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Derivation

1. Initial program 43.8

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

2. Applied simplify43.8

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

4. Applied flip--43.8

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

5. Applied simplify0.5

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

7. Applied div-inv0.6

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

8. Applied times-frac0.6

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

9. Applied simplify0.5

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

Runtime

Time bar (total: 2.4m)Debug logProfile

herbie shell --seed '#(1072743783 989954326 4239155542 3782239461 3602631542 1719177920)' 
(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)))