Error

Derivation

1. Initial program 52.5

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

3. Applied flip-+52.5

   \[\leadsto \frac{\color{blue}{\frac{\left(-b\right) \cdot \left(-b\right) - \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c} \cdot \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{\left(-b\right) - \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}}}{3 \cdot a}\]

4. Applied associate-/l/52.5

   \[\leadsto \color{blue}{\frac{\left(-b\right) \cdot \left(-b\right) - \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c} \cdot \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{\left(3 \cdot a\right) \cdot \left(\left(-b\right) - \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}\right)}}\]

5. Simplified0.5

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

7. Applied associate-*l*0.5

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

9. Applied times-frac0.4

   \[\leadsto \color{blue}{\frac{3}{3} \cdot \frac{c \cdot a}{a \cdot \left(\left(-b\right) - \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}\right)}}\]

10. Simplified0.4

    \[\leadsto \color{blue}{1} \cdot \frac{c \cdot a}{a \cdot \left(\left(-b\right) - \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}\right)}\]

11. Simplified0.1

    \[\leadsto 1 \cdot \color{blue}{\frac{c}{\left(-b\right) - \sqrt{(\left(-3 \cdot a\right) \cdot c + \left(b \cdot b\right))_*}}}\]

12. Final simplification0.1

    \[\leadsto \frac{c}{\left(-b\right) - \sqrt{(\left(-3 \cdot a\right) \cdot c + \left(b \cdot b\right))_*}}\]

Reproduce

herbie shell --seed 2018360 +o rules:numerics
(FPCore (a b c d)
  :name "Cubic critical, 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) (* (* 3 a) c)))) (* 3 a)))

Details

Time bar (total: 1.2m)Debug log