Error

Derivation

1. Initial program 52.2

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

2. Simplified52.2

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

3. Taylor expanded around inf 6.4

   \[\leadsto \color{blue}{-1 \cdot \frac{c}{b}}\]

4. Simplified6.4

   \[\leadsto \color{blue}{-\frac{c}{b}}\]

5. Final simplification6.4

   \[\leadsto -\frac{c}{b}\]

Reproduce

herbie shell --seed 2019051 
(FPCore (a b c)
  :name "Quadratic roots, 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) (* (* 4 a) c)))) (* 2 a)))