Error

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Derivation

1. Split input into 2 regimes

2. if x < -3.3723825016084254e-11

   1. Initial program 12.5

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

   2. Simplified6.9

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

   if -3.3723825016084254e-11 < x

   1. Initial program 4.0

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

   3. Applied add-cube-cbrt4.1

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

4. Final simplification4.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -3.3723825016084254 \cdot 10^{-11}:\\ \;\;\;\;\left(c \cdot b - \left(\left(k \cdot j\right) \cdot 27.0 + i \cdot \left(4.0 \cdot x\right)\right)\right) + \left(\left(x \cdot 18.0\right) \cdot \left(y \cdot z\right) - a \cdot 4.0\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\sqrt[3]{t \cdot \left(z \cdot \left(\left(x \cdot 18.0\right) \cdot y\right)\right)} \cdot \left(\sqrt[3]{t \cdot \left(z \cdot \left(\left(x \cdot 18.0\right) \cdot y\right)\right)} \cdot \sqrt[3]{t \cdot \left(z \cdot \left(\left(x \cdot 18.0\right) \cdot y\right)\right)}\right) - \left(a \cdot 4.0\right) \cdot t\right) + c \cdot b\right) - i \cdot \left(4.0 \cdot x\right)\right) - k \cdot \left(27.0 \cdot j\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019005 
(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

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