Average Error: 12.5 → 10.3
Time: 1.2m
Precision: 64
Internal precision: 128
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
⬇
\[\begin{array}{l} \mathbf{if}\;a \le 2.3403364003398004 \cdot 10^{+122}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + {\left(\sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)}\right)}^3\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot \left(t \cdot c - y \cdot i\right) - \left(b \cdot z\right) \cdot c\right) + \left(b \cdot i - x \cdot t\right) \cdot a\\ \end{array}\]

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

Derivation

  1. Split input into 2 regimes.

  2. if a < 2.3403364003398004e+122

    1. Initial program 10.4

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

    3. Applied add-cube-cbrt 10.7

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

    if 2.3403364003398004e+122 < a

    1. Initial program 29.4

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

    2. Applied taylor 23.1

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

    3. Taylor expanded around inf 23.1

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

    4. Applied simplify 7.3

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

Runtime

Time bar (total: 1.2m) Debug log

Please include this information when filing a bug report:

herbie --seed '#(3736595957 782161910 3919562515 2826787545 34303917 2518565596)'
(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)))))