Average Error: 5.3 → 2.3
Time: 1.2m
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(\left(t \cdot \left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4.0\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4.0\right) \cdot i \le -5.347124524497702 \cdot 10^{+225}:\\ \;\;\;\;\left(\left(c \cdot b + \left(\left(\left(y \cdot z\right) \cdot t\right) \cdot \left(x \cdot 18.0\right) - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\\ \mathbf{elif}\;\left(\left(t \cdot \left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4.0\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4.0\right) \cdot i \le 1.2291636294681866 \cdot 10^{+296}:\\ \;\;\;\;\left(\left(\left(t \cdot \left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4.0\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot k\right) \cdot 27.0\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(t \cdot z\right) \cdot y\right) \cdot \left(x \cdot 18.0\right) - \left(a \cdot 4.0\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(27.0 \cdot k\right) \cdot j\\ \end{array}\]
\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}\;\left(\left(t \cdot \left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4.0\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4.0\right) \cdot i \le -5.347124524497702 \cdot 10^{+225}:\\
\;\;\;\;\left(\left(c \cdot b + \left(\left(\left(y \cdot z\right) \cdot t\right) \cdot \left(x \cdot 18.0\right) - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\\

\mathbf{elif}\;\left(\left(t \cdot \left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4.0\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4.0\right) \cdot i \le 1.2291636294681866 \cdot 10^{+296}:\\
\;\;\;\;\left(\left(\left(t \cdot \left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4.0\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot k\right) \cdot 27.0\\

\mathbf{else}:\\
\;\;\;\;\left(\left(\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) + c \cdot b\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(27.0 \cdot k\right) \cdot j\\

\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 r16625582 = x;
        double r16625583 = 18.0;
        double r16625584 = r16625582 * r16625583;
        double r16625585 = y;
        double r16625586 = r16625584 * r16625585;
        double r16625587 = z;
        double r16625588 = r16625586 * r16625587;
        double r16625589 = t;
        double r16625590 = r16625588 * r16625589;
        double r16625591 = a;
        double r16625592 = 4.0;
        double r16625593 = r16625591 * r16625592;
        double r16625594 = r16625593 * r16625589;
        double r16625595 = r16625590 - r16625594;
        double r16625596 = b;
        double r16625597 = c;
        double r16625598 = r16625596 * r16625597;
        double r16625599 = r16625595 + r16625598;
        double r16625600 = r16625582 * r16625592;
        double r16625601 = i;
        double r16625602 = r16625600 * r16625601;
        double r16625603 = r16625599 - r16625602;
        double r16625604 = j;
        double r16625605 = 27.0;
        double r16625606 = r16625604 * r16625605;
        double r16625607 = k;
        double r16625608 = r16625606 * r16625607;
        double r16625609 = r16625603 - r16625608;
        return r16625609;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r16625610 = t;
        double r16625611 = x;
        double r16625612 = 18.0;
        double r16625613 = r16625611 * r16625612;
        double r16625614 = y;
        double r16625615 = r16625613 * r16625614;
        double r16625616 = z;
        double r16625617 = r16625615 * r16625616;
        double r16625618 = r16625610 * r16625617;
        double r16625619 = a;
        double r16625620 = 4.0;
        double r16625621 = r16625619 * r16625620;
        double r16625622 = r16625621 * r16625610;
        double r16625623 = r16625618 - r16625622;
        double r16625624 = c;
        double r16625625 = b;
        double r16625626 = r16625624 * r16625625;
        double r16625627 = r16625623 + r16625626;
        double r16625628 = r16625611 * r16625620;
        double r16625629 = i;
        double r16625630 = r16625628 * r16625629;
        double r16625631 = r16625627 - r16625630;
        double r16625632 = -5.347124524497702e+225;
        bool r16625633 = r16625631 <= r16625632;
        double r16625634 = r16625614 * r16625616;
        double r16625635 = r16625634 * r16625610;
        double r16625636 = r16625635 * r16625613;
        double r16625637 = r16625636 - r16625622;
        double r16625638 = r16625626 + r16625637;
        double r16625639 = r16625638 - r16625630;
        double r16625640 = j;
        double r16625641 = 27.0;
        double r16625642 = r16625640 * r16625641;
        double r16625643 = k;
        double r16625644 = r16625642 * r16625643;
        double r16625645 = r16625639 - r16625644;
        double r16625646 = 1.2291636294681866e+296;
        bool r16625647 = r16625631 <= r16625646;
        double r16625648 = r16625640 * r16625643;
        double r16625649 = r16625648 * r16625641;
        double r16625650 = r16625631 - r16625649;
        double r16625651 = r16625610 * r16625616;
        double r16625652 = r16625651 * r16625614;
        double r16625653 = r16625652 * r16625613;
        double r16625654 = r16625653 - r16625622;
        double r16625655 = r16625654 + r16625626;
        double r16625656 = r16625655 - r16625630;
        double r16625657 = r16625641 * r16625643;
        double r16625658 = r16625657 * r16625640;
        double r16625659 = r16625656 - r16625658;
        double r16625660 = r16625647 ? r16625650 : r16625659;
        double r16625661 = r16625633 ? r16625645 : r16625660;
        return r16625661;
}

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 (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) < -5.347124524497702e+225

    1. Initial program 15.6

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

    3. Applied associate-*l*12.0

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

    5. Applied associate-*l*8.6

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

    6. Taylor expanded around -inf 10.4

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

    if -5.347124524497702e+225 < (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) < 1.2291636294681866e+296

    1. Initial program 0.4

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

    2. Taylor expanded around 0 0.3

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

    if 1.2291636294681866e+296 < (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i))

    1. Initial program 44.0

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

    3. Applied associate-*l*28.2

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

    5. Applied associate-*l*8.5

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

    7. Applied associate-*l*8.4

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

  4. Final simplification2.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(t \cdot \left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4.0\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4.0\right) \cdot i \le -5.347124524497702 \cdot 10^{+225}:\\ \;\;\;\;\left(\left(c \cdot b + \left(\left(\left(y \cdot z\right) \cdot t\right) \cdot \left(x \cdot 18.0\right) - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\\ \mathbf{elif}\;\left(\left(t \cdot \left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4.0\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4.0\right) \cdot i \le 1.2291636294681866 \cdot 10^{+296}:\\ \;\;\;\;\left(\left(\left(t \cdot \left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4.0\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot k\right) \cdot 27.0\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(t \cdot z\right) \cdot y\right) \cdot \left(x \cdot 18.0\right) - \left(a \cdot 4.0\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(27.0 \cdot k\right) \cdot j\\ \end{array}\]

Reproduce

herbie shell --seed 2019107 +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)))