Average Error: 5.6 → 2.0
Time: 32.7s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -2.290721253144602 \cdot 10^{-39}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(4.0 \cdot x\right) \cdot i\right) - j \cdot \left(27.0 \cdot k\right)\\ \mathbf{elif}\;t \le 22289.977042498147:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(\left(t \cdot z\right) \cdot y\right) \cdot \left(x \cdot 18.0\right) - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(4.0 \cdot x\right) \cdot i\right) - \sqrt[3]{\left(j \cdot 27.0\right) \cdot k} \cdot \left(\sqrt[3]{\left(j \cdot 27.0\right) \cdot k} \cdot \sqrt[3]{\left(j \cdot 27.0\right) \cdot k}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(4.0 \cdot x\right) \cdot i\right) - j \cdot \left(27.0 \cdot k\right)\\ \end{array}\]
\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k
↓
\begin{array}{l}
\mathbf{if}\;t \le -2.290721253144602 \cdot 10^{-39}:\\
\;\;\;\;\left(\left(b \cdot c + \left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(4.0 \cdot x\right) \cdot i\right) - j \cdot \left(27.0 \cdot k\right)\\

\mathbf{elif}\;t \le 22289.977042498147:\\
\;\;\;\;\left(\left(b \cdot c + \left(\left(\left(t \cdot z\right) \cdot y\right) \cdot \left(x \cdot 18.0\right) - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(4.0 \cdot x\right) \cdot i\right) - \sqrt[3]{\left(j \cdot 27.0\right) \cdot k} \cdot \left(\sqrt[3]{\left(j \cdot 27.0\right) \cdot k} \cdot \sqrt[3]{\left(j \cdot 27.0\right) \cdot k}\right)\\

\mathbf{else}:\\
\;\;\;\;\left(\left(b \cdot c + \left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(4.0 \cdot x\right) \cdot i\right) - j \cdot \left(27.0 \cdot k\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 r4389571 = x;
        double r4389572 = 18.0;
        double r4389573 = r4389571 * r4389572;
        double r4389574 = y;
        double r4389575 = r4389573 * r4389574;
        double r4389576 = z;
        double r4389577 = r4389575 * r4389576;
        double r4389578 = t;
        double r4389579 = r4389577 * r4389578;
        double r4389580 = a;
        double r4389581 = 4.0;
        double r4389582 = r4389580 * r4389581;
        double r4389583 = r4389582 * r4389578;
        double r4389584 = r4389579 - r4389583;
        double r4389585 = b;
        double r4389586 = c;
        double r4389587 = r4389585 * r4389586;
        double r4389588 = r4389584 + r4389587;
        double r4389589 = r4389571 * r4389581;
        double r4389590 = i;
        double r4389591 = r4389589 * r4389590;
        double r4389592 = r4389588 - r4389591;
        double r4389593 = j;
        double r4389594 = 27.0;
        double r4389595 = r4389593 * r4389594;
        double r4389596 = k;
        double r4389597 = r4389595 * r4389596;
        double r4389598 = r4389592 - r4389597;
        return r4389598;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r4389599 = t;
        double r4389600 = -2.290721253144602e-39;
        bool r4389601 = r4389599 <= r4389600;
        double r4389602 = b;
        double r4389603 = c;
        double r4389604 = r4389602 * r4389603;
        double r4389605 = x;
        double r4389606 = 18.0;
        double r4389607 = r4389605 * r4389606;
        double r4389608 = y;
        double r4389609 = r4389607 * r4389608;
        double r4389610 = z;
        double r4389611 = r4389609 * r4389610;
        double r4389612 = r4389611 * r4389599;
        double r4389613 = a;
        double r4389614 = 4.0;
        double r4389615 = r4389613 * r4389614;
        double r4389616 = r4389615 * r4389599;
        double r4389617 = r4389612 - r4389616;
        double r4389618 = r4389604 + r4389617;
        double r4389619 = r4389614 * r4389605;
        double r4389620 = i;
        double r4389621 = r4389619 * r4389620;
        double r4389622 = r4389618 - r4389621;
        double r4389623 = j;
        double r4389624 = 27.0;
        double r4389625 = k;
        double r4389626 = r4389624 * r4389625;
        double r4389627 = r4389623 * r4389626;
        double r4389628 = r4389622 - r4389627;
        double r4389629 = 22289.977042498147;
        bool r4389630 = r4389599 <= r4389629;
        double r4389631 = r4389599 * r4389610;
        double r4389632 = r4389631 * r4389608;
        double r4389633 = r4389632 * r4389607;
        double r4389634 = r4389633 - r4389616;
        double r4389635 = r4389604 + r4389634;
        double r4389636 = r4389635 - r4389621;
        double r4389637 = r4389623 * r4389624;
        double r4389638 = r4389637 * r4389625;
        double r4389639 = cbrt(r4389638);
        double r4389640 = r4389639 * r4389639;
        double r4389641 = r4389639 * r4389640;
        double r4389642 = r4389636 - r4389641;
        double r4389643 = r4389630 ? r4389642 : r4389628;
        double r4389644 = r4389601 ? r4389628 : r4389643;
        return r4389644;
}

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 2 regimes

  2. if t < -2.290721253144602e-39 or 22289.977042498147 < t

    1. Initial program 2.0

      \[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
    2. Using strategy rm

    3. Applied associate-*l*2.0

      \[\leadsto \left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \color{blue}{j \cdot \left(27.0 \cdot k\right)}\]

    if -2.290721253144602e-39 < t < 22289.977042498147

    1. Initial program 8.0

      \[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
    2. Using strategy rm

    3. Applied associate-*l*4.4

      \[\leadsto \left(\left(\left(\color{blue}{\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot \left(z \cdot t\right)} - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
    4. Using strategy rm

    5. Applied associate-*l*1.6

      \[\leadsto \left(\left(\left(\color{blue}{\left(x \cdot 18.0\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)} - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
    6. Using strategy rm

    7. Applied add-cube-cbrt1.9

      \[\leadsto \left(\left(\left(\left(x \cdot 18.0\right) \cdot \left(y \cdot \left(z \cdot t\right)\right) - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \color{blue}{\left(\sqrt[3]{\left(j \cdot 27.0\right) \cdot k} \cdot \sqrt[3]{\left(j \cdot 27.0\right) \cdot k}\right) \cdot \sqrt[3]{\left(j \cdot 27.0\right) \cdot k}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification2.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -2.290721253144602 \cdot 10^{-39}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(4.0 \cdot x\right) \cdot i\right) - j \cdot \left(27.0 \cdot k\right)\\ \mathbf{elif}\;t \le 22289.977042498147:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(\left(t \cdot z\right) \cdot y\right) \cdot \left(x \cdot 18.0\right) - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(4.0 \cdot x\right) \cdot i\right) - \sqrt[3]{\left(j \cdot 27.0\right) \cdot k} \cdot \left(\sqrt[3]{\left(j \cdot 27.0\right) \cdot k} \cdot \sqrt[3]{\left(j \cdot 27.0\right) \cdot k}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(4.0 \cdot x\right) \cdot i\right) - j \cdot \left(27.0 \cdot k\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019152 +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)))