\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
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: 38.3 s
Input Error: 11.1
Output Error: 10.6
Log: ⚲
Profile: 🕒
\(\begin{cases} {\left(\sqrt[3]{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)}\right)}^3 & \text{when } x \le -2.435617111960463 \cdot 10^{-232} \\ \left(c \cdot t - y \cdot i\right) \cdot j - \left(c \cdot z - a \cdot i\right) \cdot b & \text{when } x \le 7.04423202968854 \cdot 10^{-264} \\ \left(x \cdot \left(z \cdot y - a \cdot t\right) + \left(\left(c \cdot j\right) \cdot t + a \cdot \left(b \cdot i\right)\right)\right) - \left(\left(b \cdot c\right) \cdot z + \left(i \cdot y\right) \cdot j\right) & \text{when } x \le 8.290226761514204 \cdot 10^{+70} \\ {\left(\sqrt[3]{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)}\right)}^3 & \text{otherwise} \end{cases}\)

    if x < -2.435617111960463e-232 or 8.290226761514204e+70 < x

    1. Started with
      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
      9.1
    2. Using strategy rm
      9.1
    3. Applied add-cube-cbrt to get
      \[\color{red}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)} \leadsto \color{blue}{{\left(\sqrt[3]{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)}\right)}^3}\]
      10.0

    if -2.435617111960463e-232 < x < 7.04423202968854e-264

    1. Started with
      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
      17.0
    2. Applied taylor to get
      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \leadsto \left(0 - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
      8.0
    3. Taylor expanded around 0 to get
      \[\left(\color{red}{0} - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \leadsto \left(\color{blue}{0} - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
      8.0
    4. Applied simplify to get
      \[\color{red}{\left(0 - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)} \leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j - \left(c \cdot z - a \cdot i\right) \cdot b}\]
      8.0

    if 7.04423202968854e-264 < x < 8.290226761514204e+70

    1. Started with
      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
      12.3
    2. Using strategy rm
      12.3
    3. Applied add-cube-cbrt to get
      \[\color{red}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)} \leadsto \color{blue}{{\left(\sqrt[3]{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)}\right)}^3}\]
      13.1
    4. Applied taylor to get
      \[{\left(\sqrt[3]{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)}\right)}^3 \leadsto {\left(\sqrt[3]{\left(j \cdot \left(c \cdot t\right) + \left(y \cdot \left(x \cdot z\right) + b \cdot \left(a \cdot i\right)\right)\right) - \left(t \cdot \left(a \cdot x\right) + \left(j \cdot \left(y \cdot i\right) + b \cdot \left(c \cdot z\right)\right)\right)}\right)}^3\]
      9.9
    5. Taylor expanded around 0 to get
      \[{\color{red}{\left(\sqrt[3]{\left(j \cdot \left(c \cdot t\right) + \left(y \cdot \left(x \cdot z\right) + b \cdot \left(a \cdot i\right)\right)\right) - \left(t \cdot \left(a \cdot x\right) + \left(j \cdot \left(y \cdot i\right) + b \cdot \left(c \cdot z\right)\right)\right)}\right)}}^3 \leadsto {\color{blue}{\left(\sqrt[3]{\left(j \cdot \left(c \cdot t\right) + \left(y \cdot \left(x \cdot z\right) + b \cdot \left(a \cdot i\right)\right)\right) - \left(t \cdot \left(a \cdot x\right) + \left(j \cdot \left(y \cdot i\right) + b \cdot \left(c \cdot z\right)\right)\right)}\right)}}^3\]
      9.9
    6. Applied simplify to get
      \[\color{red}{{\left(\sqrt[3]{\left(j \cdot \left(c \cdot t\right) + \left(y \cdot \left(x \cdot z\right) + b \cdot \left(a \cdot i\right)\right)\right) - \left(t \cdot \left(a \cdot x\right) + \left(j \cdot \left(y \cdot i\right) + b \cdot \left(c \cdot z\right)\right)\right)}\right)}^3} \leadsto \color{blue}{\left(x \cdot \left(z \cdot y - a \cdot t\right) + \left(\left(c \cdot j\right) \cdot t + a \cdot \left(b \cdot i\right)\right)\right) - \left(\left(b \cdot c\right) \cdot z + \left(i \cdot y\right) \cdot j\right)}\]
      12.5
  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)))))