Average Error: 11.3 → 8.8
Time: 39.2s
Precision: 64
Internal Precision: 128
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;j \le -1.1888143925939686 \cdot 10^{-69} \lor \neg \left(j \le 7.828490148124833 \cdot 10^{+94}\right):\\ \;\;\;\;\left(\left(y \cdot z - t \cdot a\right) \cdot x - \left(\sqrt[3]{z \cdot c - i \cdot a} \cdot \left(\sqrt[3]{z \cdot c - i \cdot a} \cdot \sqrt[3]{z \cdot c - i \cdot a}\right)\right) \cdot b\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot \left(t \cdot j\right) + \left(-i\right) \cdot \left(y \cdot j\right)\right) + \left(\left(y \cdot z - t \cdot a\right) \cdot x - b \cdot \left(z \cdot c - i \cdot a\right)\right)\\ \end{array}\]

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 j < -1.1888143925939686e-69 or 7.828490148124833e+94 < j

    1. Initial program 6.7

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

    3. Applied add-cube-cbrt7.0

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

    if -1.1888143925939686e-69 < j < 7.828490148124833e+94

    1. Initial program 14.1

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

    3. Applied sub-neg14.1

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

    4. Applied distribute-rgt-in14.1

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

    6. Applied associate-*l*12.2

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

    7. Taylor expanded around -inf 10.0

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

    8. Simplified10.0

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

  4. Final simplification8.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;j \le -1.1888143925939686 \cdot 10^{-69} \lor \neg \left(j \le 7.828490148124833 \cdot 10^{+94}\right):\\ \;\;\;\;\left(\left(y \cdot z - t \cdot a\right) \cdot x - \left(\sqrt[3]{z \cdot c - i \cdot a} \cdot \left(\sqrt[3]{z \cdot c - i \cdot a} \cdot \sqrt[3]{z \cdot c - i \cdot a}\right)\right) \cdot b\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot \left(t \cdot j\right) + \left(-i\right) \cdot \left(y \cdot j\right)\right) + \left(\left(y \cdot z - t \cdot a\right) \cdot x - b \cdot \left(z \cdot c - i \cdot a\right)\right)\\ \end{array}\]

Runtime

Time bar (total: 39.2s)Debug logProfile

herbie shell --seed 2018273 
(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)))))