Average Error: 5.2 → 5.2
Time: 39.7s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -5.667148220609564 \cdot 10^{-100}:\\ \;\;\;\;\left(\left(b \cdot c + \left(t \cdot \left(\left(18.0 \cdot \left(x \cdot y\right)\right) \cdot z\right) - t \cdot \left(a \cdot 4.0\right)\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - k \cdot \left(j \cdot 27.0\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + \left(18.0 \cdot \left(\left(x \cdot t\right) \cdot \left(y \cdot z\right)\right) - t \cdot \left(a \cdot 4.0\right)\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - k \cdot \left(j \cdot 27.0\right)\\ \end{array}\]
\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}\;z \le -5.667148220609564 \cdot 10^{-100}:\\
\;\;\;\;\left(\left(b \cdot c + \left(t \cdot \left(\left(18.0 \cdot \left(x \cdot y\right)\right) \cdot z\right) - t \cdot \left(a \cdot 4.0\right)\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - k \cdot \left(j \cdot 27.0\right)\\

\mathbf{else}:\\
\;\;\;\;\left(\left(b \cdot c + \left(18.0 \cdot \left(\left(x \cdot t\right) \cdot \left(y \cdot z\right)\right) - t \cdot \left(a \cdot 4.0\right)\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - k \cdot \left(j \cdot 27.0\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 r6966571 = x;
        double r6966572 = 18.0;
        double r6966573 = r6966571 * r6966572;
        double r6966574 = y;
        double r6966575 = r6966573 * r6966574;
        double r6966576 = z;
        double r6966577 = r6966575 * r6966576;
        double r6966578 = t;
        double r6966579 = r6966577 * r6966578;
        double r6966580 = a;
        double r6966581 = 4.0;
        double r6966582 = r6966580 * r6966581;
        double r6966583 = r6966582 * r6966578;
        double r6966584 = r6966579 - r6966583;
        double r6966585 = b;
        double r6966586 = c;
        double r6966587 = r6966585 * r6966586;
        double r6966588 = r6966584 + r6966587;
        double r6966589 = r6966571 * r6966581;
        double r6966590 = i;
        double r6966591 = r6966589 * r6966590;
        double r6966592 = r6966588 - r6966591;
        double r6966593 = j;
        double r6966594 = 27.0;
        double r6966595 = r6966593 * r6966594;
        double r6966596 = k;
        double r6966597 = r6966595 * r6966596;
        double r6966598 = r6966592 - r6966597;
        return r6966598;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r6966599 = z;
        double r6966600 = -5.667148220609564e-100;
        bool r6966601 = r6966599 <= r6966600;
        double r6966602 = b;
        double r6966603 = c;
        double r6966604 = r6966602 * r6966603;
        double r6966605 = t;
        double r6966606 = 18.0;
        double r6966607 = x;
        double r6966608 = y;
        double r6966609 = r6966607 * r6966608;
        double r6966610 = r6966606 * r6966609;
        double r6966611 = r6966610 * r6966599;
        double r6966612 = r6966605 * r6966611;
        double r6966613 = a;
        double r6966614 = 4.0;
        double r6966615 = r6966613 * r6966614;
        double r6966616 = r6966605 * r6966615;
        double r6966617 = r6966612 - r6966616;
        double r6966618 = r6966604 + r6966617;
        double r6966619 = r6966607 * r6966614;
        double r6966620 = i;
        double r6966621 = r6966619 * r6966620;
        double r6966622 = r6966618 - r6966621;
        double r6966623 = k;
        double r6966624 = j;
        double r6966625 = 27.0;
        double r6966626 = r6966624 * r6966625;
        double r6966627 = r6966623 * r6966626;
        double r6966628 = r6966622 - r6966627;
        double r6966629 = r6966607 * r6966605;
        double r6966630 = r6966608 * r6966599;
        double r6966631 = r6966629 * r6966630;
        double r6966632 = r6966606 * r6966631;
        double r6966633 = r6966632 - r6966616;
        double r6966634 = r6966604 + r6966633;
        double r6966635 = r6966634 - r6966621;
        double r6966636 = r6966635 - r6966627;
        double r6966637 = r6966601 ? r6966628 : r6966636;
        return r6966637;
}

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 z < -5.667148220609564e-100

    1. Initial program 5.5

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

    2. Taylor expanded around 0 5.4

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

    if -5.667148220609564e-100 < z

    1. Initial program 5.2

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

    2. Taylor expanded around inf 4.4

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

    4. Applied associate-*r*5.0

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

  4. Final simplification5.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -5.667148220609564 \cdot 10^{-100}:\\ \;\;\;\;\left(\left(b \cdot c + \left(t \cdot \left(\left(18.0 \cdot \left(x \cdot y\right)\right) \cdot z\right) - t \cdot \left(a \cdot 4.0\right)\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - k \cdot \left(j \cdot 27.0\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + \left(18.0 \cdot \left(\left(x \cdot t\right) \cdot \left(y \cdot z\right)\right) - t \cdot \left(a \cdot 4.0\right)\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - k \cdot \left(j \cdot 27.0\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019146 
(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)))