Error

Derivation

1. Split input into 2 regimes

2. if z < -5.595282481905591e+24 or 7.074420817155232e+69 < 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. Taylor expanded around 0 7.0

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

   4. Applied add-cube-cbrt7.2

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

   if -5.595282481905591e+24 < z < 7.074420817155232e+69

   1. Initial program 4.7

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

   2. Simplified1.7

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

4. Final simplification3.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -5.595282481905591 \cdot 10^{+24} \lor \neg \left(z \le 7.074420817155232 \cdot 10^{+69}\right):\\ \;\;\;\;\left(\left(b \cdot c + \left(\sqrt[3]{t \cdot \left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right)} \cdot \left(\sqrt[3]{t \cdot \left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right)} \cdot \sqrt[3]{t \cdot \left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right)}\right) - t \cdot \left(4.0 \cdot a\right)\right)\right) - i \cdot \left(4.0 \cdot x\right)\right) - \left(k \cdot j\right) \cdot 27.0\\ \mathbf{else}:\\ \;\;\;\;(t \cdot \left(\left(z \cdot y\right) \cdot \left(x \cdot 18.0\right)\right) + \left((\left(4.0 \cdot a\right) \cdot \left(-t\right) + \left(b \cdot c\right))_*\right))_* - (j \cdot \left(k \cdot 27.0\right) + \left(i \cdot \left(4.0 \cdot x\right)\right))_*\\ \end{array}\]

Reproduce

herbie shell --seed 2019005 +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: 21.3s)Debug log