Error

Try it out

Derivation

1. Initial program 43.7

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

2. Initial simplification43.7

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

4. Applied flip--43.7

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

5. Applied associate-/l/43.7

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

6. Simplified0.4

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

8. Applied times-frac0.2

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

9. Simplified0.2

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

10. Final simplification0.2

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

Runtime

Time bar (total: 1.6m)Debug logProfile

herbie shell --seed 2018225 
(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)))