\[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
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: 26.3 s
Input Error: 3.2
Output Error: 2.4
Log: ⚲
Profile: 🕒
\(\left(\left(\left(t \cdot x\right) \cdot z\right) \cdot \left(y \cdot 18.0\right) + \left(b \cdot c - \left(j \cdot k\right) \cdot 27.0\right)\right) - \left(t \cdot a + x \cdot i\right) \cdot 4.0\)
  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
    \[\color{red}{\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k} \leadsto \color{blue}{\left(\left(t \cdot z\right) \cdot \left(18.0 \cdot \left(x \cdot y\right)\right) - 4.0 \cdot \left(t \cdot a + i \cdot x\right)\right) + \left(c \cdot b - j \cdot \left(27.0 \cdot k\right)\right)}\]
    3.2
  3. Using strategy rm
    3.2
  4. Applied add-sqr-sqrt to get
    \[\left(\color{red}{\left(t \cdot z\right) \cdot \left(18.0 \cdot \left(x \cdot y\right)\right)} - 4.0 \cdot \left(t \cdot a + i \cdot x\right)\right) + \left(c \cdot b - j \cdot \left(27.0 \cdot k\right)\right) \leadsto \left(\color{blue}{{\left(\sqrt{\left(t \cdot z\right) \cdot \left(18.0 \cdot \left(x \cdot y\right)\right)}\right)}^2} - 4.0 \cdot \left(t \cdot a + i \cdot x\right)\right) + \left(c \cdot b - j \cdot \left(27.0 \cdot k\right)\right)\]
    12.8
  5. Applied taylor to get
    \[\left({\left(\sqrt{\left(t \cdot z\right) \cdot \left(18.0 \cdot \left(x \cdot y\right)\right)}\right)}^2 - 4.0 \cdot \left(t \cdot a + i \cdot x\right)\right) + \left(c \cdot b - j \cdot \left(27.0 \cdot k\right)\right) \leadsto \left({\left(\sqrt{18.0 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)}\right)}^2 - 4.0 \cdot \left(t \cdot a + i \cdot x\right)\right) + \left(c \cdot b - j \cdot \left(27.0 \cdot k\right)\right)\]
    12.2
  6. Taylor expanded around inf to get
    \[\left({\left(\sqrt{\color{red}{18.0 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)}}\right)}^2 - 4.0 \cdot \left(t \cdot a + i \cdot x\right)\right) + \left(c \cdot b - j \cdot \left(27.0 \cdot k\right)\right) \leadsto \left({\left(\sqrt{\color{blue}{18.0 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)}}\right)}^2 - 4.0 \cdot \left(t \cdot a + i \cdot x\right)\right) + \left(c \cdot b - j \cdot \left(27.0 \cdot k\right)\right)\]
    12.2
  7. Applied simplify to get
    \[\left({\left(\sqrt{18.0 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)}\right)}^2 - 4.0 \cdot \left(t \cdot a + i \cdot x\right)\right) + \left(c \cdot b - j \cdot \left(27.0 \cdot k\right)\right) \leadsto \left(\left(\left(t \cdot x\right) \cdot z\right) \cdot \left(y \cdot 18.0\right) + \left(b \cdot c - \left(j \cdot k\right) \cdot 27.0\right)\right) - \left(t \cdot a + x \cdot i\right) \cdot 4.0\]
    2.4
  8. Applied final simplification
  9. 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)))