\[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
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: 36.1 s
Input Error: 3.1
Output Error: 3.3
Log: ⚲
Profile: 🕒
\(\left(\left({\left(\left(y \cdot z\right) \cdot \left(t \cdot 18.0\right)\right)}^{1} - 4.0 \cdot i\right) \cdot x - 4.0 \cdot \left(t \cdot a\right)\right) + \left(b \cdot c - \left(j \cdot 27.0\right) \cdot k\right)\)
  1. Started with
    \[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
    3.1
  2. Applied simplify to get
    \[\color{red}{\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k} \leadsto \color{blue}{\left(\left(t \cdot z\right) \cdot \left(18.0 \cdot \left(x \cdot y\right)\right) - 4.0 \cdot \left(t \cdot a + i \cdot x\right)\right) + \left(c \cdot b - j \cdot \left(27.0 \cdot k\right)\right)}\]
    3.1
  3. Applied taylor to get
    \[\left(\left(t \cdot z\right) \cdot \left(18.0 \cdot \left(x \cdot y\right)\right) - 4.0 \cdot \left(t \cdot a + i \cdot x\right)\right) + \left(c \cdot b - j \cdot \left(27.0 \cdot k\right)\right) \leadsto \left(18.0 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right) - \left(4.0 \cdot \left(i \cdot x\right) + 4.0 \cdot \left(a \cdot t\right)\right)\right) + \left(c \cdot b - j \cdot \left(27.0 \cdot k\right)\right)\]
    2.6
  4. Taylor expanded around inf to get
    \[\color{red}{\left(18.0 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right) - \left(4.0 \cdot \left(i \cdot x\right) + 4.0 \cdot \left(a \cdot t\right)\right)\right)} + \left(c \cdot b - j \cdot \left(27.0 \cdot k\right)\right) \leadsto \color{blue}{\left(18.0 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right) - \left(4.0 \cdot \left(i \cdot x\right) + 4.0 \cdot \left(a \cdot t\right)\right)\right)} + \left(c \cdot b - j \cdot \left(27.0 \cdot k\right)\right)\]
    2.6
  5. Applied simplify to get
    \[\color{red}{\left(18.0 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right) - \left(4.0 \cdot \left(i \cdot x\right) + 4.0 \cdot \left(a \cdot t\right)\right)\right) + \left(c \cdot b - j \cdot \left(27.0 \cdot k\right)\right)} \leadsto \color{blue}{\left(\left(x \cdot \left(z \cdot t\right)\right) \cdot \left(y \cdot 18.0\right) - 4.0 \cdot \left(x \cdot i + t \cdot a\right)\right) + \left(b \cdot c - \left(j \cdot 27.0\right) \cdot k\right)}\]
    2.7
  6. Using strategy rm
    2.7
  7. Applied distribute-lft-in to get
    \[\left(\left(x \cdot \left(z \cdot t\right)\right) \cdot \left(y \cdot 18.0\right) - \color{red}{4.0 \cdot \left(x \cdot i + t \cdot a\right)}\right) + \left(b \cdot c - \left(j \cdot 27.0\right) \cdot k\right) \leadsto \left(\left(x \cdot \left(z \cdot t\right)\right) \cdot \left(y \cdot 18.0\right) - \color{blue}{\left(4.0 \cdot \left(x \cdot i\right) + 4.0 \cdot \left(t \cdot a\right)\right)}\right) + \left(b \cdot c - \left(j \cdot 27.0\right) \cdot k\right)\]
    2.7
  8. Applied associate--r+ to get
    \[\color{red}{\left(\left(x \cdot \left(z \cdot t\right)\right) \cdot \left(y \cdot 18.0\right) - \left(4.0 \cdot \left(x \cdot i\right) + 4.0 \cdot \left(t \cdot a\right)\right)\right)} + \left(b \cdot c - \left(j \cdot 27.0\right) \cdot k\right) \leadsto \color{blue}{\left(\left(\left(x \cdot \left(z \cdot t\right)\right) \cdot \left(y \cdot 18.0\right) - 4.0 \cdot \left(x \cdot i\right)\right) - 4.0 \cdot \left(t \cdot a\right)\right)} + \left(b \cdot c - \left(j \cdot 27.0\right) \cdot k\right)\]
    2.7
  9. Applied simplify to get
    \[\left(\color{red}{\left(\left(x \cdot \left(z \cdot t\right)\right) \cdot \left(y \cdot 18.0\right) - 4.0 \cdot \left(x \cdot i\right)\right)} - 4.0 \cdot \left(t \cdot a\right)\right) + \left(b \cdot c - \left(j \cdot 27.0\right) \cdot k\right) \leadsto \left(\color{blue}{\left(\left(y \cdot z\right) \cdot \left(t \cdot 18.0\right) - 4.0 \cdot i\right) \cdot x} - 4.0 \cdot \left(t \cdot a\right)\right) + \left(b \cdot c - \left(j \cdot 27.0\right) \cdot k\right)\]
    3.3
  10. Using strategy rm
    3.3
  11. Applied pow1 to get
    \[\left(\left(\left(y \cdot z\right) \cdot \color{red}{\left(t \cdot 18.0\right)} - 4.0 \cdot i\right) \cdot x - 4.0 \cdot \left(t \cdot a\right)\right) + \left(b \cdot c - \left(j \cdot 27.0\right) \cdot k\right) \leadsto \left(\left(\left(y \cdot z\right) \cdot \color{blue}{{\left(t \cdot 18.0\right)}^{1}} - 4.0 \cdot i\right) \cdot x - 4.0 \cdot \left(t \cdot a\right)\right) + \left(b \cdot c - \left(j \cdot 27.0\right) \cdot k\right)\]
    2.4
  12. Applied pow1 to get
    \[\left(\left(\color{red}{\left(y \cdot z\right)} \cdot {\left(t \cdot 18.0\right)}^{1} - 4.0 \cdot i\right) \cdot x - 4.0 \cdot \left(t \cdot a\right)\right) + \left(b \cdot c - \left(j \cdot 27.0\right) \cdot k\right) \leadsto \left(\left(\color{blue}{{\left(y \cdot z\right)}^{1}} \cdot {\left(t \cdot 18.0\right)}^{1} - 4.0 \cdot i\right) \cdot x - 4.0 \cdot \left(t \cdot a\right)\right) + \left(b \cdot c - \left(j \cdot 27.0\right) \cdot k\right)\]
    2.4
  13. Applied pow-prod-down to get
    \[\left(\left(\color{red}{{\left(y \cdot z\right)}^{1} \cdot {\left(t \cdot 18.0\right)}^{1}} - 4.0 \cdot i\right) \cdot x - 4.0 \cdot \left(t \cdot a\right)\right) + \left(b \cdot c - \left(j \cdot 27.0\right) \cdot k\right) \leadsto \left(\left(\color{blue}{{\left(\left(y \cdot z\right) \cdot \left(t \cdot 18.0\right)\right)}^{1}} - 4.0 \cdot i\right) \cdot x - 4.0 \cdot \left(t \cdot a\right)\right) + \left(b \cdot c - \left(j \cdot 27.0\right) \cdot k\right)\]
    3.3
  14. 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)))