Average Error: 11.5 → 11.5
Time: 1.1m
Precision: 64
Internal Precision: 576
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;i \le 3.7207160560314225 \cdot 10^{+113}:\\ \;\;\;\;\left(t \cdot c - y \cdot i\right) \cdot j + \left(\left(y \cdot z - t \cdot a\right) \cdot x - \left(\sqrt[3]{b \cdot \left(z \cdot c - i \cdot a\right)} \cdot \left(\sqrt[3]{b} \cdot \sqrt[3]{z \cdot c - i \cdot a}\right)\right) \cdot \sqrt[3]{b \cdot \left(z \cdot c - i \cdot a\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right) + \left(b \cdot a - y \cdot j\right) \cdot i\\ \end{array}\]

Error

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

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes

  2. if i < 3.7207160560314225e+113

    1. Initial program 10.3

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
    2. Using strategy rm

    3. Applied add-cube-cbrt10.6

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\sqrt[3]{b \cdot \left(c \cdot z - i \cdot a\right)} \cdot \sqrt[3]{b \cdot \left(c \cdot z - i \cdot a\right)}\right) \cdot \sqrt[3]{b \cdot \left(c \cdot z - i \cdot a\right)}}\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
    4. Using strategy rm

    5. Applied cbrt-prod10.6

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\sqrt[3]{b \cdot \left(c \cdot z - i \cdot a\right)} \cdot \color{blue}{\left(\sqrt[3]{b} \cdot \sqrt[3]{c \cdot z - i \cdot a}\right)}\right) \cdot \sqrt[3]{b \cdot \left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]

    if 3.7207160560314225e+113 < i

    1. Initial program 22.0

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]

    2. Taylor expanded around inf 24.9

      \[\leadsto \color{blue}{\left(t \cdot \left(j \cdot c\right) + a \cdot \left(i \cdot b\right)\right) - i \cdot \left(j \cdot y\right)}\]

    3. Simplified19.5

      \[\leadsto \color{blue}{\left(c \cdot j\right) \cdot t + i \cdot \left(b \cdot a - y \cdot j\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification11.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;i \le 3.7207160560314225 \cdot 10^{+113}:\\ \;\;\;\;\left(t \cdot c - y \cdot i\right) \cdot j + \left(\left(y \cdot z - t \cdot a\right) \cdot x - \left(\sqrt[3]{b \cdot \left(z \cdot c - i \cdot a\right)} \cdot \left(\sqrt[3]{b} \cdot \sqrt[3]{z \cdot c - i \cdot a}\right)\right) \cdot \sqrt[3]{b \cdot \left(z \cdot c - i \cdot a\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right) + \left(b \cdot a - y \cdot j\right) \cdot i\\ \end{array}\]

Runtime

Time bar (total: 1.1m)Debug logProfile

herbie shell --seed 2018219 
(FPCore (x y z t a b c i j)
  :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)))))