\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
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: 51.0 s
Input Error: 13.3
Output Error: 10.0
Log: ⚲
Profile: 🕒
\(\begin{cases} \left(x \cdot \left(y \cdot z - t \cdot a\right) - {\left(\sqrt[3]{b \cdot \left(c \cdot z - i \cdot a\right)}\right)}^3\right) + j \cdot \left(c \cdot t - i \cdot y\right) & \text{when } x \le -2.4891124693180655 \cdot 10^{-232} \\ \left(\left(c \cdot t - i \cdot y\right) \cdot j + b \cdot \left(a \cdot i - z \cdot c\right)\right) - t \cdot \left(x \cdot a\right) & \text{when } x \le 5.7727905786021696 \cdot 10^{-27} \\ \left(x \cdot \left(y \cdot z - t \cdot a\right) - {\left(\sqrt[3]{b \cdot \left(c \cdot z - i \cdot a\right)}\right)}^3\right) + j \cdot \left(c \cdot t - i \cdot y\right) & \text{otherwise} \end{cases}\)

    if x < -2.4891124693180655e-232 or 5.7727905786021696e-27 < x

    1. Started with
      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
      9.8
    2. Using strategy rm
      9.8
    3. Applied add-cube-cbrt to get
      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{red}{b \cdot \left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{{\left(\sqrt[3]{b \cdot \left(c \cdot z - i \cdot a\right)}\right)}^3}\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
      10.1

    if -2.4891124693180655e-232 < x < 5.7727905786021696e-27

    1. Started with
      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
      19.3
    2. Applied taylor to get
      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \leadsto \left(b \cdot \left(a \cdot i\right) - \left(b \cdot \left(c \cdot z\right) + a \cdot \left(t \cdot x\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
      9.9
    3. Taylor expanded around inf to get
      \[\color{red}{\left(b \cdot \left(a \cdot i\right) - \left(b \cdot \left(c \cdot z\right) + a \cdot \left(t \cdot x\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \leadsto \color{blue}{\left(b \cdot \left(a \cdot i\right) - \left(b \cdot \left(c \cdot z\right) + a \cdot \left(t \cdot x\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right)\]
      9.9
    4. Applied simplify to get
      \[\color{red}{\left(b \cdot \left(a \cdot i\right) - \left(b \cdot \left(c \cdot z\right) + a \cdot \left(t \cdot x\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)} \leadsto \color{blue}{\left(\left(c \cdot t - i \cdot y\right) \cdot j + b \cdot \left(a \cdot i - z \cdot c\right)\right) - t \cdot \left(x \cdot a\right)}\]
      9.9
  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)))))