\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
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: 35.0 s
Input Error: 12.1
Output Error: 10.0
Log: ⚲
Profile: 🕒
\(\begin{cases} {\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)}\right)}^3 + j \cdot \left(c \cdot t - i \cdot y\right) & \text{when } x \le -1.4403270105419575 \cdot 10^{-96} \\ \left(i \cdot b - t \cdot x\right) \cdot a + \left(\left(c \cdot t - i \cdot y\right) \cdot j - \left(b \cdot c\right) \cdot z\right) & \text{when } x \le -7.950125894115203 \cdot 10^{-156} \\ {\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)}\right)}^3 + j \cdot \left(c \cdot t - i \cdot y\right) & \text{when } x \le -2.021147807924823 \cdot 10^{-272} \\ \left(\left(c \cdot t - i \cdot y\right) \cdot j + b \cdot \left(a \cdot i - z \cdot c\right)\right) - t \cdot \left(x \cdot a\right) & \text{when } x \le 3.614117157412892 \cdot 10^{-128} \\ {\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)}\right)}^3 + j \cdot \left(c \cdot t - i \cdot y\right) & \text{otherwise} \end{cases}\)

    if x < -1.4403270105419575e-96 or -7.950125894115203e-156 < x < -2.021147807924823e-272 or 3.614117157412892e-128 < x

    1. Started with
      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
      9.4
    2. Using strategy rm
      9.4
    3. Applied add-cube-cbrt to get
      \[\color{red}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)}\right)}^3} + j \cdot \left(c \cdot t - i \cdot y\right)\]
      10.1

    if -1.4403270105419575e-96 < x < -7.950125894115203e-156

    1. Started with
      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
      19.6
    2. Using strategy rm
      19.6
    3. Applied add-cube-cbrt to get
      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{red}{j \cdot \left(c \cdot t - i \cdot y\right)} \leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{{\left(\sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)}\right)}^3}\]
      19.9
    4. Applied taylor to get
      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + {\left(\sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)}\right)}^3 \leadsto \left(b \cdot \left(a \cdot i\right) - \left(b \cdot \left(c \cdot z\right) + a \cdot \left(t \cdot x\right)\right)\right) + {\left(\sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)}\right)}^3\]
      10.3
    5. Taylor expanded around inf to get
      \[\color{red}{\left(b \cdot \left(a \cdot i\right) - \left(b \cdot \left(c \cdot z\right) + a \cdot \left(t \cdot x\right)\right)\right)} + {\left(\sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)}\right)}^3 \leadsto \color{blue}{\left(b \cdot \left(a \cdot i\right) - \left(b \cdot \left(c \cdot z\right) + a \cdot \left(t \cdot x\right)\right)\right)} + {\left(\sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)}\right)}^3\]
      10.3
    6. Applied simplify to get
      \[\color{red}{\left(b \cdot \left(a \cdot i\right) - \left(b \cdot \left(c \cdot z\right) + a \cdot \left(t \cdot x\right)\right)\right) + {\left(\sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)}\right)}^3} \leadsto \color{blue}{\left(i \cdot b - t \cdot x\right) \cdot a + \left(\left(c \cdot t - i \cdot y\right) \cdot j - \left(b \cdot c\right) \cdot z\right)}\]
      8.4

    if -2.021147807924823e-272 < x < 3.614117157412892e-128

    1. Started with
      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
      18.8
    2. Applied taylor to get
      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \leadsto \left(b \cdot \left(a \cdot i\right) - \left(b \cdot \left(c \cdot z\right) + a \cdot \left(t \cdot x\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
      10.1
    3. Taylor expanded around inf to get
      \[\color{red}{\left(b \cdot \left(a \cdot i\right) - \left(b \cdot \left(c \cdot z\right) + a \cdot \left(t \cdot x\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \leadsto \color{blue}{\left(b \cdot \left(a \cdot i\right) - \left(b \cdot \left(c \cdot z\right) + a \cdot \left(t \cdot x\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right)\]
      10.1
    4. Applied simplify to get
      \[\color{red}{\left(b \cdot \left(a \cdot i\right) - \left(b \cdot \left(c \cdot z\right) + a \cdot \left(t \cdot x\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)} \leadsto \color{blue}{\left(\left(c \cdot t - i \cdot y\right) \cdot j + b \cdot \left(a \cdot i - z \cdot c\right)\right) - t \cdot \left(x \cdot a\right)}\]
      10.2
  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)))))