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Derivation

1. Initial program 28.8

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

2. Applied simplify28.8

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

4. Applied flip--28.8

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

5. Applied simplify0.6

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

7. Applied associate-/r*0.6

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

8. Applied simplify0.5

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

9. Applied simplify0.5

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

Runtime

Time bar (total: 1.7m)Debug logProfile

herbie shell --seed 2018170 
(FPCore (a b c d)
  :name "Cubic critical, narrow range"
  :pre (and (< 1.0536712127723509e-08 a 94906265.62425156) (< 1.0536712127723509e-08 b 94906265.62425156) (< 1.0536712127723509e-08 c 94906265.62425156))
  (/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a)))