Error

Derivation

1. Initial program 52.6

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

2. Applied simplify52.6

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

4. Applied flip--52.7

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

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 *-un-lft-identity0.5

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

8. Applied times-frac0.6

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

9. Applied simplify0.5

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

10. Applied simplify0.5

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

Runtime

Time bar (total: 1.7m)Debug logProfile

herbie shell --seed '#(1071373924 2949776965 1885069702 3247780810 90874544 2263903749)' 
(FPCore (a b c d)
  :name "Cubic critical, wide range"
  :pre (and (< 4.930380657631324e-32 a 2.028240960365167e+31) (< 4.930380657631324e-32 b 2.028240960365167e+31) (< 4.930380657631324e-32 c 2.028240960365167e+31))
  (/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a)))