Average Error: 11.8 → 11.5
Time: 1.1m
Precision: 64
Internal Precision: 576
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1.0412696191654271 \cdot 10^{-33} \lor \neg \left(x \le 6.885802525054383 \cdot 10^{-159}\right):\\ \;\;\;\;\left(\left(y \cdot z - a \cdot t\right) \cdot x - b \cdot \left(z \cdot c - i \cdot a\right)\right) + \left(\left(\sqrt[3]{c \cdot t - i \cdot y} \cdot \sqrt[3]{c \cdot t - i \cdot y}\right) \cdot j\right) \cdot \sqrt[3]{c \cdot t - i \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot \left(i \cdot a - z \cdot c\right) - \left(x \cdot t\right) \cdot a\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \end{array}\]

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 x < -1.0412696191654271e-33 or 6.885802525054383e-159 < x

    1. Initial program 8.7

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

    3. Applied add-cube-cbrt8.9

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

    4. Applied associate-*r*8.9

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

    if -1.0412696191654271e-33 < x < 6.885802525054383e-159

    1. Initial program 16.1

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

    2. Taylor expanded around inf 14.2

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

    3. Simplified15.0

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

  4. Final simplification11.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.0412696191654271 \cdot 10^{-33} \lor \neg \left(x \le 6.885802525054383 \cdot 10^{-159}\right):\\ \;\;\;\;\left(\left(y \cdot z - a \cdot t\right) \cdot x - b \cdot \left(z \cdot c - i \cdot a\right)\right) + \left(\left(\sqrt[3]{c \cdot t - i \cdot y} \cdot \sqrt[3]{c \cdot t - i \cdot y}\right) \cdot j\right) \cdot \sqrt[3]{c \cdot t - i \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot \left(i \cdot a - z \cdot c\right) - \left(x \cdot t\right) \cdot a\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \end{array}\]

Runtime

Time bar (total: 1.1m)Debug logProfile

herbie shell --seed 2018216 
(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)))))