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Derivation

1. Initial program 43.6

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

2. Initial simplification43.6

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

4. Applied flip--43.6

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

5. Applied associate-/l/43.6

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

6. Simplified0.4

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

8. Applied associate-/l*0.3

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

10. Applied distribute-rgt-in0.3

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

11. Final simplification0.3

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

Runtime

Time bar (total: 29.0s)Debug logProfile

herbie shell --seed 2018296 
(FPCore (a b c)
  :name "Quadratic roots, medium range"
  :pre (and (< 1.1102230246251565e-16 a 9007199254740992.0) (< 1.1102230246251565e-16 b 9007199254740992.0) (< 1.1102230246251565e-16 c 9007199254740992.0))
  (/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a)))