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Derivation

1. Split input into 3 regimes

2. if t < -297358749019.0774

   1. Initial program 1.6

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

   3. Applied associate-*l*9.2

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

   4. Taylor expanded around -inf 1.9

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

   if -297358749019.0774 < t < 8.6762674955213

   1. Initial program 7.4

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

   3. Applied associate-*l*4.3

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

   5. Applied associate-*l*1.7

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

   if 8.6762674955213 < t

   1. Initial program 2.1

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

   2. Initial simplification1.7

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

4. Final simplification1.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -297358749019.0774:\\ \;\;\;\;\left(\left(b \cdot c + \left(18.0 \cdot \left(t \cdot \left(\left(z \cdot y\right) \cdot x\right)\right) - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - k \cdot \left(j \cdot 27.0\right)\\ \mathbf{elif}\;t \le 8.6762674955213:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(\left(z \cdot t\right) \cdot y\right) \cdot \left(18.0 \cdot x\right) - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - k \cdot \left(j \cdot 27.0\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - \left(\left(j \cdot k\right) \cdot 27.0 + \left(x \cdot 4.0\right) \cdot i\right)\right) + t \cdot \left(\left(18.0 \cdot x\right) \cdot \left(z \cdot y\right) - a \cdot 4.0\right)\\ \end{array}\]

Runtime

Time bar (total: 54.8s)Debug logProfile

herbie shell --seed 2018352 
(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)))