times-frac 31.3

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

   8. Applied taylor 15.2

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

   9. Taylor expanded around -inf 15.2

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

   10. Applied simplify 12.4

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

   11. Applied simplify 2.4

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

   if -9.612559777483023e+27 < b < -1.4807562139587436e-235

   1. Initial program 30.7

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

   3. Applied flip-- 30.9

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

   4. Applied simplify 17.5

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

   6. Applied *-un-lft-identity 17.5

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

   7. Applied times-frac 14.1

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

   if -1.4807562139587436e-235 < b < 2.0227608047655974e+110

   1. Initial program 10.2

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

   if 2.0227608047655974e+110 < b

   1. Initial program 48.7

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

   2. Applied taylor 13.0

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

   3. Taylor expanded around inf 13.0

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

   4. Applied simplify 0.0

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

   5. Applied simplify 0.0

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

Runtime

Time bar (total: 22.3s) Debug logProfile

Please include this information when filing a bug report:

herbie shell --seed '#(1067773715 2765207660 218871639 3688798924 2755544087 2054563380)'
(FPCore (a b c)
  :name "quadm (p42, negative)"

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

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