Error

Target

Derivation

1. Split input into 4 regimes

2. if b < -7.060089202421629e+125

   1. Initial program 52.3

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

   2. Applied simplify52.3

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

   3. Taylor expanded around -inf 3.9

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

   4. Applied simplify3.9

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

   if -7.060089202421629e+125 < b < 5.94703430650783e-258

   1. Initial program 9.4

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

   2. Applied simplify9.4

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

   if 5.94703430650783e-258 < b < 3.8683527837232445e+135

   1. Initial program 35.8

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

   2. Applied simplify35.8

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

   4. Applied flip--35.9

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

   5. Applied simplify15.1

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

   7. Applied *-un-lft-identity15.1

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

   8. Applied times-frac15.1

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

   9. Applied times-frac15.1

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

   10. Applied simplify15.1

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

   11. Applied simplify7.4

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

   if 3.8683527837232445e+135 < b

   1. Initial program 61.2

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

   2. Applied simplify61.2

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

   3. Taylor expanded around inf 38.4

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

   4. Applied simplify1.5

      \[\leadsto \color{blue}{\frac{-c}{\frac{b}{1}}}\]
3. Recombined 4 regimes into one program.

4. Applied simplify6.4

   \[\leadsto \color{blue}{\begin{array}{l} \mathbf{if}\;b \le -7.060089202421629 \cdot 10^{+125}:\\ \;\;\;\;-\frac{b}{a}\\ \mathbf{if}\;b \le 5.94703430650783 \cdot 10^{-258}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - \left(c \cdot 4\right) \cdot a} - b}{2 \cdot a}\\ \mathbf{if}\;b \le 3.8683527837232445 \cdot 10^{+135}:\\ \;\;\;\;\frac{-c}{b + \sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4}} \cdot \frac{4}{2}\\ \mathbf{else}:\\ \;\;\;\;-\frac{c}{b}\\ \end{array}}\]

Runtime

Time bar (total: 1.8m)Debug logProfile

herbie shell --seed '#(1071979731 1496239409 439705970 2863295848 982327776 189749553)' 
(FPCore (a b c)
  :name "quadp (p42, positive)"

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

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