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Target

Derivation

1. Split input into 3 regimes

2. if b < -7.831748553927705e+153

   1. Initial program 60.8

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

   2. Initial simplification60.8

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

   4. Applied div-sub60.8

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

   6. Applied div-inv60.8

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

   7. Taylor expanded around -inf 2.3

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

   if -7.831748553927705e+153 < b < 9.075353573798497e-157

   1. Initial program 10.5

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

   2. Initial simplification10.5

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

   4. Applied div-sub10.5

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

   if 9.075353573798497e-157 < b

   1. Initial program 48.9

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

   2. Initial simplification48.9

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

   4. Applied div-sub49.4

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

   5. Taylor expanded around inf 13.3

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

   6. Simplified13.3

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

4. Final simplification10.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -7.831748553927705 \cdot 10^{+153}:\\ \;\;\;\;\left(\frac{c}{b} - \frac{b}{a} \cdot \frac{1}{2}\right) - \frac{b}{2 \cdot a}\\ \mathbf{elif}\;b \le 9.075353573798497 \cdot 10^{-157}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - c \cdot \left(a \cdot 4\right)}}{2 \cdot a} - \frac{b}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;-\frac{c}{b}\\ \end{array}\]

Runtime

Time bar (total: 36.0s)Debug logProfile

herbie shell --seed 2018295 
(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)))