Average Error: 5.7 → 1.7
Time: 4.8s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -24694289992.637722 \lor \neg \left(z \le 9.08093554736774664 \cdot 10^{-57}\right):\\ \;\;\;\;\left(\left(\left(\left(z \cdot 18\right) \cdot \left(\left(x \cdot y\right) \cdot t\right) - a \cdot \left(4 \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x \cdot \left(\left(\left(18 \cdot y\right) \cdot z\right) \cdot t\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \end{array}\]
\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 -24694289992.637722 \lor \neg \left(z \le 9.08093554736774664 \cdot 10^{-57}\right):\\
\;\;\;\;\left(\left(\left(\left(z \cdot 18\right) \cdot \left(\left(x \cdot y\right) \cdot t\right) - a \cdot \left(4 \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\\

\mathbf{else}:\\
\;\;\;\;\left(\left(\left(x \cdot \left(\left(\left(18 \cdot y\right) \cdot z\right) \cdot t\right) - \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\\

\end{array}
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return ((((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k));
}
↓
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double VAR;
	if (((z <= -24694289992.637722) || !(z <= 9.080935547367747e-57))) {
		VAR = ((((((z * 18.0) * ((x * y) * t)) - (a * (4.0 * t))) + (b * c)) - ((x * 4.0) * i)) - (j * (27.0 * k)));
	} else {
		VAR = (((((x * (((18.0 * y) * z) * t)) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k));
	}
	return VAR;
}

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 < -24694289992.637722 or 9.080935547367747e-57 < z

    1. Initial program 7.0

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

    3. Applied *-commutative7.0

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

    4. Applied associate-*l*2.2

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

    6. Applied associate-*l*2.1

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

    8. Applied *-commutative2.1

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

    9. Applied associate-*l*2.1

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

    10. Applied associate-*l*2.1

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

    11. Applied associate-*r*2.3

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

    13. Applied associate-*l*2.4

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

    if -24694289992.637722 < z < 9.080935547367747e-57

    1. Initial program 4.6

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

    3. Applied associate-*l*4.7

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

    4. Applied associate-*l*1.4

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

    5. Applied associate-*l*1.2

      \[\leadsto \left(\left(\left(\color{blue}{x \cdot \left(\left(\left(18 \cdot y\right) \cdot z\right) \cdot t\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -24694289992.637722 \lor \neg \left(z \le 9.08093554736774664 \cdot 10^{-57}\right):\\ \;\;\;\;\left(\left(\left(\left(z \cdot 18\right) \cdot \left(\left(x \cdot y\right) \cdot t\right) - a \cdot \left(4 \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x \cdot \left(\left(\left(18 \cdot y\right) \cdot z\right) \cdot t\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \end{array}\]

Reproduce

herbie shell --seed 2020078 
(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)))