\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
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: 35.6 s
Input Error: 11.2
Output Error: 9.0
Log: ⚲
Profile: 🕒
\(\begin{cases} \left(a \cdot \left(i \cdot b - x \cdot t\right) + \left(t \cdot c - i \cdot y\right) \cdot j\right) + \left(x \cdot y - c \cdot b\right) \cdot z & \text{when } a \le -1.1873747320740424 \cdot 10^{-139} \\ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + {\left(\sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)}\right)}^3 & \text{when } a \le 3.201627152220651 \cdot 10^{+111} \\ \left(a \cdot \left(i \cdot b - x \cdot t\right) + \left(t \cdot c - i \cdot y\right) \cdot j\right) + \left(x \cdot y - c \cdot b\right) \cdot z & \text{otherwise} \end{cases}\)

    if a < -1.1873747320740424e-139 or 3.201627152220651e+111 < a

    1. Started with
      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
      14.1
    2. Using strategy rm
      14.1
    3. Applied add-cube-cbrt to get
      \[\color{red}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)}\right)}^3} + j \cdot \left(c \cdot t - i \cdot y\right)\]
      14.7
    4. Applied taylor to get
      \[{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)}\right)}^3 + j \cdot \left(c \cdot t - i \cdot y\right) \leadsto {\left(\sqrt[3]{\left(y \cdot \left(x \cdot z\right) + b \cdot \left(a \cdot i\right)\right) - \left(t \cdot \left(a \cdot x\right) + b \cdot \left(c \cdot z\right)\right)}\right)}^3 + j \cdot \left(c \cdot t - i \cdot y\right)\]
      15.3
    5. Taylor expanded around 0 to get
      \[{\color{red}{\left(\sqrt[3]{\left(y \cdot \left(x \cdot z\right) + b \cdot \left(a \cdot i\right)\right) - \left(t \cdot \left(a \cdot x\right) + b \cdot \left(c \cdot z\right)\right)}\right)}}^3 + j \cdot \left(c \cdot t - i \cdot y\right) \leadsto {\color{blue}{\left(\sqrt[3]{\left(y \cdot \left(x \cdot z\right) + b \cdot \left(a \cdot i\right)\right) - \left(t \cdot \left(a \cdot x\right) + b \cdot \left(c \cdot z\right)\right)}\right)}}^3 + j \cdot \left(c \cdot t - i \cdot y\right)\]
      15.3
    6. Applied simplify to get
      \[\color{red}{{\left(\sqrt[3]{\left(y \cdot \left(x \cdot z\right) + b \cdot \left(a \cdot i\right)\right) - \left(t \cdot \left(a \cdot x\right) + b \cdot \left(c \cdot z\right)\right)}\right)}^3 + j \cdot \left(c \cdot t - i \cdot y\right)} \leadsto \color{blue}{\left(a \cdot \left(i \cdot b - x \cdot t\right) + \left(t \cdot c - i \cdot y\right) \cdot j\right) + \left(x \cdot y - c \cdot b\right) \cdot z}\]
      8.5

    if -1.1873747320740424e-139 < a < 3.201627152220651e+111

    1. Started with
      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
      9.0
    2. Using strategy rm
      9.0
    3. Applied add-cube-cbrt to get
      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{red}{j \cdot \left(c \cdot t - i \cdot y\right)} \leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{{\left(\sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)}\right)}^3}\]
      9.3
  1. 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)))))