\[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
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: 17.4 s
Input Error: 3.2
Output Error: 3.2
Log: ⚲
Profile: 🕒
\((\left(\left(18.0 \cdot t\right) \cdot y\right) * \left(z \cdot x\right) + \left(b \cdot c\right))_* - (4.0 * \left((i * x + \left(a \cdot t\right))_*\right) + \left(\left(k \cdot 27.0\right) \cdot j\right))_*\)
  1. Started with
    \[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
    3.2
  2. Applied simplify to get
    \[\color{red}{\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k} \leadsto \color{blue}{(\left(t \cdot z\right) * \left(18.0 \cdot \left(x \cdot y\right)\right) + \left(c \cdot b\right))_* - (4.0 * \left((i * x + \left(t \cdot a\right))_*\right) + \left(j \cdot \left(27.0 \cdot k\right)\right))_*}\]
    3.1
  3. Applied taylor to get
    \[(\left(t \cdot z\right) * \left(18.0 \cdot \left(x \cdot y\right)\right) + \left(c \cdot b\right))_* - (4.0 * \left((i * x + \left(t \cdot a\right))_*\right) + \left(j \cdot \left(27.0 \cdot k\right)\right))_* \leadsto (\left(t \cdot z\right) * \left(18.0 \cdot \left(y \cdot x\right)\right) + \left(b \cdot c\right))_* - (4.0 * \left((i * x + \left(t \cdot a\right))_*\right) + \left(27.0 \cdot \left(j \cdot k\right)\right))_*\]
    2.8
  4. Taylor expanded around 0 to get
    \[\color{red}{(\left(t \cdot z\right) * \left(18.0 \cdot \left(y \cdot x\right)\right) + \left(b \cdot c\right))_* - (4.0 * \left((i * x + \left(t \cdot a\right))_*\right) + \left(27.0 \cdot \left(j \cdot k\right)\right))_*} \leadsto \color{blue}{(\left(t \cdot z\right) * \left(18.0 \cdot \left(y \cdot x\right)\right) + \left(b \cdot c\right))_* - (4.0 * \left((i * x + \left(t \cdot a\right))_*\right) + \left(27.0 \cdot \left(j \cdot k\right)\right))_*}\]
    2.8
  5. Using strategy rm
    2.8
  6. Applied associate-*r* to get
    \[(\left(t \cdot z\right) * \color{red}{\left(18.0 \cdot \left(y \cdot x\right)\right)} + \left(b \cdot c\right))_* - (4.0 * \left((i * x + \left(t \cdot a\right))_*\right) + \left(27.0 \cdot \left(j \cdot k\right)\right))_* \leadsto (\left(t \cdot z\right) * \color{blue}{\left(\left(18.0 \cdot y\right) \cdot x\right)} + \left(b \cdot c\right))_* - (4.0 * \left((i * x + \left(t \cdot a\right))_*\right) + \left(27.0 \cdot \left(j \cdot k\right)\right))_*\]
    3.1
  7. Using strategy rm
    3.1
  8. Applied fma-udef to get
    \[\color{red}{(\left(t \cdot z\right) * \left(\left(18.0 \cdot y\right) \cdot x\right) + \left(b \cdot c\right))_*} - (4.0 * \left((i * x + \left(t \cdot a\right))_*\right) + \left(27.0 \cdot \left(j \cdot k\right)\right))_* \leadsto \color{blue}{\left(\left(t \cdot z\right) \cdot \left(\left(18.0 \cdot y\right) \cdot x\right) + b \cdot c\right)} - (4.0 * \left((i * x + \left(t \cdot a\right))_*\right) + \left(27.0 \cdot \left(j \cdot k\right)\right))_*\]
    3.1
  9. Applied associate--l+ to get
    \[\color{red}{\left(\left(t \cdot z\right) \cdot \left(\left(18.0 \cdot y\right) \cdot x\right) + b \cdot c\right) - (4.0 * \left((i * x + \left(t \cdot a\right))_*\right) + \left(27.0 \cdot \left(j \cdot k\right)\right))_*} \leadsto \color{blue}{\left(t \cdot z\right) \cdot \left(\left(18.0 \cdot y\right) \cdot x\right) + \left(b \cdot c - (4.0 * \left((i * x + \left(t \cdot a\right))_*\right) + \left(27.0 \cdot \left(j \cdot k\right)\right))_*\right)}\]
    3.1
  10. Applied taylor to get
    \[\left(t \cdot z\right) \cdot \left(\left(18.0 \cdot y\right) \cdot x\right) + \left(b \cdot c - (4.0 * \left((i * x + \left(t \cdot a\right))_*\right) + \left(27.0 \cdot \left(j \cdot k\right)\right))_*\right) \leadsto 18.0 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right) + \left(b \cdot c - (4.0 * \left((i * x + \left(t \cdot a\right))_*\right) + \left(27.0 \cdot \left(j \cdot k\right)\right))_*\right)\]
    2.1
  11. Taylor expanded around inf to get
    \[\color{red}{18.0 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)} + \left(b \cdot c - (4.0 * \left((i * x + \left(t \cdot a\right))_*\right) + \left(27.0 \cdot \left(j \cdot k\right)\right))_*\right) \leadsto \color{blue}{18.0 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)} + \left(b \cdot c - (4.0 * \left((i * x + \left(t \cdot a\right))_*\right) + \left(27.0 \cdot \left(j \cdot k\right)\right))_*\right)\]
    2.1
  12. Applied simplify to get
    \[18.0 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right) + \left(b \cdot c - (4.0 * \left((i * x + \left(t \cdot a\right))_*\right) + \left(27.0 \cdot \left(j \cdot k\right)\right))_*\right) \leadsto (\left(\left(18.0 \cdot t\right) \cdot y\right) * \left(z \cdot x\right) + \left(b \cdot c\right))_* - (4.0 * \left((i * x + \left(a \cdot t\right))_*\right) + \left(\left(k \cdot 27.0\right) \cdot j\right))_*\]
    3.2
  13. Applied final simplification

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)))