Average Error: 12.1 → 11.9
Time: 10.1s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le 9.528674436944476709065209317168156533936 \cdot 10^{109}:\\ \;\;\;\;\left(\left(\left(\sqrt[3]{x} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)} - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(t \cdot \left(j \cdot c\right) + \left(-j\right) \cdot \left(i \cdot y\right)\right)\\ \end{array}\]
\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}\;t \le 9.528674436944476709065209317168156533936 \cdot 10^{109}:\\
\;\;\;\;\left(\left(\left(\sqrt[3]{x} \cdot \sqrt[3]{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)\\

\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(-j\right) \cdot \left(i \cdot y\right)\right)\\

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r113565 = x;
        double r113566 = y;
        double r113567 = z;
        double r113568 = r113566 * r113567;
        double r113569 = t;
        double r113570 = a;
        double r113571 = r113569 * r113570;
        double r113572 = r113568 - r113571;
        double r113573 = r113565 * r113572;
        double r113574 = b;
        double r113575 = c;
        double r113576 = r113575 * r113567;
        double r113577 = i;
        double r113578 = r113577 * r113570;
        double r113579 = r113576 - r113578;
        double r113580 = r113574 * r113579;
        double r113581 = r113573 - r113580;
        double r113582 = j;
        double r113583 = r113575 * r113569;
        double r113584 = r113577 * r113566;
        double r113585 = r113583 - r113584;
        double r113586 = r113582 * r113585;
        double r113587 = r113581 + r113586;
        return r113587;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r113588 = t;
        double r113589 = 9.528674436944477e+109;
        bool r113590 = r113588 <= r113589;
        double r113591 = x;
        double r113592 = cbrt(r113591);
        double r113593 = y;
        double r113594 = z;
        double r113595 = r113593 * r113594;
        double r113596 = a;
        double r113597 = r113588 * r113596;
        double r113598 = r113595 - r113597;
        double r113599 = cbrt(r113598);
        double r113600 = r113592 * r113599;
        double r113601 = r113591 * r113598;
        double r113602 = cbrt(r113601);
        double r113603 = r113600 * r113602;
        double r113604 = r113603 * r113602;
        double r113605 = b;
        double r113606 = c;
        double r113607 = r113606 * r113594;
        double r113608 = i;
        double r113609 = r113608 * r113596;
        double r113610 = r113607 - r113609;
        double r113611 = r113605 * r113610;
        double r113612 = r113604 - r113611;
        double r113613 = j;
        double r113614 = r113606 * r113588;
        double r113615 = r113608 * r113593;
        double r113616 = r113614 - r113615;
        double r113617 = r113613 * r113616;
        double r113618 = r113612 + r113617;
        double r113619 = r113601 - r113611;
        double r113620 = r113613 * r113606;
        double r113621 = r113588 * r113620;
        double r113622 = -r113613;
        double r113623 = r113622 * r113615;
        double r113624 = r113621 + r113623;
        double r113625 = r113619 + r113624;
        double r113626 = r113590 ? r113618 : r113625;
        return r113626;
}

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 t < 9.528674436944477e+109

    1. Initial program 11.3

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

    3. Applied add-cube-cbrt11.6

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

    5. Applied cbrt-prod11.6

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

    if 9.528674436944477e+109 < t

    1. Initial program 19.5

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

    3. Applied add-cube-cbrt19.9

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

    4. Applied associate-*l*19.8

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

    6. Applied sub-neg19.8

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

    7. Applied distribute-lft-in19.8

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

    8. Applied distribute-lft-in19.8

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

    9. Simplified15.3

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

    10. Simplified15.2

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

  4. Final simplification11.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le 9.528674436944476709065209317168156533936 \cdot 10^{109}:\\ \;\;\;\;\left(\left(\left(\sqrt[3]{x} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)} - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(t \cdot \left(j \cdot c\right) + \left(-j\right) \cdot \left(i \cdot y\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019354 
(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)))))