Average Error: 11.6 → 11.0
Time: 34.7s
Precision: 64
Internal precision: 384
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
⬇
\[\begin{array}{l} \mathbf{if}\;j \le -2.8887058926386322 \cdot 10^{-70}:\\ \;\;\;\;\left(c \cdot \left(t \cdot j\right) + \left(\left(z \cdot y - a \cdot t\right) \cdot x - \left(z \cdot c - i \cdot a\right) \cdot b\right)\right) + \left(-i \cdot y\right) \cdot j\\ \mathbf{if}\;j \le 1.0632117078023356 \cdot 10^{+177}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - a \cdot t\right) + \left(i \cdot j\right) \cdot \left(-y\right)\right) - \left(\left(z \cdot c - i \cdot a\right) \cdot b - \left(c \cdot j\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot \left(t \cdot j\right) + \left(\left(z \cdot y - a \cdot t\right) \cdot x - \left(z \cdot c - i \cdot a\right) \cdot b\right)\right) + \left(-i \cdot y\right) \cdot j\\ \end{array}\]

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 j < -2.8887058926386322e-70 or 1.0632117078023356e+177 < j

    1. Initial program 7.8

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

    3. Applied add-cube-cbrt 8.2

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

    5. Applied sub-neg 8.2

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

    6. Applied distribute-rgt-in 8.2

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

    7. Applied associate-+r+ 8.2

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

    8. Applied simplify 12.0

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

    if -2.8887058926386322e-70 < j < 1.0632117078023356e+177

    1. Initial program 13.4

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

    3. Applied add-cube-cbrt 14.1

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

    5. Applied sub-neg 14.1

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

    6. Applied distribute-lft-in 14.1

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

    7. Applied associate-+r+ 14.1

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

    8. Applied simplify 12.1

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

    9. Applied taylor 10.5

      \[\leadsto \left(\left(j \cdot c\right) \cdot t + \left(\left(z \cdot y - a \cdot t\right) \cdot x - \left(z \cdot c - i \cdot a\right) \cdot b\right)\right) + -1 \cdot \left(y \cdot \left(j \cdot i\right)\right)\]

    10. Taylor expanded around inf 10.5

      \[\leadsto \left(\left(j \cdot c\right) \cdot t + \left(\left(z \cdot y - a \cdot t\right) \cdot x - \left(z \cdot c - i \cdot a\right) \cdot b\right)\right) + \color{blue}{-1 \cdot \left(y \cdot \left(j \cdot i\right)\right)}\]

    11. Applied simplify 10.5

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

Runtime

Time bar (total: 34.7s) Debug logProfile

Please include this information when filing a bug report:

herbie shell --seed '#(1064524629 4159152179 2999149171 575749698 4006532819 692958815)'
(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)))))