Average Error: 11.4 → 11.7
Time: 33.0s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;j \le -1.0391983979041883 \cdot 10^{-175}:\\ \;\;\;\;\left(c \cdot t - y \cdot i\right) \cdot j + \left(\left(\left(x \cdot z\right) \cdot y - a \cdot \left(x \cdot t\right)\right) - \left(c \cdot z - a \cdot i\right) \cdot b\right)\\ \mathbf{elif}\;j \le 4.5121373396646204 \cdot 10^{-262}:\\ \;\;\;\;\left(\left(y \cdot z\right) \cdot x - a \cdot \left(x \cdot t\right)\right) - \left(c \cdot z - a \cdot i\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot t - y \cdot i\right) \cdot j + \left(\left(\left(x \cdot z\right) \cdot y - a \cdot \left(x \cdot t\right)\right) - \left(c \cdot z - a \cdot i\right) \cdot b\right)\\ \end{array}\]
\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}\;j \le -1.0391983979041883 \cdot 10^{-175}:\\
\;\;\;\;\left(c \cdot t - y \cdot i\right) \cdot j + \left(\left(\left(x \cdot z\right) \cdot y - a \cdot \left(x \cdot t\right)\right) - \left(c \cdot z - a \cdot i\right) \cdot b\right)\\

\mathbf{elif}\;j \le 4.5121373396646204 \cdot 10^{-262}:\\
\;\;\;\;\left(\left(y \cdot z\right) \cdot x - a \cdot \left(x \cdot t\right)\right) - \left(c \cdot z - a \cdot i\right) \cdot b\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r2622518 = x;
        double r2622519 = y;
        double r2622520 = z;
        double r2622521 = r2622519 * r2622520;
        double r2622522 = t;
        double r2622523 = a;
        double r2622524 = r2622522 * r2622523;
        double r2622525 = r2622521 - r2622524;
        double r2622526 = r2622518 * r2622525;
        double r2622527 = b;
        double r2622528 = c;
        double r2622529 = r2622528 * r2622520;
        double r2622530 = i;
        double r2622531 = r2622530 * r2622523;
        double r2622532 = r2622529 - r2622531;
        double r2622533 = r2622527 * r2622532;
        double r2622534 = r2622526 - r2622533;
        double r2622535 = j;
        double r2622536 = r2622528 * r2622522;
        double r2622537 = r2622530 * r2622519;
        double r2622538 = r2622536 - r2622537;
        double r2622539 = r2622535 * r2622538;
        double r2622540 = r2622534 + r2622539;
        return r2622540;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r2622541 = j;
        double r2622542 = -1.0391983979041883e-175;
        bool r2622543 = r2622541 <= r2622542;
        double r2622544 = c;
        double r2622545 = t;
        double r2622546 = r2622544 * r2622545;
        double r2622547 = y;
        double r2622548 = i;
        double r2622549 = r2622547 * r2622548;
        double r2622550 = r2622546 - r2622549;
        double r2622551 = r2622550 * r2622541;
        double r2622552 = x;
        double r2622553 = z;
        double r2622554 = r2622552 * r2622553;
        double r2622555 = r2622554 * r2622547;
        double r2622556 = a;
        double r2622557 = r2622552 * r2622545;
        double r2622558 = r2622556 * r2622557;
        double r2622559 = r2622555 - r2622558;
        double r2622560 = r2622544 * r2622553;
        double r2622561 = r2622556 * r2622548;
        double r2622562 = r2622560 - r2622561;
        double r2622563 = b;
        double r2622564 = r2622562 * r2622563;
        double r2622565 = r2622559 - r2622564;
        double r2622566 = r2622551 + r2622565;
        double r2622567 = 4.5121373396646204e-262;
        bool r2622568 = r2622541 <= r2622567;
        double r2622569 = r2622547 * r2622553;
        double r2622570 = r2622569 * r2622552;
        double r2622571 = r2622570 - r2622558;
        double r2622572 = r2622571 - r2622564;
        double r2622573 = r2622568 ? r2622572 : r2622566;
        double r2622574 = r2622543 ? r2622566 : r2622573;
        return r2622574;
}

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 < -1.0391983979041883e-175 or 4.5121373396646204e-262 < j

    1. Initial program 10.3

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

    3. Applied add-cube-cbrt10.6

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

    4. Applied associate-*l*10.6

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

    5. Taylor expanded around -inf 10.7

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

    7. Applied associate-*r*10.6

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

    if -1.0391983979041883e-175 < j < 4.5121373396646204e-262

    1. Initial program 16.4

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

    3. Applied add-cube-cbrt16.7

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

    4. Applied associate-*l*16.7

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

    5. Taylor expanded around -inf 16.6

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

    6. Taylor expanded around 0 16.2

      \[\leadsto \left(\left(x \cdot \left(z \cdot y\right) - a \cdot \left(x \cdot t\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{0}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification11.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;j \le -1.0391983979041883 \cdot 10^{-175}:\\ \;\;\;\;\left(c \cdot t - y \cdot i\right) \cdot j + \left(\left(\left(x \cdot z\right) \cdot y - a \cdot \left(x \cdot t\right)\right) - \left(c \cdot z - a \cdot i\right) \cdot b\right)\\ \mathbf{elif}\;j \le 4.5121373396646204 \cdot 10^{-262}:\\ \;\;\;\;\left(\left(y \cdot z\right) \cdot x - a \cdot \left(x \cdot t\right)\right) - \left(c \cdot z - a \cdot i\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot t - y \cdot i\right) \cdot j + \left(\left(\left(x \cdot z\right) \cdot y - a \cdot \left(x \cdot t\right)\right) - \left(c \cdot z - a \cdot i\right) \cdot b\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019129 
(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)))))