Error

Derivation

1. Initial program 44.0

   \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a}\]

2. Applied simplify44.0

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

4. Applied flip--44.0

   \[\leadsto \frac{\color{blue}{\frac{\sqrt{b \cdot b - \left(a \cdot c\right) \cdot 3} \cdot \sqrt{b \cdot b - \left(a \cdot c\right) \cdot 3} - b \cdot b}{\sqrt{b \cdot b - \left(a \cdot c\right) \cdot 3} + b}}}{3 \cdot a}\]

5. Applied simplify0.5

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

7. Applied *-un-lft-identity0.5

   \[\leadsto \frac{\frac{\left(-a\right) \cdot \left(c \cdot 3\right)}{\color{blue}{1 \cdot \left(\sqrt{b \cdot b - \left(a \cdot c\right) \cdot 3} + b\right)}}}{3 \cdot a}\]

8. Applied times-frac0.5

   \[\leadsto \frac{\color{blue}{\frac{-a}{1} \cdot \frac{c \cdot 3}{\sqrt{b \cdot b - \left(a \cdot c\right) \cdot 3} + b}}}{3 \cdot a}\]

9. Applied associate-/l*0.5

   \[\leadsto \color{blue}{\frac{\frac{-a}{1}}{\frac{3 \cdot a}{\frac{c \cdot 3}{\sqrt{b \cdot b - \left(a \cdot c\right) \cdot 3} + b}}}}\]

10. Applied simplify0.4

    \[\leadsto \frac{\frac{-a}{1}}{\color{blue}{\frac{b + \sqrt{b \cdot b - \left(c \cdot a\right) \cdot 3}}{\frac{c}{a}}}}\]

Runtime

Time bar (total: 2.0m)Debug logProfile

herbie shell --seed '#(1070609872 3456127585 2380521889 2328837196 1765472538 734540918)' 
(FPCore (a b c d)
  :name "Cubic critical, 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) (* (* 3 a) c)))) (* 3 a)))