Error

Derivation

1. Split input into 3 regimes

2. if b < -1.614282986419709e+71

   1. Initial program 38.0

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

   2. Taylor expanded around -inf 5.9

      \[\leadsto \color{blue}{\frac{-2}{3} \cdot \frac{b}{a}}\]

   if -1.614282986419709e+71 < b < 1.302164828124397e-34

   1. Initial program 15.1

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

   3. Applied div-inv15.2

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

   if 1.302164828124397e-34 < b

   1. Initial program 53.3

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

   3. Applied clear-num53.3

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

   4. Applied simplify53.3

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

   5. Taylor expanded around 0 8.3

      \[\leadsto \frac{1}{\color{blue}{-2 \cdot \frac{b}{c}}}\]

   6. Applied simplify7.6

      \[\leadsto \color{blue}{\frac{\frac{c}{-2}}{b}}\]
3. Recombined 3 regimes into one program.

Runtime

Time bar (total: 2.0m)Debug logProfile

herbie shell --seed '#(1070609872 3456127585 2380521889 2328837196 1765472538 734540918)' +o rules:numerics
(FPCore (a b c d)
  :name "Cubic critical"
  (/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a)))