\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
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: 15.3 s
Input Error: 11.0
Output Error: 11.0
Log: ⚲
Profile: 🕒
\((b * \left(a \cdot i - c \cdot z\right) + \left((\left(t \cdot c - i \cdot y\right) * j + \left(x \cdot \left(y \cdot z - a \cdot t\right)\right))_*\right))_*\)
  1. Started with
    \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
    11.0
  2. Applied simplify to get
    \[\color{red}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)} \leadsto \color{blue}{(\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - b \cdot \left(c \cdot z - i \cdot a\right)}\]
    11.0
  3. Using strategy rm
    11.0
  4. Applied add-cube-cbrt to get
    \[\color{red}{(\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - b \cdot \left(c \cdot z - i \cdot a\right)} \leadsto \color{blue}{{\left(\sqrt[3]{(\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - b \cdot \left(c \cdot z - i \cdot a\right)}\right)}^3}\]
    11.9
  5. Applied taylor to get
    \[{\left(\sqrt[3]{(\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - b \cdot \left(c \cdot z - i \cdot a\right)}\right)}^3 \leadsto {\left(\sqrt[3]{\left((\left(c \cdot t - y \cdot i\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* + b \cdot \left(a \cdot i\right)\right) - b \cdot \left(c \cdot z\right)}\right)}^3\]
    11.9
  6. Taylor expanded around 0 to get
    \[{\color{red}{\left(\sqrt[3]{\left((\left(c \cdot t - y \cdot i\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* + b \cdot \left(a \cdot i\right)\right) - b \cdot \left(c \cdot z\right)}\right)}}^3 \leadsto {\color{blue}{\left(\sqrt[3]{\left((\left(c \cdot t - y \cdot i\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* + b \cdot \left(a \cdot i\right)\right) - b \cdot \left(c \cdot z\right)}\right)}}^3\]
    11.9
  7. Applied simplify to get
    \[\color{red}{{\left(\sqrt[3]{\left((\left(c \cdot t - y \cdot i\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* + b \cdot \left(a \cdot i\right)\right) - b \cdot \left(c \cdot z\right)}\right)}^3} \leadsto \color{blue}{(b * \left(a \cdot i - c \cdot z\right) + \left((\left(t \cdot c - i \cdot y\right) * j + \left(x \cdot \left(y \cdot z - a \cdot t\right)\right))_*\right))_*}\]
    11.0

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)))))