\[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
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: 52.0 s
Input Error: 5.6
Output Error: 2.2
Log: ⚲
Profile: 🕒
\(\begin{cases} \left(18.0 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right) - 4.0 \cdot \left(t \cdot a + i \cdot x\right)\right) + \left(c \cdot b - j \cdot \left(27.0 \cdot k\right)\right) & \text{when } y \le -1.0209693993561548 \cdot 10^{+104} \\ \left(t \cdot \left(z \cdot \left(18.0 \cdot \left(x \cdot y\right)\right)\right) - 4.0 \cdot \left(t \cdot a + i \cdot x\right)\right) + \left(c \cdot b - j \cdot \left(27.0 \cdot k\right)\right) & \text{when } y \le 8.525533328043029 \cdot 10^{-150} \\ \left(18.0 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right) - 4.0 \cdot \left(t \cdot a + i \cdot x\right)\right) + \left(c \cdot b - j \cdot \left(27.0 \cdot k\right)\right) & \text{otherwise} \end{cases}\)

    if y < -1.0209693993561548e+104 or 8.525533328043029e-150 < y

    1. Started with
      \[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
      9.8
    2. Applied simplify to get
      \[\color{red}{\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k} \leadsto \color{blue}{\left(\left(t \cdot z\right) \cdot \left(18.0 \cdot \left(x \cdot y\right)\right) - 4.0 \cdot \left(t \cdot a + i \cdot x\right)\right) + \left(c \cdot b - j \cdot \left(27.0 \cdot k\right)\right)}\]
      7.2
    3. Applied taylor to get
      \[\left(\left(t \cdot z\right) \cdot \left(18.0 \cdot \left(x \cdot y\right)\right) - 4.0 \cdot \left(t \cdot a + i \cdot x\right)\right) + \left(c \cdot b - j \cdot \left(27.0 \cdot k\right)\right) \leadsto \left(18.0 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right) - 4.0 \cdot \left(t \cdot a + i \cdot x\right)\right) + \left(c \cdot b - j \cdot \left(27.0 \cdot k\right)\right)\]
      2.7
    4. Taylor expanded around inf to get
      \[\left(\color{red}{18.0 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)} - 4.0 \cdot \left(t \cdot a + i \cdot x\right)\right) + \left(c \cdot b - j \cdot \left(27.0 \cdot k\right)\right) \leadsto \left(\color{blue}{18.0 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)} - 4.0 \cdot \left(t \cdot a + i \cdot x\right)\right) + \left(c \cdot b - j \cdot \left(27.0 \cdot k\right)\right)\]
      2.7

    if -1.0209693993561548e+104 < y < 8.525533328043029e-150

    1. Started with
      \[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
      1.6
    2. Applied simplify to get
      \[\color{red}{\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k} \leadsto \color{blue}{\left(\left(t \cdot z\right) \cdot \left(18.0 \cdot \left(x \cdot y\right)\right) - 4.0 \cdot \left(t \cdot a + i \cdot x\right)\right) + \left(c \cdot b - j \cdot \left(27.0 \cdot k\right)\right)}\]
      4.7
    3. Using strategy rm
      4.7
    4. Applied associate-*l* to get
      \[\left(\color{red}{\left(t \cdot z\right) \cdot \left(18.0 \cdot \left(x \cdot y\right)\right)} - 4.0 \cdot \left(t \cdot a + i \cdot x\right)\right) + \left(c \cdot b - j \cdot \left(27.0 \cdot k\right)\right) \leadsto \left(\color{blue}{t \cdot \left(z \cdot \left(18.0 \cdot \left(x \cdot y\right)\right)\right)} - 4.0 \cdot \left(t \cdot a + i \cdot x\right)\right) + \left(c \cdot b - j \cdot \left(27.0 \cdot k\right)\right)\]
      1.7
  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)))