Error

Derivation

1. Initial program 28.2

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

3. Applied flip-+28.2

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

4. Applied simplify0.4

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

6. Applied prod-diff0.4

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

7. Applied simplify0.4

   \[\leadsto \frac{\frac{c \cdot \left(a \cdot 4\right)}{\left(-b\right) - \sqrt{(b \cdot b + \left(-c \cdot \left(4 \cdot a\right)\right))_* + \color{blue}{0}}}}{2 \cdot a}\]

Runtime

Time bar (total: 2.6m)Debug logProfile

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