\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
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: 22.1 s
Input Error: 12.2
Output Error: 10.4
Log: ⚲
Profile: 🕒
\(\begin{cases} {\left(\sqrt[3]{(\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_*}\right)}^3 - b \cdot \left(c \cdot z - i \cdot a\right) & \text{when } x \le -2.021147807924823 \cdot 10^{-272} \\ (\left(c \cdot t - i \cdot y\right) * j + 0)_* - b \cdot \left(c \cdot z - i \cdot a\right) & \text{when } x \le 8.450803752675009 \cdot 10^{-143} \\ {\left(\sqrt[3]{(\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_*}\right)}^3 - b \cdot \left(c \cdot z - i \cdot a\right) & \text{otherwise} \end{cases}\)

    if x < -2.021147807924823e-272 or 8.450803752675009e-143 < x

    1. Started with
      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
      9.9
    2. Applied simplify to get
      \[\color{red}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)} \leadsto \color{blue}{(\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - b \cdot \left(c \cdot z - i \cdot a\right)}\]
      9.9
    3. Using strategy rm
      9.9
    4. Applied add-cube-cbrt to get
      \[\color{red}{(\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_*} - b \cdot \left(c \cdot z - i \cdot a\right) \leadsto \color{blue}{{\left(\sqrt[3]{(\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_*}\right)}^3} - b \cdot \left(c \cdot z - i \cdot a\right)\]
      10.5

    if -2.021147807924823e-272 < x < 8.450803752675009e-143

    1. Started with
      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
      20.7
    2. Applied simplify to get
      \[\color{red}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)} \leadsto \color{blue}{(\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - b \cdot \left(c \cdot z - i \cdot a\right)}\]
      20.7
    3. Applied taylor to get
      \[(\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - b \cdot \left(c \cdot z - i \cdot a\right) \leadsto (\left(c \cdot t - i \cdot y\right) * j + 0)_* - b \cdot \left(c \cdot z - i \cdot a\right)\]
      9.7
    4. Taylor expanded around 0 to get
      \[(\left(c \cdot t - i \cdot y\right) * j + \color{red}{0})_* - b \cdot \left(c \cdot z - i \cdot a\right) \leadsto (\left(c \cdot t - i \cdot y\right) * j + \color{blue}{0})_* - b \cdot \left(c \cdot z - i \cdot a\right)\]
      9.7
  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)))))