Average Error: 5.6 → 3.7
Time: 8.6s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -5.5038978783466573 \cdot 10^{-5}:\\ \;\;\;\;t \cdot \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) \cdot \sqrt[3]{z} - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\right)\right)\right)\\ \mathbf{elif}\;z \le 1.12710979643317163 \cdot 10^{-39}:\\ \;\;\;\;\left(18 \cdot \left(t \cdot \left(x \cdot \left(z \cdot y\right)\right)\right) + t \cdot \left(-a \cdot 4\right)\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot \sqrt{z}\right) \cdot \sqrt{z} - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)\\ \end{array}\]
\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}\;z \le -5.5038978783466573 \cdot 10^{-5}:\\
\;\;\;\;t \cdot \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) \cdot \sqrt[3]{z} - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\right)\right)\right)\\

\mathbf{elif}\;z \le 1.12710979643317163 \cdot 10^{-39}:\\
\;\;\;\;\left(18 \cdot \left(t \cdot \left(x \cdot \left(z \cdot y\right)\right)\right) + t \cdot \left(-a \cdot 4\right)\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\right)\right)\right)\\

\mathbf{else}:\\
\;\;\;\;t \cdot \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot \sqrt{z}\right) \cdot \sqrt{z} - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\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 k) {
        double r98455 = x;
        double r98456 = 18.0;
        double r98457 = r98455 * r98456;
        double r98458 = y;
        double r98459 = r98457 * r98458;
        double r98460 = z;
        double r98461 = r98459 * r98460;
        double r98462 = t;
        double r98463 = r98461 * r98462;
        double r98464 = a;
        double r98465 = 4.0;
        double r98466 = r98464 * r98465;
        double r98467 = r98466 * r98462;
        double r98468 = r98463 - r98467;
        double r98469 = b;
        double r98470 = c;
        double r98471 = r98469 * r98470;
        double r98472 = r98468 + r98471;
        double r98473 = r98455 * r98465;
        double r98474 = i;
        double r98475 = r98473 * r98474;
        double r98476 = r98472 - r98475;
        double r98477 = j;
        double r98478 = 27.0;
        double r98479 = r98477 * r98478;
        double r98480 = k;
        double r98481 = r98479 * r98480;
        double r98482 = r98476 - r98481;
        return r98482;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r98483 = z;
        double r98484 = -5.503897878346657e-05;
        bool r98485 = r98483 <= r98484;
        double r98486 = t;
        double r98487 = x;
        double r98488 = 18.0;
        double r98489 = r98487 * r98488;
        double r98490 = y;
        double r98491 = r98489 * r98490;
        double r98492 = cbrt(r98483);
        double r98493 = r98492 * r98492;
        double r98494 = r98491 * r98493;
        double r98495 = r98494 * r98492;
        double r98496 = a;
        double r98497 = 4.0;
        double r98498 = r98496 * r98497;
        double r98499 = r98495 - r98498;
        double r98500 = r98486 * r98499;
        double r98501 = b;
        double r98502 = c;
        double r98503 = r98501 * r98502;
        double r98504 = r98487 * r98497;
        double r98505 = i;
        double r98506 = r98504 * r98505;
        double r98507 = j;
        double r98508 = 27.0;
        double r98509 = k;
        double r98510 = r98508 * r98509;
        double r98511 = r98507 * r98510;
        double r98512 = r98506 + r98511;
        double r98513 = r98503 - r98512;
        double r98514 = r98500 + r98513;
        double r98515 = 1.1271097964331716e-39;
        bool r98516 = r98483 <= r98515;
        double r98517 = r98483 * r98490;
        double r98518 = r98487 * r98517;
        double r98519 = r98486 * r98518;
        double r98520 = r98488 * r98519;
        double r98521 = -r98498;
        double r98522 = r98486 * r98521;
        double r98523 = r98520 + r98522;
        double r98524 = r98523 + r98513;
        double r98525 = sqrt(r98483);
        double r98526 = r98491 * r98525;
        double r98527 = r98526 * r98525;
        double r98528 = r98527 - r98498;
        double r98529 = r98486 * r98528;
        double r98530 = r98507 * r98508;
        double r98531 = r98530 * r98509;
        double r98532 = r98506 + r98531;
        double r98533 = r98503 - r98532;
        double r98534 = r98529 + r98533;
        double r98535 = r98516 ? r98524 : r98534;
        double r98536 = r98485 ? r98514 : r98535;
        return r98536;
}

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 z < -5.503897878346657e-05

    1. Initial program 6.0

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

    2. Simplified6.0

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

    4. Applied associate-*l*6.0

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

    6. Applied add-cube-cbrt6.2

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

    7. Applied associate-*r*6.2

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

    if -5.503897878346657e-05 < z < 1.1271097964331716e-39

    1. Initial program 5.0

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

    2. Simplified5.0

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

    4. Applied associate-*l*4.9

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

    6. Applied add-cube-cbrt4.9

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

    7. Applied associate-*r*4.9

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

    9. Applied sub-neg4.9

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

    10. Applied distribute-lft-in4.9

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

    11. Simplified1.2

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

    if 1.1271097964331716e-39 < z

    1. Initial program 6.5

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

    2. Simplified6.5

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

    4. Applied add-sqr-sqrt6.5

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

    5. Applied associate-*r*6.5

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

  4. Final simplification3.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -5.5038978783466573 \cdot 10^{-5}:\\ \;\;\;\;t \cdot \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) \cdot \sqrt[3]{z} - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\right)\right)\right)\\ \mathbf{elif}\;z \le 1.12710979643317163 \cdot 10^{-39}:\\ \;\;\;\;\left(18 \cdot \left(t \cdot \left(x \cdot \left(z \cdot y\right)\right)\right) + t \cdot \left(-a \cdot 4\right)\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot \sqrt{z}\right) \cdot \sqrt{z} - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020046 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1"
  :precision binary64
  (- (- (+ (- (* (* (* (* x 18) y) z) t) (* (* a 4) t)) (* b c)) (* (* x 4) i)) (* (* j 27) k)))