Average Error: 11.8 → 11.9
Time: 2.2m
Precision: 64
Internal Precision: 384
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;i \le -3.464091833904971 \cdot 10^{+94}:\\ \;\;\;\;\left(a \cdot b - j \cdot y\right) \cdot i + \left(t \cdot c\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right) \cdot \left(\sqrt[3]{x} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \end{array}\]

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 i < -3.464091833904971e+94

    1. Initial program 20.7

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

    2. Taylor expanded around inf 31.8

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

    3. Applied simplify20.5

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

    if -3.464091833904971e+94 < i

    1. Initial program 10.5

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

    3. Applied add-cube-cbrt10.8

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

    5. Applied cbrt-prod10.8

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

Runtime

Time bar (total: 2.2m)Debug logProfile

herbie shell --seed '#(1063154770 1824007522 645063331 41291047 494775821 1237684644)' 
(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)))))