Error

Target

Derivation

1. Split input into 3 regimes

2. if b < -1.3356192400654382e+154

   1. Initial program 60.9

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

   2. Initial simplification60.9

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

   3. Taylor expanded around inf 60.9

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

   4. Simplified60.8

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

   6. Applied clear-num60.8

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

   7. Taylor expanded around -inf 52.2

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

   if -1.3356192400654382e+154 < b < 1.01261065157807e-130

   1. Initial program 10.7

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

   2. Initial simplification10.7

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

   3. Taylor expanded around inf 10.7

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

   4. Simplified10.7

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

   if 1.01261065157807e-130 < b

   1. Initial program 50.4

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

   2. Initial simplification50.4

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

   3. Taylor expanded around inf 50.4

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

   4. Simplified50.4

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

   6. Applied clear-num50.4

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

   7. Taylor expanded around 0 12.5

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

   8. Simplified12.5

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

4. Final simplification16.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -1.3356192400654382 \cdot 10^{+154}:\\ \;\;\;\;\frac{-1}{2} \cdot \frac{b}{a}\\ \mathbf{elif}\;b \le 1.01261065157807 \cdot 10^{-130}:\\ \;\;\;\;\frac{\sqrt{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*} - b}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{-\frac{b}{c}}\\ \end{array}\]

Runtime

Time bar (total: 25.1s)Debug logProfile

herbie shell --seed 2018235 +o rules:numerics
(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)))