\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
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: 28.2 s
Input Error: 11.2
Output Error: 9.9
Log:
Profile: 🕒
\(\begin{cases} (\left(c \cdot t - i \cdot y\right) * j + \left(\frac{1}{\frac{\frac{1}{x}}{z \cdot y - a \cdot t}}\right))_* - b \cdot \left(c \cdot z - i \cdot a\right) & \text{when } x \le -5.600952199368653 \cdot 10^{-246} \\ (\left(c \cdot t - i \cdot y\right) * j + 0)_* - b \cdot \left(c \cdot z - i \cdot a\right) & \text{when } x \le 4.1518798656938537 \cdot 10^{-227} \\ (\left(c \cdot t - i \cdot y\right) * j + \left(\frac{1}{\frac{\frac{1}{x}}{z \cdot y - a \cdot t}}\right))_* - b \cdot \left(c \cdot z - i \cdot a\right) & \text{otherwise} \end{cases}\)

    if x < -5.600952199368653e-246 or 4.1518798656938537e-227 < x

    1. Started with
      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
      10.0
    2. Applied simplify to get
      \[\color{red}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)} \leadsto \color{blue}{(\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - b \cdot \left(c \cdot z - i \cdot a\right)}\]
      10.0
    3. Using strategy rm
      10.0
    4. Applied flip-- to get
      \[(\left(c \cdot t - i \cdot y\right) * j + \left(\color{red}{\left(y \cdot z - t \cdot a\right)} \cdot x\right))_* - b \cdot \left(c \cdot z - i \cdot a\right) \leadsto (\left(c \cdot t - i \cdot y\right) * j + \left(\color{blue}{\frac{{\left(y \cdot z\right)}^2 - {\left(t \cdot a\right)}^2}{y \cdot z + t \cdot a}} \cdot x\right))_* - b \cdot \left(c \cdot z - i \cdot a\right)\]
      22.3
    5. Applied associate-*l/ to get
      \[(\left(c \cdot t - i \cdot y\right) * j + \color{red}{\left(\frac{{\left(y \cdot z\right)}^2 - {\left(t \cdot a\right)}^2}{y \cdot z + t \cdot a} \cdot x\right)})_* - b \cdot \left(c \cdot z - i \cdot a\right) \leadsto (\left(c \cdot t - i \cdot y\right) * j + \color{blue}{\left(\frac{\left({\left(y \cdot z\right)}^2 - {\left(t \cdot a\right)}^2\right) \cdot x}{y \cdot z + t \cdot a}\right)})_* - b \cdot \left(c \cdot z - i \cdot a\right)\]
      24.9
    6. Using strategy rm
      24.9
    7. Applied clear-num to get
      \[(\left(c \cdot t - i \cdot y\right) * j + \color{red}{\left(\frac{\left({\left(y \cdot z\right)}^2 - {\left(t \cdot a\right)}^2\right) \cdot x}{y \cdot z + t \cdot a}\right)})_* - b \cdot \left(c \cdot z - i \cdot a\right) \leadsto (\left(c \cdot t - i \cdot y\right) * j + \color{blue}{\left(\frac{1}{\frac{y \cdot z + t \cdot a}{\left({\left(y \cdot z\right)}^2 - {\left(t \cdot a\right)}^2\right) \cdot x}}\right)})_* - b \cdot \left(c \cdot z - i \cdot a\right)\]
      24.9
    8. Applied simplify to get
      \[(\left(c \cdot t - i \cdot y\right) * j + \left(\frac{1}{\color{red}{\frac{y \cdot z + t \cdot a}{\left({\left(y \cdot z\right)}^2 - {\left(t \cdot a\right)}^2\right) \cdot x}}}\right))_* - b \cdot \left(c \cdot z - i \cdot a\right) \leadsto (\left(c \cdot t - i \cdot y\right) * j + \left(\frac{1}{\color{blue}{\frac{\frac{1}{x}}{z \cdot y - a \cdot t}}}\right))_* - b \cdot \left(c \cdot z - i \cdot a\right)\]
      10.1

    if -5.600952199368653e-246 < x < 4.1518798656938537e-227

    1. Started with
      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
      17.6
    2. Applied simplify to get
      \[\color{red}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)} \leadsto \color{blue}{(\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - b \cdot \left(c \cdot z - i \cdot a\right)}\]
      17.6
    3. Applied taylor to get
      \[(\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - b \cdot \left(c \cdot z - i \cdot a\right) \leadsto (\left(c \cdot t - i \cdot y\right) * j + 0)_* - b \cdot \left(c \cdot z - i \cdot a\right)\]
      8.3
    4. Taylor expanded around 0 to get
      \[(\left(c \cdot t - i \cdot y\right) * j + \color{red}{0})_* - b \cdot \left(c \cdot z - i \cdot a\right) \leadsto (\left(c \cdot t - i \cdot y\right) * j + \color{blue}{0})_* - b \cdot \left(c \cdot z - i \cdot a\right)\]
      8.3

  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)))))