Error

Derivation

1. Initial program 43.7

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

2. Applied simplify43.7

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

4. Applied flip--43.7

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

5. Applied simplify0.4

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

7. Applied *-un-lft-identity0.4

   \[\leadsto \frac{\frac{\left(c \cdot 4\right) \cdot \left(-a\right)}{\color{blue}{1 \cdot \left(\sqrt{(\left(a \cdot 4\right) \cdot \left(-c\right) + \left(b \cdot b\right))_*} + b\right)}}}{2 \cdot a}\]

8. Applied times-frac0.4

   \[\leadsto \frac{\color{blue}{\frac{c \cdot 4}{1} \cdot \frac{-a}{\sqrt{(\left(a \cdot 4\right) \cdot \left(-c\right) + \left(b \cdot b\right))_*} + b}}}{2 \cdot a}\]

9. Applied simplify0.4

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

Runtime

Time bar (total: 2.4m)Debug logProfile

herbie shell --seed 2020178 +o rules:numerics
(FPCore (a b c)
  :name "Quadratic roots, medium range"
  :pre (and (< 1.1102230246251565e-16 a 9007199254740992.0) (< 1.1102230246251565e-16 b 9007199254740992.0) (< 1.1102230246251565e-16 c 9007199254740992.0))
  (/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a)))