Error

Derivation

1. Initial program 28.1

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

2. Applied simplify28.1

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

4. Applied flip--28.2

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

5. Applied simplify0.6

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

7. Applied clear-num0.6

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

8. Applied simplify0.3

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

9. Applied simplify0.3

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

Runtime

Time bar (total: 1.3m)Debug logProfile

herbie shell --seed '#(1071373924 2949776965 1885069702 3247780810 90874544 2263903749)' +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)))