Average Error: 12.4 → 9.6
Time: 7.3s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -3.31775490019201837 \cdot 10^{84} \lor \neg \left(b \le 4954531051790429180\right):\\ \;\;\;\;\left(\left(x \cdot \left(\sqrt[3]{y \cdot z - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right)\right) \cdot \sqrt[3]{y \cdot z - t \cdot a} - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(b \cdot c\right) \cdot z + \left(-a \cdot \left(i \cdot b\right)\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \end{array}\]
\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 -3.31775490019201837 \cdot 10^{84} \lor \neg \left(b \le 4954531051790429180\right):\\
\;\;\;\;\left(\left(x \cdot \left(\sqrt[3]{y \cdot z - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right)\right) \cdot \sqrt[3]{y \cdot z - t \cdot a} - 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) - \left(\left(b \cdot c\right) \cdot z + \left(-a \cdot \left(i \cdot b\right)\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 r583493 = x;
        double r583494 = y;
        double r583495 = z;
        double r583496 = r583494 * r583495;
        double r583497 = t;
        double r583498 = a;
        double r583499 = r583497 * r583498;
        double r583500 = r583496 - r583499;
        double r583501 = r583493 * r583500;
        double r583502 = b;
        double r583503 = c;
        double r583504 = r583503 * r583495;
        double r583505 = i;
        double r583506 = r583505 * r583498;
        double r583507 = r583504 - r583506;
        double r583508 = r583502 * r583507;
        double r583509 = r583501 - r583508;
        double r583510 = j;
        double r583511 = r583503 * r583497;
        double r583512 = r583505 * r583494;
        double r583513 = r583511 - r583512;
        double r583514 = r583510 * r583513;
        double r583515 = r583509 + r583514;
        return r583515;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r583516 = b;
        double r583517 = -3.3177549001920184e+84;
        bool r583518 = r583516 <= r583517;
        double r583519 = 4.954531051790429e+18;
        bool r583520 = r583516 <= r583519;
        double r583521 = !r583520;
        bool r583522 = r583518 || r583521;
        double r583523 = x;
        double r583524 = y;
        double r583525 = z;
        double r583526 = r583524 * r583525;
        double r583527 = t;
        double r583528 = a;
        double r583529 = r583527 * r583528;
        double r583530 = r583526 - r583529;
        double r583531 = cbrt(r583530);
        double r583532 = r583531 * r583531;
        double r583533 = r583523 * r583532;
        double r583534 = r583533 * r583531;
        double r583535 = c;
        double r583536 = r583535 * r583525;
        double r583537 = i;
        double r583538 = r583537 * r583528;
        double r583539 = r583536 - r583538;
        double r583540 = r583516 * r583539;
        double r583541 = r583534 - r583540;
        double r583542 = j;
        double r583543 = r583535 * r583527;
        double r583544 = r583537 * r583524;
        double r583545 = r583543 - r583544;
        double r583546 = r583542 * r583545;
        double r583547 = r583541 + r583546;
        double r583548 = r583523 * r583530;
        double r583549 = r583516 * r583535;
        double r583550 = r583549 * r583525;
        double r583551 = r583537 * r583516;
        double r583552 = r583528 * r583551;
        double r583553 = -r583552;
        double r583554 = r583550 + r583553;
        double r583555 = r583548 - r583554;
        double r583556 = r583555 + r583546;
        double r583557 = r583522 ? r583547 : r583556;
        return r583557;
}

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

Target

Original12.4
Target16.1
Herbie9.6
\[\begin{array}{l} \mathbf{if}\;t \lt -8.1209789191959122 \cdot 10^{-33}:\\ \;\;\;\;x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{elif}\;t \lt -4.7125538182184851 \cdot 10^{-169}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ \mathbf{elif}\;t \lt -7.63353334603158369 \cdot 10^{-308}:\\ \;\;\;\;x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{elif}\;t \lt 1.0535888557455487 \cdot 10^{-139}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if b < -3.3177549001920184e+84 or 4.954531051790429e+18 < b

    1. Initial program 7.3

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

    3. Applied add-cube-cbrt7.5

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

    4. Applied associate-*r*7.5

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

    if -3.3177549001920184e+84 < b < 4.954531051790429e+18

    1. Initial program 14.7

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

    3. Applied sub-neg14.7

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

    4. Applied distribute-lft-in14.7

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

    6. Applied distribute-rgt-neg-out14.7

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

    7. Simplified12.5

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

    9. Applied associate-*r*10.5

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

  4. Final simplification9.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -3.31775490019201837 \cdot 10^{84} \lor \neg \left(b \le 4954531051790429180\right):\\ \;\;\;\;\left(\left(x \cdot \left(\sqrt[3]{y \cdot z - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right)\right) \cdot \sqrt[3]{y \cdot z - t \cdot a} - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(b \cdot c\right) \cdot z + \left(-a \cdot \left(i \cdot b\right)\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020060 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< t -8.120978919195912e-33) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -4.712553818218485e-169) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2) (pow (* i y) 2))) (+ (* c t) (* i y)))) (if (< t -7.633533346031584e-308) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 1.0535888557455487e-139) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2) (pow (* i y) 2))) (+ (* c t) (* i y)))) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))