Average Error: 5.6 → 3.5
Time: 40.6s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -3.38031238438186204 \cdot 10^{25}:\\ \;\;\;\;\left(\left(\left(\left(18 \cdot t\right) \cdot \left(x \cdot \left(z \cdot y\right)\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - x \cdot \left(4 \cdot i\right)\right) - \left(\left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right) \cdot \left(j \cdot 27\right)\right) \cdot \sqrt[3]{k}\\ \mathbf{elif}\;t \le 1.8846834206973961 \cdot 10^{35}:\\ \;\;\;\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(t \cdot z\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \end{array}\]
\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k
↓
\begin{array}{l}
\mathbf{if}\;t \le -3.38031238438186204 \cdot 10^{25}:\\
\;\;\;\;\left(\left(\left(\left(18 \cdot t\right) \cdot \left(x \cdot \left(z \cdot y\right)\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - x \cdot \left(4 \cdot i\right)\right) - \left(\left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right) \cdot \left(j \cdot 27\right)\right) \cdot \sqrt[3]{k}\\

\mathbf{elif}\;t \le 1.8846834206973961 \cdot 10^{35}:\\
\;\;\;\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(t \cdot z\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\

\mathbf{else}:\\
\;\;\;\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r94449 = x;
        double r94450 = 18.0;
        double r94451 = r94449 * r94450;
        double r94452 = y;
        double r94453 = r94451 * r94452;
        double r94454 = z;
        double r94455 = r94453 * r94454;
        double r94456 = t;
        double r94457 = r94455 * r94456;
        double r94458 = a;
        double r94459 = 4.0;
        double r94460 = r94458 * r94459;
        double r94461 = r94460 * r94456;
        double r94462 = r94457 - r94461;
        double r94463 = b;
        double r94464 = c;
        double r94465 = r94463 * r94464;
        double r94466 = r94462 + r94465;
        double r94467 = r94449 * r94459;
        double r94468 = i;
        double r94469 = r94467 * r94468;
        double r94470 = r94466 - r94469;
        double r94471 = j;
        double r94472 = 27.0;
        double r94473 = r94471 * r94472;
        double r94474 = k;
        double r94475 = r94473 * r94474;
        double r94476 = r94470 - r94475;
        return r94476;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r94477 = t;
        double r94478 = -3.380312384381862e+25;
        bool r94479 = r94477 <= r94478;
        double r94480 = 18.0;
        double r94481 = r94480 * r94477;
        double r94482 = x;
        double r94483 = z;
        double r94484 = y;
        double r94485 = r94483 * r94484;
        double r94486 = r94482 * r94485;
        double r94487 = r94481 * r94486;
        double r94488 = a;
        double r94489 = 4.0;
        double r94490 = r94488 * r94489;
        double r94491 = r94490 * r94477;
        double r94492 = r94487 - r94491;
        double r94493 = b;
        double r94494 = c;
        double r94495 = r94493 * r94494;
        double r94496 = r94492 + r94495;
        double r94497 = i;
        double r94498 = r94489 * r94497;
        double r94499 = r94482 * r94498;
        double r94500 = r94496 - r94499;
        double r94501 = k;
        double r94502 = cbrt(r94501);
        double r94503 = r94502 * r94502;
        double r94504 = j;
        double r94505 = 27.0;
        double r94506 = r94504 * r94505;
        double r94507 = r94503 * r94506;
        double r94508 = r94507 * r94502;
        double r94509 = r94500 - r94508;
        double r94510 = 1.884683420697396e+35;
        bool r94511 = r94477 <= r94510;
        double r94512 = r94482 * r94480;
        double r94513 = r94512 * r94484;
        double r94514 = r94477 * r94483;
        double r94515 = r94513 * r94514;
        double r94516 = r94515 - r94491;
        double r94517 = r94516 + r94495;
        double r94518 = r94482 * r94489;
        double r94519 = r94518 * r94497;
        double r94520 = r94517 - r94519;
        double r94521 = r94506 * r94501;
        double r94522 = r94520 - r94521;
        double r94523 = r94484 * r94483;
        double r94524 = r94512 * r94523;
        double r94525 = r94524 * r94477;
        double r94526 = r94525 - r94491;
        double r94527 = r94526 + r94495;
        double r94528 = r94527 - r94519;
        double r94529 = r94528 - r94521;
        double r94530 = r94511 ? r94522 : r94529;
        double r94531 = r94479 ? r94509 : r94530;
        return r94531;
}

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

Bits error versus k

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 3 regimes

  2. if t < -3.380312384381862e+25

    1. Initial program 2.1

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]

    2. Taylor expanded around inf 1.9

      \[\leadsto \left(\left(\left(\color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(z \cdot y\right)\right)\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
    3. Using strategy rm

    4. Applied associate-*r*1.9

      \[\leadsto \left(\left(\left(\color{blue}{\left(18 \cdot t\right) \cdot \left(x \cdot \left(z \cdot y\right)\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
    5. Using strategy rm

    6. Applied associate-*l*2.0

      \[\leadsto \left(\left(\left(\left(18 \cdot t\right) \cdot \left(x \cdot \left(z \cdot y\right)\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \color{blue}{x \cdot \left(4 \cdot i\right)}\right) - \left(j \cdot 27\right) \cdot k\]
    7. Using strategy rm

    8. Applied add-cube-cbrt2.2

      \[\leadsto \left(\left(\left(\left(18 \cdot t\right) \cdot \left(x \cdot \left(z \cdot y\right)\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - x \cdot \left(4 \cdot i\right)\right) - \left(j \cdot 27\right) \cdot \color{blue}{\left(\left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right) \cdot \sqrt[3]{k}\right)}\]

    9. Applied associate-*r*2.2

      \[\leadsto \left(\left(\left(\left(18 \cdot t\right) \cdot \left(x \cdot \left(z \cdot y\right)\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - x \cdot \left(4 \cdot i\right)\right) - \color{blue}{\left(\left(j \cdot 27\right) \cdot \left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right)\right) \cdot \sqrt[3]{k}}\]

    10. Simplified2.2

      \[\leadsto \left(\left(\left(\left(18 \cdot t\right) \cdot \left(x \cdot \left(z \cdot y\right)\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - x \cdot \left(4 \cdot i\right)\right) - \color{blue}{\left(\left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right) \cdot \left(j \cdot 27\right)\right)} \cdot \sqrt[3]{k}\]

    if -3.380312384381862e+25 < t < 1.884683420697396e+35

    1. Initial program 7.2

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
    2. Using strategy rm

    3. Applied associate-*l*4.2

      \[\leadsto \left(\left(\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]

    4. Simplified4.2

      \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot \color{blue}{\left(t \cdot z\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]

    if 1.884683420697396e+35 < t

    1. Initial program 1.7

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
    2. Using strategy rm

    3. Applied associate-*l*1.8

      \[\leadsto \left(\left(\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right)} \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
  3. Recombined 3 regimes into one program.

  4. Final simplification3.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -3.38031238438186204 \cdot 10^{25}:\\ \;\;\;\;\left(\left(\left(\left(18 \cdot t\right) \cdot \left(x \cdot \left(z \cdot y\right)\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - x \cdot \left(4 \cdot i\right)\right) - \left(\left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right) \cdot \left(j \cdot 27\right)\right) \cdot \sqrt[3]{k}\\ \mathbf{elif}\;t \le 1.8846834206973961 \cdot 10^{35}:\\ \;\;\;\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(t \cdot z\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \end{array}\]

Reproduce

herbie shell --seed 2019198 +o rules:numerics
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1"
  (- (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* (* j 27.0) k)))