Average Error: 12.3 → 12.0
Time: 33.5s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;i \le -2.734577024275635776606896347876237358818 \cdot 10^{-142}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\left(c \cdot t\right) \cdot j + \left(-i\right) \cdot \left(y \cdot j\right)\right)\\ \mathbf{elif}\;i \le 3.189483550666528306044484300359716331537 \cdot 10^{-261}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(c \cdot \left(t \cdot j\right) + \left(-i \cdot y\right) \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(t \cdot \left(j \cdot c\right) + \left(-i \cdot y\right) \cdot j\right)\\ \end{array}\]
\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}\;i \le -2.734577024275635776606896347876237358818 \cdot 10^{-142}:\\
\;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\left(c \cdot t\right) \cdot j + \left(-i\right) \cdot \left(y \cdot j\right)\right)\\

\mathbf{elif}\;i \le 3.189483550666528306044484300359716331537 \cdot 10^{-261}:\\
\;\;\;\;\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) + \left(-i \cdot y\right) \cdot j\right)\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r9433555 = x;
        double r9433556 = y;
        double r9433557 = z;
        double r9433558 = r9433556 * r9433557;
        double r9433559 = t;
        double r9433560 = a;
        double r9433561 = r9433559 * r9433560;
        double r9433562 = r9433558 - r9433561;
        double r9433563 = r9433555 * r9433562;
        double r9433564 = b;
        double r9433565 = c;
        double r9433566 = r9433565 * r9433557;
        double r9433567 = i;
        double r9433568 = r9433567 * r9433560;
        double r9433569 = r9433566 - r9433568;
        double r9433570 = r9433564 * r9433569;
        double r9433571 = r9433563 - r9433570;
        double r9433572 = j;
        double r9433573 = r9433565 * r9433559;
        double r9433574 = r9433567 * r9433556;
        double r9433575 = r9433573 - r9433574;
        double r9433576 = r9433572 * r9433575;
        double r9433577 = r9433571 + r9433576;
        return r9433577;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r9433578 = i;
        double r9433579 = -2.7345770242756358e-142;
        bool r9433580 = r9433578 <= r9433579;
        double r9433581 = x;
        double r9433582 = y;
        double r9433583 = z;
        double r9433584 = r9433582 * r9433583;
        double r9433585 = t;
        double r9433586 = a;
        double r9433587 = r9433585 * r9433586;
        double r9433588 = r9433584 - r9433587;
        double r9433589 = r9433581 * r9433588;
        double r9433590 = b;
        double r9433591 = c;
        double r9433592 = r9433591 * r9433583;
        double r9433593 = r9433578 * r9433586;
        double r9433594 = r9433592 - r9433593;
        double r9433595 = r9433590 * r9433594;
        double r9433596 = r9433589 - r9433595;
        double r9433597 = r9433591 * r9433585;
        double r9433598 = j;
        double r9433599 = r9433597 * r9433598;
        double r9433600 = -r9433578;
        double r9433601 = r9433582 * r9433598;
        double r9433602 = r9433600 * r9433601;
        double r9433603 = r9433599 + r9433602;
        double r9433604 = r9433596 + r9433603;
        double r9433605 = 3.1894835506665283e-261;
        bool r9433606 = r9433578 <= r9433605;
        double r9433607 = r9433585 * r9433598;
        double r9433608 = r9433591 * r9433607;
        double r9433609 = r9433578 * r9433582;
        double r9433610 = -r9433609;
        double r9433611 = r9433610 * r9433598;
        double r9433612 = r9433608 + r9433611;
        double r9433613 = r9433596 + r9433612;
        double r9433614 = r9433598 * r9433591;
        double r9433615 = r9433585 * r9433614;
        double r9433616 = r9433615 + r9433611;
        double r9433617 = r9433596 + r9433616;
        double r9433618 = r9433606 ? r9433613 : r9433617;
        double r9433619 = r9433580 ? r9433604 : r9433618;
        return r9433619;
}

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 3 regimes

  2. if i < -2.7345770242756358e-142

    1. Initial program 14.3

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

    3. Applied sub-neg14.3

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

    4. Applied distribute-rgt-in14.3

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

    6. Applied distribute-lft-neg-in14.3

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

    7. Applied associate-*l*12.4

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

    if -2.7345770242756358e-142 < i < 3.1894835506665283e-261

    1. Initial program 10.0

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

    3. Applied sub-neg10.0

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

    4. Applied distribute-rgt-in10.0

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

    6. Applied associate-*l*10.6

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

    if 3.1894835506665283e-261 < i

    1. Initial program 12.0

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

    3. Applied sub-neg12.0

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

    4. Applied distribute-rgt-in12.0

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

    5. Taylor expanded around inf 12.4

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

  4. Final simplification12.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;i \le -2.734577024275635776606896347876237358818 \cdot 10^{-142}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\left(c \cdot t\right) \cdot j + \left(-i\right) \cdot \left(y \cdot j\right)\right)\\ \mathbf{elif}\;i \le 3.189483550666528306044484300359716331537 \cdot 10^{-261}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(c \cdot \left(t \cdot j\right) + \left(-i \cdot y\right) \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(t \cdot \left(j \cdot c\right) + \left(-i \cdot y\right) \cdot j\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019173 +o rules:numerics
(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)))))