Error

Derivation

1. Split input into 3 regimes

2. if b < -1.343034689126741e+154

   1. Initial program 60.9

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

   2. Applied simplify60.8

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

   4. Applied associate-/r*60.8

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

   5. Taylor expanded around -inf 52.2

      \[\leadsto \frac{\color{blue}{\frac{-1}{3} \cdot b}}{a}\]

   if -1.343034689126741e+154 < b < 8.459181707232342e+155

   1. Initial program 21.8

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

   2. Applied simplify21.8

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

   4. Applied associate-/r*21.9

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

   if 8.459181707232342e+155 < b

   1. Initial program 62.9

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

   2. Applied simplify62.9

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

   3. Taylor expanded around 0 39.4

      \[\leadsto \frac{\color{blue}{b} - b}{3 \cdot a}\]

   4. Applied simplify39.4

      \[\leadsto \color{blue}{0}\]
3. Recombined 3 regimes into one program.

Runtime

Time bar (total: 33.8s)Debug logProfile

herbie shell --seed '#(1064173506 2580572819 2847706409 4129882574 1125180799 1845288547)' +o rules:numerics
(FPCore (a b c d)
  :name "Cubic critical"
  (/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a)))