Average Error: 5.4 → 5.2
Time: 48.2s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -7.711355120201642 \cdot 10^{-286}:\\ \;\;\;\;\left(\left(c \cdot b - k \cdot \left(j \cdot 27.0\right)\right) - \left(i \cdot x\right) \cdot 4.0\right) + t \cdot \left(\left(y \cdot \left(z \cdot 18.0\right)\right) \cdot x - a \cdot 4.0\right)\\ \mathbf{elif}\;t \le 1.95010356846324 \cdot 10^{-100}:\\ \;\;\;\;\left(\left(-4.0\right) \cdot a\right) \cdot t + \left(\left(c \cdot b - k \cdot \left(j \cdot 27.0\right)\right) - \left(i \cdot x\right) \cdot 4.0\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(c \cdot b - k \cdot \left(j \cdot 27.0\right)\right) - \left(i \cdot x\right) \cdot 4.0\right) + t \cdot \left(\left(y \cdot \left(z \cdot 18.0\right)\right) \cdot x - a \cdot 4.0\right)\\ \end{array}\]
\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}\;t \le -7.711355120201642 \cdot 10^{-286}:\\
\;\;\;\;\left(\left(c \cdot b - k \cdot \left(j \cdot 27.0\right)\right) - \left(i \cdot x\right) \cdot 4.0\right) + t \cdot \left(\left(y \cdot \left(z \cdot 18.0\right)\right) \cdot x - a \cdot 4.0\right)\\

\mathbf{elif}\;t \le 1.95010356846324 \cdot 10^{-100}:\\
\;\;\;\;\left(\left(-4.0\right) \cdot a\right) \cdot t + \left(\left(c \cdot b - k \cdot \left(j \cdot 27.0\right)\right) - \left(i \cdot x\right) \cdot 4.0\right)\\

\mathbf{else}:\\
\;\;\;\;\left(\left(c \cdot b - k \cdot \left(j \cdot 27.0\right)\right) - \left(i \cdot x\right) \cdot 4.0\right) + t \cdot \left(\left(y \cdot \left(z \cdot 18.0\right)\right) \cdot x - a \cdot 4.0\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 r5625592 = x;
        double r5625593 = 18.0;
        double r5625594 = r5625592 * r5625593;
        double r5625595 = y;
        double r5625596 = r5625594 * r5625595;
        double r5625597 = z;
        double r5625598 = r5625596 * r5625597;
        double r5625599 = t;
        double r5625600 = r5625598 * r5625599;
        double r5625601 = a;
        double r5625602 = 4.0;
        double r5625603 = r5625601 * r5625602;
        double r5625604 = r5625603 * r5625599;
        double r5625605 = r5625600 - r5625604;
        double r5625606 = b;
        double r5625607 = c;
        double r5625608 = r5625606 * r5625607;
        double r5625609 = r5625605 + r5625608;
        double r5625610 = r5625592 * r5625602;
        double r5625611 = i;
        double r5625612 = r5625610 * r5625611;
        double r5625613 = r5625609 - r5625612;
        double r5625614 = j;
        double r5625615 = 27.0;
        double r5625616 = r5625614 * r5625615;
        double r5625617 = k;
        double r5625618 = r5625616 * r5625617;
        double r5625619 = r5625613 - r5625618;
        return r5625619;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r5625620 = t;
        double r5625621 = -7.711355120201642e-286;
        bool r5625622 = r5625620 <= r5625621;
        double r5625623 = c;
        double r5625624 = b;
        double r5625625 = r5625623 * r5625624;
        double r5625626 = k;
        double r5625627 = j;
        double r5625628 = 27.0;
        double r5625629 = r5625627 * r5625628;
        double r5625630 = r5625626 * r5625629;
        double r5625631 = r5625625 - r5625630;
        double r5625632 = i;
        double r5625633 = x;
        double r5625634 = r5625632 * r5625633;
        double r5625635 = 4.0;
        double r5625636 = r5625634 * r5625635;
        double r5625637 = r5625631 - r5625636;
        double r5625638 = y;
        double r5625639 = z;
        double r5625640 = 18.0;
        double r5625641 = r5625639 * r5625640;
        double r5625642 = r5625638 * r5625641;
        double r5625643 = r5625642 * r5625633;
        double r5625644 = a;
        double r5625645 = r5625644 * r5625635;
        double r5625646 = r5625643 - r5625645;
        double r5625647 = r5625620 * r5625646;
        double r5625648 = r5625637 + r5625647;
        double r5625649 = 1.95010356846324e-100;
        bool r5625650 = r5625620 <= r5625649;
        double r5625651 = -r5625635;
        double r5625652 = r5625651 * r5625644;
        double r5625653 = r5625652 * r5625620;
        double r5625654 = r5625653 + r5625637;
        double r5625655 = r5625650 ? r5625654 : r5625648;
        double r5625656 = r5625622 ? r5625648 : r5625655;
        return r5625656;
}

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 < -7.711355120201642e-286 or 1.95010356846324e-100 < t

    1. Initial program 4.3

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

    2. Simplified4.9

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

    4. Applied *-un-lft-identity4.9

      \[\leadsto \left(\left(c \cdot b - \left(27.0 \cdot j\right) \cdot k\right) - 4.0 \cdot \left(x \cdot i\right)\right) + \left(\left(x \cdot 18.0\right) \cdot \left(y \cdot z\right) - a \cdot 4.0\right) \cdot \color{blue}{\left(1 \cdot t\right)}\]

    5. Applied associate-*r*4.9

      \[\leadsto \left(\left(c \cdot b - \left(27.0 \cdot j\right) \cdot k\right) - 4.0 \cdot \left(x \cdot i\right)\right) + \color{blue}{\left(\left(\left(x \cdot 18.0\right) \cdot \left(y \cdot z\right) - a \cdot 4.0\right) \cdot 1\right) \cdot t}\]

    6. Simplified4.9

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

    8. Applied associate-*l*4.9

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

    if -7.711355120201642e-286 < t < 1.95010356846324e-100

    1. Initial program 8.5

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

    2. Simplified10.2

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

    4. Applied *-un-lft-identity10.2

      \[\leadsto \left(\left(c \cdot b - \left(27.0 \cdot j\right) \cdot k\right) - 4.0 \cdot \left(x \cdot i\right)\right) + \left(\left(x \cdot 18.0\right) \cdot \left(y \cdot z\right) - a \cdot 4.0\right) \cdot \color{blue}{\left(1 \cdot t\right)}\]

    5. Applied associate-*r*10.2

      \[\leadsto \left(\left(c \cdot b - \left(27.0 \cdot j\right) \cdot k\right) - 4.0 \cdot \left(x \cdot i\right)\right) + \color{blue}{\left(\left(\left(x \cdot 18.0\right) \cdot \left(y \cdot z\right) - a \cdot 4.0\right) \cdot 1\right) \cdot t}\]

    6. Simplified10.2

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

    8. Applied associate-*l*10.3

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

    9. Taylor expanded around 0 6.0

      \[\leadsto \left(\left(c \cdot b - \left(27.0 \cdot j\right) \cdot k\right) - 4.0 \cdot \left(x \cdot i\right)\right) + \left(\color{blue}{0} - a \cdot 4.0\right) \cdot t\]
  3. Recombined 2 regimes into one program.

  4. Final simplification5.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -7.711355120201642 \cdot 10^{-286}:\\ \;\;\;\;\left(\left(c \cdot b - k \cdot \left(j \cdot 27.0\right)\right) - \left(i \cdot x\right) \cdot 4.0\right) + t \cdot \left(\left(y \cdot \left(z \cdot 18.0\right)\right) \cdot x - a \cdot 4.0\right)\\ \mathbf{elif}\;t \le 1.95010356846324 \cdot 10^{-100}:\\ \;\;\;\;\left(\left(-4.0\right) \cdot a\right) \cdot t + \left(\left(c \cdot b - k \cdot \left(j \cdot 27.0\right)\right) - \left(i \cdot x\right) \cdot 4.0\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(c \cdot b - k \cdot \left(j \cdot 27.0\right)\right) - \left(i \cdot x\right) \cdot 4.0\right) + t \cdot \left(\left(y \cdot \left(z \cdot 18.0\right)\right) \cdot x - a \cdot 4.0\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019143 
(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)))