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. Initial simplification44.0

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

4. Applied flip--44.0

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

5. Applied associate-/l/44.0

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

6. Simplified0.5

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

8. Applied times-frac0.5

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

9. Simplified0.5

   \[\leadsto \color{blue}{\left(\frac{1}{3} \cdot c\right)} \cdot \frac{-3}{\sqrt{(-3 \cdot \left(c \cdot a\right) + \left(b \cdot b\right))_*} + b}\]
10. Using strategy rm

11. Applied pow10.5

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

12. Applied pow10.5

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

13. Applied pow-prod-down0.5

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

14. Simplified0.2

    \[\leadsto {\color{blue}{\left(\frac{-c}{b + \sqrt{(-3 \cdot \left(c \cdot a\right) + \left(b \cdot b\right))_*}}\right)}}^{1}\]
15. Using strategy rm

16. Applied div-inv0.3

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

17. Final simplification0.3

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

Runtime

Time bar (total: 26.3s)Debug logProfile

herbie shell --seed 2018354 +o rules:numerics
(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)))