Error

Try it out

Derivation

1. Split input into 2 regimes

2. if z < -1.3357439743981973e+33 or 2968448.138240671 < z

   1. Initial program 7.1

      \[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
   2. Using strategy rm

   3. Applied associate-*l*7.1

      \[\leadsto \left(\left(\left(\left(\color{blue}{\left(x \cdot \left(18.0 \cdot y\right)\right)} \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]

   4. Taylor expanded around -inf 7.0

      \[\leadsto \left(\left(\left(\left(\left(x \cdot \left(18.0 \cdot y\right)\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \color{blue}{27.0 \cdot \left(j \cdot k\right)}\]
   5. Using strategy rm

   6. Applied add-cube-cbrt7.2

      \[\leadsto \left(\left(\left(\color{blue}{\left(\left(\sqrt[3]{\left(x \cdot \left(18.0 \cdot y\right)\right) \cdot z} \cdot \sqrt[3]{\left(x \cdot \left(18.0 \cdot y\right)\right) \cdot z}\right) \cdot \sqrt[3]{\left(x \cdot \left(18.0 \cdot y\right)\right) \cdot z}\right)} \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - 27.0 \cdot \left(j \cdot k\right)\]

   if -1.3357439743981973e+33 < z < 2968448.138240671

   1. Initial program 4.1

      \[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
   2. Using strategy rm

   3. Applied associate-*l*4.2

      \[\leadsto \left(\left(\left(\left(\color{blue}{\left(x \cdot \left(18.0 \cdot y\right)\right)} \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]

   4. Taylor expanded around -inf 4.2

      \[\leadsto \left(\left(\left(\left(\left(x \cdot \left(18.0 \cdot y\right)\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \color{blue}{27.0 \cdot \left(j \cdot k\right)}\]

   5. Taylor expanded around inf 1.2

      \[\leadsto \left(\left(\left(\color{blue}{\left(18.0 \cdot \left(x \cdot \left(z \cdot y\right)\right)\right)} \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - 27.0 \cdot \left(j \cdot k\right)\]
3. Recombined 2 regimes into one program.

4. Final simplification3.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.3357439743981973 \cdot 10^{+33} \lor \neg \left(z \le 2968448.138240671\right):\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(\sqrt[3]{\left(x \cdot \left(18.0 \cdot y\right)\right) \cdot z} \cdot \left(\sqrt[3]{\left(x \cdot \left(18.0 \cdot y\right)\right) \cdot z} \cdot \sqrt[3]{\left(x \cdot \left(18.0 \cdot y\right)\right) \cdot z}\right)\right) \cdot t - t \cdot \left(4.0 \cdot a\right)\right)\right) - i \cdot \left(4.0 \cdot x\right)\right) - \left(k \cdot j\right) \cdot 27.0\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(18.0 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \cdot t - t \cdot \left(4.0 \cdot a\right)\right) + b \cdot c\right) - i \cdot \left(4.0 \cdot x\right)\right) - \left(k \cdot j\right) \cdot 27.0\\ \end{array}\]

Reproduce

herbie shell --seed 2019010 +o rules:numerics
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1"
  (- (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* (* j 27.0) k)))

Details

Time bar (total: 19.9s)Debug log