\[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
Test:
Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1
Bits:
128 bits
Bits error versus x
Bits error versus y
Bits error versus z
Bits error versus t
Bits error versus a
Bits error versus b
Bits error versus c
Bits error versus i
Bits error versus j
Bits error versus k
Time: 24.0 s
Input Error: 6.5
Output Error: 4.3
Log: ⚲
Profile: 🕒
\(\begin{cases} (\left(t \cdot z\right) * \left(18.0 \cdot \left(x \cdot y\right)\right) + \left(c \cdot b\right))_* - (4.0 * \left((i * x + \left(t \cdot a\right))_*\right) + \left(\left(j \cdot 27.0\right) \cdot k\right))_* & \text{when } z \le -8.486167276677909 \cdot 10^{-96} \\ (\left(z \cdot t\right) * 0 + \left(c \cdot b\right))_* - (4.0 * \left((i * x + \left(a \cdot t\right))_*\right) + \left(\left(j \cdot k\right) \cdot 27.0\right))_* & \text{when } z \le 1.1566624905940529 \cdot 10^{-175} \\ (\left(t \cdot z\right) * \left(18.0 \cdot \left(x \cdot y\right)\right) + \left(c \cdot b\right))_* - (4.0 * \left((i * x + \left(t \cdot a\right))_*\right) + \left(\left(j \cdot 27.0\right) \cdot k\right))_* & \text{otherwise} \end{cases}\)

    if z < -8.486167276677909e-96 or 1.1566624905940529e-175 < z

    1. Started with
      \[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
      5.6
    2. Applied simplify to get
      \[\color{red}{\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k} \leadsto \color{blue}{(\left(t \cdot z\right) * \left(18.0 \cdot \left(x \cdot y\right)\right) + \left(c \cdot b\right))_* - (4.0 * \left((i * x + \left(t \cdot a\right))_*\right) + \left(j \cdot \left(27.0 \cdot k\right)\right))_*}\]
      6.4
    3. Using strategy rm
      6.4
    4. Applied associate-*r* to get
      \[(\left(t \cdot z\right) * \left(18.0 \cdot \left(x \cdot y\right)\right) + \left(c \cdot b\right))_* - (4.0 * \left((i * x + \left(t \cdot a\right))_*\right) + \color{red}{\left(j \cdot \left(27.0 \cdot k\right)\right)})_* \leadsto (\left(t \cdot z\right) * \left(18.0 \cdot \left(x \cdot y\right)\right) + \left(c \cdot b\right))_* - (4.0 * \left((i * x + \left(t \cdot a\right))_*\right) + \color{blue}{\left(\left(j \cdot 27.0\right) \cdot k\right)})_*\]
      6.3

    if -8.486167276677909e-96 < z < 1.1566624905940529e-175

    1. Started with
      \[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
      8.4
    2. Applied simplify to get
      \[\color{red}{\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k} \leadsto \color{blue}{(\left(t \cdot z\right) * \left(18.0 \cdot \left(x \cdot y\right)\right) + \left(c \cdot b\right))_* - (4.0 * \left((i * x + \left(t \cdot a\right))_*\right) + \left(j \cdot \left(27.0 \cdot k\right)\right))_*}\]
      8.3
    3. Using strategy rm
      8.3
    4. Applied add-cube-cbrt to get
      \[(\left(t \cdot z\right) * \color{red}{\left(18.0 \cdot \left(x \cdot y\right)\right)} + \left(c \cdot b\right))_* - (4.0 * \left((i * x + \left(t \cdot a\right))_*\right) + \left(j \cdot \left(27.0 \cdot k\right)\right))_* \leadsto (\left(t \cdot z\right) * \color{blue}{\left({\left(\sqrt[3]{18.0 \cdot \left(x \cdot y\right)}\right)}^3\right)} + \left(c \cdot b\right))_* - (4.0 * \left((i * x + \left(t \cdot a\right))_*\right) + \left(j \cdot \left(27.0 \cdot k\right)\right))_*\]
      8.3
    5. Applied taylor to get
      \[(\left(t \cdot z\right) * \left({\left(\sqrt[3]{18.0 \cdot \left(x \cdot y\right)}\right)}^3\right) + \left(c \cdot b\right))_* - (4.0 * \left((i * x + \left(t \cdot a\right))_*\right) + \left(j \cdot \left(27.0 \cdot k\right)\right))_* \leadsto (\left(t \cdot z\right) * 0 + \left(c \cdot b\right))_* - (4.0 * \left((i * x + \left(t \cdot a\right))_*\right) + \left(j \cdot \left(27.0 \cdot k\right)\right))_*\]
      0.1
    6. Taylor expanded around inf to get
      \[(\left(t \cdot z\right) * \color{red}{0} + \left(c \cdot b\right))_* - (4.0 * \left((i * x + \left(t \cdot a\right))_*\right) + \left(j \cdot \left(27.0 \cdot k\right)\right))_* \leadsto (\left(t \cdot z\right) * \color{blue}{0} + \left(c \cdot b\right))_* - (4.0 * \left((i * x + \left(t \cdot a\right))_*\right) + \left(j \cdot \left(27.0 \cdot k\right)\right))_*\]
      0.1
    7. Applied simplify to get
      \[(\left(t \cdot z\right) * 0 + \left(c \cdot b\right))_* - (4.0 * \left((i * x + \left(t \cdot a\right))_*\right) + \left(j \cdot \left(27.0 \cdot k\right)\right))_* \leadsto (\left(z \cdot t\right) * 0 + \left(c \cdot b\right))_* - (4.0 * \left((i * x + \left(a \cdot t\right))_*\right) + \left(\left(j \cdot k\right) \cdot 27.0\right))_*\]
      0.1
    8. Applied final simplification
  1. Removed slow pow expressions

Original test:


(lambda ((x default) (y default) (z default) (t default) (a default) (b default) (c default) (i default) (j default) (k default))
  #: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)))