Error

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Derivation

1. Split input into 2 regimes

2. if x < 1.3099434334785528e+80

   1. Initial program 12.3

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

   3. Applied sub-neg12.3

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

   4. Applied distribute-lft-in12.3

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

   6. Applied distribute-lft-neg-in12.3

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

   7. Applied associate-*r*11.8

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

   9. Applied add-cube-cbrt11.9

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

   if 1.3099434334785528e+80 < x

   1. Initial program 7.4

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

   3. Applied add-cube-cbrt7.6

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

   4. Applied associate-*r*7.6

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

4. Final simplification11.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \le 1.3099434334785528 \cdot 10^{+80}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(\left(\left(-a\right) \cdot \left(x \cdot t\right) + \sqrt[3]{\left(y \cdot z\right) \cdot x} \cdot \left(\sqrt[3]{\left(y \cdot z\right) \cdot x} \cdot \sqrt[3]{\left(y \cdot z\right) \cdot x}\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y \cdot z - t \cdot a\right) \cdot x - \sqrt[3]{z \cdot c - a \cdot i} \cdot \left(b \cdot \left(\sqrt[3]{z \cdot c - a \cdot i} \cdot \sqrt[3]{z \cdot c - a \cdot i}\right)\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019022 +o rules:numerics
(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)))))

Details

Time bar (total: 21.2s)Debug log