Average Error: 12.1 → 9.8
Time: 16.0s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -6.83346635036375763 \cdot 10^{180}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\sqrt[3]{j} \cdot \sqrt[3]{j}\right) \cdot \left(\sqrt[3]{j} \cdot \left(c \cdot t - i \cdot y\right)\right)\\ \mathbf{elif}\;b \le 0.0155641473725553429:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(z \cdot b\right) \cdot c + \left(-a \cdot \left(i \cdot b\right)\right)\right)\right) + \left(\left(c \cdot t\right) \cdot j + \left(-i \cdot \left(j \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\left(c \cdot t\right) \cdot j + \left(-\left(i \cdot j\right) \cdot y\right)\right)\\ \end{array}\]
\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}\;b \le -6.83346635036375763 \cdot 10^{180}:\\
\;\;\;\;\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 \left(c \cdot t - i \cdot y\right)\right)\\

\mathbf{elif}\;b \le 0.0155641473725553429:\\
\;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(z \cdot b\right) \cdot c + \left(-a \cdot \left(i \cdot b\right)\right)\right)\right) + \left(\left(c \cdot t\right) \cdot j + \left(-i \cdot \left(j \cdot y\right)\right)\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(\left(c \cdot t\right) \cdot j + \left(-\left(i \cdot j\right) \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 r174463 = x;
        double r174464 = y;
        double r174465 = z;
        double r174466 = r174464 * r174465;
        double r174467 = t;
        double r174468 = a;
        double r174469 = r174467 * r174468;
        double r174470 = r174466 - r174469;
        double r174471 = r174463 * r174470;
        double r174472 = b;
        double r174473 = c;
        double r174474 = r174473 * r174465;
        double r174475 = i;
        double r174476 = r174475 * r174468;
        double r174477 = r174474 - r174476;
        double r174478 = r174472 * r174477;
        double r174479 = r174471 - r174478;
        double r174480 = j;
        double r174481 = r174473 * r174467;
        double r174482 = r174475 * r174464;
        double r174483 = r174481 - r174482;
        double r174484 = r174480 * r174483;
        double r174485 = r174479 + r174484;
        return r174485;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r174486 = b;
        double r174487 = -6.833466350363758e+180;
        bool r174488 = r174486 <= r174487;
        double r174489 = x;
        double r174490 = y;
        double r174491 = z;
        double r174492 = r174490 * r174491;
        double r174493 = t;
        double r174494 = a;
        double r174495 = r174493 * r174494;
        double r174496 = r174492 - r174495;
        double r174497 = r174489 * r174496;
        double r174498 = c;
        double r174499 = r174498 * r174491;
        double r174500 = i;
        double r174501 = r174500 * r174494;
        double r174502 = r174499 - r174501;
        double r174503 = r174486 * r174502;
        double r174504 = r174497 - r174503;
        double r174505 = j;
        double r174506 = cbrt(r174505);
        double r174507 = r174506 * r174506;
        double r174508 = r174498 * r174493;
        double r174509 = r174500 * r174490;
        double r174510 = r174508 - r174509;
        double r174511 = r174506 * r174510;
        double r174512 = r174507 * r174511;
        double r174513 = r174504 + r174512;
        double r174514 = 0.015564147372555343;
        bool r174515 = r174486 <= r174514;
        double r174516 = r174491 * r174486;
        double r174517 = r174516 * r174498;
        double r174518 = r174500 * r174486;
        double r174519 = r174494 * r174518;
        double r174520 = -r174519;
        double r174521 = r174517 + r174520;
        double r174522 = r174497 - r174521;
        double r174523 = r174508 * r174505;
        double r174524 = r174505 * r174490;
        double r174525 = r174500 * r174524;
        double r174526 = -r174525;
        double r174527 = r174523 + r174526;
        double r174528 = r174522 + r174527;
        double r174529 = r174500 * r174505;
        double r174530 = r174529 * r174490;
        double r174531 = -r174530;
        double r174532 = r174523 + r174531;
        double r174533 = r174504 + r174532;
        double r174534 = r174515 ? r174528 : r174533;
        double r174535 = r174488 ? r174513 : r174534;
        return r174535;
}

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 b < -6.833466350363758e+180

    1. Initial program 5.5

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

    3. Applied add-cube-cbrt5.7

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

    4. Applied associate-*l*5.7

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

    if -6.833466350363758e+180 < b < 0.015564147372555343

    1. Initial program 14.0

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

    3. Applied sub-neg14.0

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

    4. Applied distribute-lft-in14.0

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

    5. Simplified14.0

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

    6. Simplified14.0

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

    8. Applied sub-neg14.0

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

    9. Applied distribute-lft-in14.0

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

    10. Simplified12.9

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

    12. Applied distribute-rgt-neg-out12.9

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

    13. Simplified11.0

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

    15. Applied associate-*r*10.8

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

    if 0.015564147372555343 < b

    1. Initial program 6.8

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

    3. Applied sub-neg6.8

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

    4. Applied distribute-lft-in6.8

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

    5. Simplified6.8

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

    6. Simplified7.9

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

    8. Applied associate-*r*7.2

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

  4. Final simplification9.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -6.83346635036375763 \cdot 10^{180}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\sqrt[3]{j} \cdot \sqrt[3]{j}\right) \cdot \left(\sqrt[3]{j} \cdot \left(c \cdot t - i \cdot y\right)\right)\\ \mathbf{elif}\;b \le 0.0155641473725553429:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(z \cdot b\right) \cdot c + \left(-a \cdot \left(i \cdot b\right)\right)\right)\right) + \left(\left(c \cdot t\right) \cdot j + \left(-i \cdot \left(j \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\left(c \cdot t\right) \cdot j + \left(-\left(i \cdot j\right) \cdot y\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020046 
(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)))))