Error

Try it out

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. Initial simplification43.8

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

4. Applied flip--43.8

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

5. Applied associate-/l/43.8

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

6. Simplified0.5

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

8. Applied distribute-rgt-neg-out0.5

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

9. Applied distribute-frac-neg0.5

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

10. Simplified0.2

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

11. Final simplification0.2

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

Runtime

Time bar (total: 1.2m)Debug logProfile

herbie shell --seed 2018225 
(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)))