\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
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: 35.7 s
Input Error: 11.3
Output Error: 9.3
Log: ⚲
Profile: 🕒
\(\begin{cases} {\left(\sqrt[3]{\left({\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^3 - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)}\right)}^3 & \text{when } b \le -5.824136700046604 \cdot 10^{+68} \\ \left(x \cdot \left(z \cdot y - a \cdot t\right) + \left(\left(c \cdot j\right) \cdot t + a \cdot \left(b \cdot i\right)\right)\right) - \left(\left(b \cdot c\right) \cdot z + \left(i \cdot y\right) \cdot j\right) & \text{when } b \le 7.113384715080684 \cdot 10^{+81} \\ {\left(\sqrt[3]{\left({\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^3 - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)}\right)}^3 & \text{otherwise} \end{cases}\)

    if b < -5.824136700046604e+68 or 7.113384715080684e+81 < b

    1. Started with
      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
      6.5
    2. Using strategy rm
      6.5
    3. Applied add-cube-cbrt to get
      \[\color{red}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)} \leadsto \color{blue}{{\left(\sqrt[3]{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)}\right)}^3}\]
      7.5
    4. Using strategy rm
      7.5
    5. Applied add-cube-cbrt to get
      \[{\left(\sqrt[3]{\left(\color{red}{x \cdot \left(y \cdot z - t \cdot a\right)} - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)}\right)}^3 \leadsto {\left(\sqrt[3]{\left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^3} - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)}\right)}^3\]
      7.5

    if -5.824136700046604e+68 < b < 7.113384715080684e+81

    1. Started with
      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
      13.0
    2. Using strategy rm
      13.0
    3. Applied add-cube-cbrt to get
      \[\color{red}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)} \leadsto \color{blue}{{\left(\sqrt[3]{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)}\right)}^3}\]
      13.8
    4. Applied taylor to get
      \[{\left(\sqrt[3]{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)}\right)}^3 \leadsto {\left(\sqrt[3]{\left(j \cdot \left(c \cdot t\right) + \left(y \cdot \left(x \cdot z\right) + b \cdot \left(a \cdot i\right)\right)\right) - \left(t \cdot \left(a \cdot x\right) + \left(j \cdot \left(y \cdot i\right) + b \cdot \left(c \cdot z\right)\right)\right)}\right)}^3\]
      14.4
    5. Taylor expanded around 0 to get
      \[{\color{red}{\left(\sqrt[3]{\left(j \cdot \left(c \cdot t\right) + \left(y \cdot \left(x \cdot z\right) + b \cdot \left(a \cdot i\right)\right)\right) - \left(t \cdot \left(a \cdot x\right) + \left(j \cdot \left(y \cdot i\right) + b \cdot \left(c \cdot z\right)\right)\right)}\right)}}^3 \leadsto {\color{blue}{\left(\sqrt[3]{\left(j \cdot \left(c \cdot t\right) + \left(y \cdot \left(x \cdot z\right) + b \cdot \left(a \cdot i\right)\right)\right) - \left(t \cdot \left(a \cdot x\right) + \left(j \cdot \left(y \cdot i\right) + b \cdot \left(c \cdot z\right)\right)\right)}\right)}}^3\]
      14.4
    6. Applied simplify to get
      \[\color{red}{{\left(\sqrt[3]{\left(j \cdot \left(c \cdot t\right) + \left(y \cdot \left(x \cdot z\right) + b \cdot \left(a \cdot i\right)\right)\right) - \left(t \cdot \left(a \cdot x\right) + \left(j \cdot \left(y \cdot i\right) + b \cdot \left(c \cdot z\right)\right)\right)}\right)}^3} \leadsto \color{blue}{\left(x \cdot \left(z \cdot y - a \cdot t\right) + \left(\left(c \cdot j\right) \cdot t + a \cdot \left(b \cdot i\right)\right)\right) - \left(\left(b \cdot c\right) \cdot z + \left(i \cdot y\right) \cdot j\right)}\]
      10.0
  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)))))