Error

Derivation

1. Initial program 28.9

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

2. Applied simplify28.9

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

4. Applied flip--28.9

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

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 *-un-lft-identity0.6

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

8. Applied times-frac0.6

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

9. Applied times-frac0.6

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

10. Applied simplify0.6

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

Runtime

Time bar (total: 1.6m)Debug logProfile

herbie shell --seed '#(1070386091 2509006183 1430610344 1025408621 36622005 1425925650)' 
(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)))