\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
Test:
Linear.Matrix:det33 from linear-1.19.1.3
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
Time: 30.2 s
Input Error: 5.6
Output Error: 5.6
Log: ⚲
Profile: 🕒
\((\left(c \cdot t - i \cdot y\right) * j + \left(x \cdot \left(y \cdot z - t \cdot a\right)\right))_* - b \cdot \left(z \cdot c - a \cdot i\right)\)
  1. Started with
    \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
    5.6
  2. Applied simplify to get
    \[\color{red}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)} \leadsto \color{blue}{(\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - b \cdot \left(c \cdot z - i \cdot a\right)}\]
    5.6
  3. Using strategy rm
    5.6
  4. Applied add-sqr-sqrt to get
    \[\color{red}{(\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_*} - b \cdot \left(c \cdot z - i \cdot a\right) \leadsto \color{blue}{{\left(\sqrt{(\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_*}\right)}^2} - b \cdot \left(c \cdot z - i \cdot a\right)\]
    18.2
  5. Applied taylor to get
    \[{\left(\sqrt{(\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_*}\right)}^2 - b \cdot \left(c \cdot z - i \cdot a\right) \leadsto {\left(\sqrt{(\left(c \cdot t - i \cdot y\right) * j + \left(y \cdot \left(x \cdot z\right) - a \cdot \left(t \cdot x\right)\right))_*}\right)}^2 - b \cdot \left(c \cdot z - i \cdot a\right)\]
    18.2
  6. Taylor expanded around inf to get
    \[{\left(\sqrt{(\left(c \cdot t - i \cdot y\right) * j + \color{red}{\left(y \cdot \left(x \cdot z\right) - a \cdot \left(t \cdot x\right)\right)})_*}\right)}^2 - b \cdot \left(c \cdot z - i \cdot a\right) \leadsto {\left(\sqrt{(\left(c \cdot t - i \cdot y\right) * j + \color{blue}{\left(y \cdot \left(x \cdot z\right) - a \cdot \left(t \cdot x\right)\right)})_*}\right)}^2 - b \cdot \left(c \cdot z - i \cdot a\right)\]
    18.2
  7. Applied simplify to get
    \[{\left(\sqrt{(\left(c \cdot t - i \cdot y\right) * j + \left(y \cdot \left(x \cdot z\right) - a \cdot \left(t \cdot x\right)\right))_*}\right)}^2 - b \cdot \left(c \cdot z - i \cdot a\right) \leadsto (\left(t \cdot c - y \cdot i\right) * j + \left(\left(y \cdot z\right) \cdot x - \left(x \cdot a\right) \cdot t\right))_* - b \cdot \left(z \cdot c - a \cdot i\right)\]
    5.8
  8. Applied final simplification
  9. Applied simplify to get
    \[\color{red}{(\left(t \cdot c - y \cdot i\right) * j + \left(\left(y \cdot z\right) \cdot x - \left(x \cdot a\right) \cdot t\right))_* - b \cdot \left(z \cdot c - a \cdot i\right)} \leadsto \color{blue}{(\left(c \cdot t - i \cdot y\right) * j + \left(x \cdot \left(y \cdot z - t \cdot a\right)\right))_* - b \cdot \left(z \cdot c - a \cdot i\right)}\]
    5.6
  10. 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))
  #:name "Linear.Matrix:det33 from linear-1.19.1.3"
  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))