Error

Derivation

1. Initial program 28.5

   \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]

2. Initial simplification28.4

   \[\leadsto \frac{\frac{\sqrt{(b \cdot b + \left(\left(a \cdot -4\right) \cdot c\right))_*} - b}{a}}{2}\]
3. Using strategy rm

4. Applied flip--28.6

   \[\leadsto \frac{\frac{\color{blue}{\frac{\sqrt{(b \cdot b + \left(\left(a \cdot -4\right) \cdot c\right))_*} \cdot \sqrt{(b \cdot b + \left(\left(a \cdot -4\right) \cdot c\right))_*} - b \cdot b}{\sqrt{(b \cdot b + \left(\left(a \cdot -4\right) \cdot c\right))_*} + b}}}{a}}{2}\]

5. Applied associate-/l/28.6

   \[\leadsto \frac{\color{blue}{\frac{\sqrt{(b \cdot b + \left(\left(a \cdot -4\right) \cdot c\right))_*} \cdot \sqrt{(b \cdot b + \left(\left(a \cdot -4\right) \cdot c\right))_*} - b \cdot b}{a \cdot \left(\sqrt{(b \cdot b + \left(\left(a \cdot -4\right) \cdot c\right))_*} + b\right)}}}{2}\]

6. Simplified0.4

   \[\leadsto \frac{\frac{\color{blue}{\left(c \cdot -4\right) \cdot a}}{a \cdot \left(\sqrt{(b \cdot b + \left(\left(a \cdot -4\right) \cdot c\right))_*} + b\right)}}{2}\]
7. Using strategy rm

8. Applied associate-/l*0.3

   \[\leadsto \frac{\color{blue}{\frac{c \cdot -4}{\frac{a \cdot \left(\sqrt{(b \cdot b + \left(\left(a \cdot -4\right) \cdot c\right))_*} + b\right)}{a}}}}{2}\]

9. Final simplification0.3

   \[\leadsto \frac{\frac{c \cdot -4}{\frac{a \cdot \left(\sqrt{(b \cdot b + \left(\left(a \cdot -4\right) \cdot c\right))_*} + b\right)}{a}}}{2}\]

Runtime

Time bar (total: 44.0s)Debug logProfile

herbie shell --seed 2018234 +o rules:numerics
(FPCore (a b c)
  :name "Quadratic roots, 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) (* (* 4 a) c)))) (* 2 a)))