Average Error: 12.0 → 10.9
Time: 7.1s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le 1.5250968462807195 \cdot 10^{-27}:\\ \;\;\;\;\left(\left(\left(\left(x \cdot y\right) \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) \cdot \sqrt[3]{z} + 1 \cdot \left(-1 \cdot \left(a \cdot \left(x \cdot t\right)\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x \cdot \left(y \cdot z\right) + x \cdot \left(-t \cdot a\right)\right) - \left(\sqrt[3]{b \cdot \left(c \cdot z - i \cdot a\right)} \cdot \sqrt[3]{b \cdot \left(c \cdot z - i \cdot a\right)}\right) \cdot \sqrt[3]{b \cdot \left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \end{array}\]
\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 1.5250968462807195 \cdot 10^{-27}:\\
\;\;\;\;\left(\left(\left(\left(x \cdot y\right) \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) \cdot \sqrt[3]{z} + 1 \cdot \left(-1 \cdot \left(a \cdot \left(x \cdot t\right)\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\

\mathbf{else}:\\
\;\;\;\;\left(\left(x \cdot \left(y \cdot z\right) + x \cdot \left(-t \cdot a\right)\right) - \left(\sqrt[3]{b \cdot \left(c \cdot z - i \cdot a\right)} \cdot \sqrt[3]{b \cdot \left(c \cdot z - i \cdot a\right)}\right) \cdot \sqrt[3]{b \cdot \left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\

\end{array}
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return (((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y))));
}
↓
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double VAR;
	if ((x <= 1.5250968462807195e-27)) {
		VAR = ((((((x * y) * (cbrt(z) * cbrt(z))) * cbrt(z)) + (1.0 * (-1.0 * (a * (x * t))))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y))));
	} else {
		VAR = ((((x * (y * z)) + (x * -(t * a))) - ((cbrt((b * ((c * z) - (i * a)))) * cbrt((b * ((c * z) - (i * a))))) * cbrt((b * ((c * z) - (i * a)))))) + (j * ((c * t) - (i * y))));
	}
	return VAR;
}

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 < 1.5250968462807195e-27

    1. Initial program 13.2

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

    3. Applied sub-neg13.2

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

    4. Applied distribute-lft-in13.2

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

    6. Applied *-un-lft-identity13.2

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

    7. Applied associate-*l*13.2

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

    8. Simplified12.4

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

    10. Applied associate-*r*11.6

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

    12. Applied add-cube-cbrt11.7

      \[\leadsto \left(\left(\left(x \cdot y\right) \cdot \color{blue}{\left(\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}\right)} + 1 \cdot \left(-1 \cdot \left(a \cdot \left(x \cdot t\right)\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]

    13. Applied associate-*r*11.7

      \[\leadsto \left(\left(\color{blue}{\left(\left(x \cdot y\right) \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) \cdot \sqrt[3]{z}} + 1 \cdot \left(-1 \cdot \left(a \cdot \left(x \cdot t\right)\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]

    if 1.5250968462807195e-27 < x

    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 sub-neg7.8

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

    4. Applied distribute-lft-in7.8

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

    6. Applied add-cube-cbrt8.0

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

  4. Final simplification10.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le 1.5250968462807195 \cdot 10^{-27}:\\ \;\;\;\;\left(\left(\left(\left(x \cdot y\right) \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) \cdot \sqrt[3]{z} + 1 \cdot \left(-1 \cdot \left(a \cdot \left(x \cdot t\right)\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x \cdot \left(y \cdot z\right) + x \cdot \left(-t \cdot a\right)\right) - \left(\sqrt[3]{b \cdot \left(c \cdot z - i \cdot a\right)} \cdot \sqrt[3]{b \cdot \left(c \cdot z - i \cdot a\right)}\right) \cdot \sqrt[3]{b \cdot \left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020078 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64
  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))