Error

Derivation

1. Initial program 28.2

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

2. Applied simplify28.2

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

4. Applied flip--28.2

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

5. Applied simplify0.5

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

7. Applied clear-num0.5

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

8. Applied simplify0.3

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

Runtime

Time bar (total: 1.8m)Debug logProfile

herbie shell --seed 2018296 +o rules:numerics
(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)))