Average Error: 5.4 → 4.5
Time: 7.7s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -6.08335225107627983 \cdot 10^{-33}:\\ \;\;\;\;t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(\sqrt[3]{\left(j \cdot 27\right) \cdot k} \cdot \sqrt[3]{\left(j \cdot 27\right) \cdot k}\right) \cdot \sqrt[3]{\left(j \cdot 27\right) \cdot k}\right)\right)\\ \mathbf{elif}\;t \le 2.11917748355629525 \cdot 10^{-168}:\\ \;\;\;\;t \cdot \left(0 - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(\sqrt[3]{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4} \cdot \sqrt[3]{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4}\right)\right) \cdot \sqrt[3]{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4} + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)\\ \end{array}\]
\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}\;t \le -6.08335225107627983 \cdot 10^{-33}:\\
\;\;\;\;t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(\sqrt[3]{\left(j \cdot 27\right) \cdot k} \cdot \sqrt[3]{\left(j \cdot 27\right) \cdot k}\right) \cdot \sqrt[3]{\left(j \cdot 27\right) \cdot k}\right)\right)\\

\mathbf{elif}\;t \le 2.11917748355629525 \cdot 10^{-168}:\\
\;\;\;\;t \cdot \left(0 - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\right)\right)\right)\\

\mathbf{else}:\\
\;\;\;\;\left(t \cdot \left(\sqrt[3]{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4} \cdot \sqrt[3]{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4}\right)\right) \cdot \sqrt[3]{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4} + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)\\

\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 ((t <= -6.08335225107628e-33)) {
		VAR = ((t * ((((x * 18.0) * y) * z) - (a * 4.0))) + ((b * c) - (((x * 4.0) * i) + ((cbrt(((j * 27.0) * k)) * cbrt(((j * 27.0) * k))) * cbrt(((j * 27.0) * k))))));
	} else {
		double VAR_1;
		if ((t <= 2.1191774835562953e-168)) {
			VAR_1 = ((t * (0.0 - (a * 4.0))) + ((b * c) - (((x * 4.0) * i) + (j * (27.0 * k)))));
		} else {
			VAR_1 = (((t * (cbrt(((((x * 18.0) * y) * z) - (a * 4.0))) * cbrt(((((x * 18.0) * y) * z) - (a * 4.0))))) * cbrt(((((x * 18.0) * y) * z) - (a * 4.0)))) + ((b * c) - (((x * 4.0) * i) + ((j * 27.0) * k))));
		}
		VAR = VAR_1;
	}
	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 3 regimes

  2. if t < -6.08335225107628e-33

    1. Initial program 2.1

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

    2. Simplified2.1

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

    4. Applied add-cube-cbrt2.3

      \[\leadsto t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \color{blue}{\left(\sqrt[3]{\left(j \cdot 27\right) \cdot k} \cdot \sqrt[3]{\left(j \cdot 27\right) \cdot k}\right) \cdot \sqrt[3]{\left(j \cdot 27\right) \cdot k}}\right)\right)\]

    if -6.08335225107628e-33 < t < 2.1191774835562953e-168

    1. Initial program 8.4

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

    2. Simplified8.4

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

    4. Applied associate-*l*8.4

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

    5. Taylor expanded around 0 6.0

      \[\leadsto t \cdot \left(\color{blue}{0} - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\right)\right)\right)\]

    if 2.1191774835562953e-168 < t

    1. Initial program 3.7

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

    2. Simplified3.7

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

    4. Applied add-cube-cbrt4.1

      \[\leadsto t \cdot \color{blue}{\left(\left(\sqrt[3]{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4} \cdot \sqrt[3]{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4}\right) \cdot \sqrt[3]{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4}\right)} + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)\]

    5. Applied associate-*r*4.1

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

  4. Final simplification4.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -6.08335225107627983 \cdot 10^{-33}:\\ \;\;\;\;t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(\sqrt[3]{\left(j \cdot 27\right) \cdot k} \cdot \sqrt[3]{\left(j \cdot 27\right) \cdot k}\right) \cdot \sqrt[3]{\left(j \cdot 27\right) \cdot k}\right)\right)\\ \mathbf{elif}\;t \le 2.11917748355629525 \cdot 10^{-168}:\\ \;\;\;\;t \cdot \left(0 - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(\sqrt[3]{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4} \cdot \sqrt[3]{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4}\right)\right) \cdot \sqrt[3]{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4} + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020091 
(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)))