Error

Derivation

1. Initial program 28.7

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

3. Applied flip-+28.7

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

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. Applied simplify0.4

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

7. Applied div-inv0.5

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

Runtime

Time bar (total: 2.2m)Debug logProfile

herbie shell --seed '#(1070991898 1055468627 4280279443 640792587 928206309 3646738750)' +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)))