Average Error: 12.1 → 9.3
Time: 30.5s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -1.746485226326191646256035493009197125697 \cdot 10^{-44} \lor \neg \left(b \le 6.97020109897896740211542344045198217806 \cdot 10^{-28}\right):\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(t \cdot \left(j \cdot c\right) + \left(-i \cdot \left(j \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(z \cdot \left(b \cdot c\right) + \left(i \cdot b\right) \cdot \left(-a\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \end{array}\]
\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}\;b \le -1.746485226326191646256035493009197125697 \cdot 10^{-44} \lor \neg \left(b \le 6.97020109897896740211542344045198217806 \cdot 10^{-28}\right):\\
\;\;\;\;\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 \left(j \cdot y\right)\right)\right)\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r104431 = x;
        double r104432 = y;
        double r104433 = z;
        double r104434 = r104432 * r104433;
        double r104435 = t;
        double r104436 = a;
        double r104437 = r104435 * r104436;
        double r104438 = r104434 - r104437;
        double r104439 = r104431 * r104438;
        double r104440 = b;
        double r104441 = c;
        double r104442 = r104441 * r104433;
        double r104443 = i;
        double r104444 = r104443 * r104436;
        double r104445 = r104442 - r104444;
        double r104446 = r104440 * r104445;
        double r104447 = r104439 - r104446;
        double r104448 = j;
        double r104449 = r104441 * r104435;
        double r104450 = r104443 * r104432;
        double r104451 = r104449 - r104450;
        double r104452 = r104448 * r104451;
        double r104453 = r104447 + r104452;
        return r104453;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r104454 = b;
        double r104455 = -1.7464852263261916e-44;
        bool r104456 = r104454 <= r104455;
        double r104457 = 6.970201098978967e-28;
        bool r104458 = r104454 <= r104457;
        double r104459 = !r104458;
        bool r104460 = r104456 || r104459;
        double r104461 = x;
        double r104462 = y;
        double r104463 = z;
        double r104464 = r104462 * r104463;
        double r104465 = t;
        double r104466 = a;
        double r104467 = r104465 * r104466;
        double r104468 = r104464 - r104467;
        double r104469 = r104461 * r104468;
        double r104470 = c;
        double r104471 = r104470 * r104463;
        double r104472 = i;
        double r104473 = r104472 * r104466;
        double r104474 = r104471 - r104473;
        double r104475 = r104454 * r104474;
        double r104476 = r104469 - r104475;
        double r104477 = j;
        double r104478 = r104477 * r104470;
        double r104479 = r104465 * r104478;
        double r104480 = r104477 * r104462;
        double r104481 = r104472 * r104480;
        double r104482 = -r104481;
        double r104483 = r104479 + r104482;
        double r104484 = r104476 + r104483;
        double r104485 = r104454 * r104470;
        double r104486 = r104463 * r104485;
        double r104487 = r104472 * r104454;
        double r104488 = -r104466;
        double r104489 = r104487 * r104488;
        double r104490 = r104486 + r104489;
        double r104491 = r104469 - r104490;
        double r104492 = r104470 * r104465;
        double r104493 = r104472 * r104462;
        double r104494 = r104492 - r104493;
        double r104495 = r104477 * r104494;
        double r104496 = r104491 + r104495;
        double r104497 = r104460 ? r104484 : r104496;
        return r104497;
}

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 b < -1.7464852263261916e-44 or 6.970201098978967e-28 < b

    1. Initial program 7.6

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

    3. Applied sub-neg7.6

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

    4. Applied distribute-lft-in7.6

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

    5. Simplified8.0

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

    6. Simplified8.1

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

    if -1.7464852263261916e-44 < b < 6.970201098978967e-28

    1. Initial program 16.0

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

    3. Applied sub-neg16.0

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

    4. Applied distribute-lft-in16.0

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

    5. Simplified13.2

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

    7. Applied distribute-rgt-neg-in13.2

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

    8. Applied associate-*r*10.4

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

    9. Simplified10.4

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

  4. Final simplification9.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -1.746485226326191646256035493009197125697 \cdot 10^{-44} \lor \neg \left(b \le 6.97020109897896740211542344045198217806 \cdot 10^{-28}\right):\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(t \cdot \left(j \cdot c\right) + \left(-i \cdot \left(j \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(z \cdot \left(b \cdot c\right) + \left(i \cdot b\right) \cdot \left(-a\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019323 +o rules:numerics
(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)))))