\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
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: 23.8 s
Input Error: 12.1
Output Error: 12.1
Log:
Profile: 🕒
\(\begin{cases} (\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - b \cdot \left(z \cdot c - a \cdot i\right) & \text{when } x \le -5.167993926186821 \cdot 10^{+131} \\ (\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - b \cdot \left(z \cdot c - a \cdot i\right) & \text{when } x \le 8.410085650213006 \cdot 10^{+92} \\ (\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - b \cdot \left(z \cdot c - a \cdot i\right) & \text{otherwise} \end{cases}\)

    if x < -5.167993926186821e+131 or 8.410085650213006e+92 < x

    1. Started with
      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
      6.7
    2. Applied simplify to get
      \[\color{red}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)} \leadsto \color{blue}{(\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - b \cdot \left(c \cdot z - i \cdot a\right)}\]
      6.7
    3. Using strategy rm
      6.7
    4. Applied add-cube-cbrt to get
      \[(\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - \color{red}{b \cdot \left(c \cdot z - i \cdot a\right)} \leadsto (\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - \color{blue}{{\left(\sqrt[3]{b \cdot \left(c \cdot z - i \cdot a\right)}\right)}^3}\]
      6.9
    5. Applied taylor to get
      \[(\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - {\left(\sqrt[3]{b \cdot \left(c \cdot z - i \cdot a\right)}\right)}^3 \leadsto (\left(c \cdot t - i \cdot y\right) * j + \left(y \cdot \left(x \cdot z\right) - a \cdot \left(t \cdot x\right)\right))_* - {\left(\sqrt[3]{b \cdot \left(c \cdot z - i \cdot a\right)}\right)}^3\]
      19.9
    6. Taylor expanded around inf to get
      \[(\left(c \cdot t - i \cdot y\right) * j + \color{red}{\left(y \cdot \left(x \cdot z\right) - a \cdot \left(t \cdot x\right)\right)})_* - {\left(\sqrt[3]{b \cdot \left(c \cdot z - i \cdot a\right)}\right)}^3 \leadsto (\left(c \cdot t - i \cdot y\right) * j + \color{blue}{\left(y \cdot \left(x \cdot z\right) - a \cdot \left(t \cdot x\right)\right)})_* - {\left(\sqrt[3]{b \cdot \left(c \cdot z - i \cdot a\right)}\right)}^3\]
      19.9
    7. Applied simplify to get
      \[(\left(c \cdot t - i \cdot y\right) * j + \left(y \cdot \left(x \cdot z\right) - a \cdot \left(t \cdot x\right)\right))_* - {\left(\sqrt[3]{b \cdot \left(c \cdot z - i \cdot a\right)}\right)}^3 \leadsto (\left(t \cdot c - y \cdot i\right) * j + \left(\left(x \cdot y\right) \cdot z - \left(a \cdot x\right) \cdot t\right))_* - b \cdot \left(z \cdot c - a \cdot i\right)\]
      19.5

    8. Applied final simplification
    9. Applied simplify to get
      \[\color{red}{(\left(t \cdot c - y \cdot i\right) * j + \left(\left(x \cdot y\right) \cdot z - \left(a \cdot x\right) \cdot t\right))_* - b \cdot \left(z \cdot c - a \cdot i\right)} \leadsto \color{blue}{(\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - b \cdot \left(z \cdot c - a \cdot i\right)}\]
      6.7

    if -5.167993926186821e+131 < x < 8.410085650213006e+92

    1. Started with
      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
      13.5
    2. Applied simplify to get
      \[\color{red}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)} \leadsto \color{blue}{(\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - b \cdot \left(c \cdot z - i \cdot a\right)}\]
      13.5
    3. Using strategy rm
      13.5
    4. Applied add-cube-cbrt to get
      \[(\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - \color{red}{b \cdot \left(c \cdot z - i \cdot a\right)} \leadsto (\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - \color{blue}{{\left(\sqrt[3]{b \cdot \left(c \cdot z - i \cdot a\right)}\right)}^3}\]
      13.8
    5. Applied taylor to get
      \[(\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - {\left(\sqrt[3]{b \cdot \left(c \cdot z - i \cdot a\right)}\right)}^3 \leadsto (\left(c \cdot t - i \cdot y\right) * j + \left(y \cdot \left(x \cdot z\right) - a \cdot \left(t \cdot x\right)\right))_* - {\left(\sqrt[3]{b \cdot \left(c \cdot z - i \cdot a\right)}\right)}^3\]
      10.7
    6. Taylor expanded around inf to get
      \[(\left(c \cdot t - i \cdot y\right) * j + \color{red}{\left(y \cdot \left(x \cdot z\right) - a \cdot \left(t \cdot x\right)\right)})_* - {\left(\sqrt[3]{b \cdot \left(c \cdot z - i \cdot a\right)}\right)}^3 \leadsto (\left(c \cdot t - i \cdot y\right) * j + \color{blue}{\left(y \cdot \left(x \cdot z\right) - a \cdot \left(t \cdot x\right)\right)})_* - {\left(\sqrt[3]{b \cdot \left(c \cdot z - i \cdot a\right)}\right)}^3\]
      10.7
    7. Applied simplify to get
      \[(\left(c \cdot t - i \cdot y\right) * j + \left(y \cdot \left(x \cdot z\right) - a \cdot \left(t \cdot x\right)\right))_* - {\left(\sqrt[3]{b \cdot \left(c \cdot z - i \cdot a\right)}\right)}^3 \leadsto (\left(t \cdot c - y \cdot i\right) * j + \left(\left(x \cdot y\right) \cdot z - \left(a \cdot x\right) \cdot t\right))_* - b \cdot \left(z \cdot c - a \cdot i\right)\]
      10.4

    8. Applied final simplification
    9. Applied simplify to get
      \[\color{red}{(\left(t \cdot c - y \cdot i\right) * j + \left(\left(x \cdot y\right) \cdot z - \left(a \cdot x\right) \cdot t\right))_* - b \cdot \left(z \cdot c - a \cdot i\right)} \leadsto \color{blue}{(\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - b \cdot \left(z \cdot c - a \cdot i\right)}\]
      13.5

  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)))))