Average Error: 5.5 → 2.1
Time: 9.6s
Precision: binary64
\[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -4.0566430257111837 \cdot 10^{-47}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right) + \left(b \cdot c - \left(\left(\sqrt[3]{j} \cdot \sqrt[3]{j}\right) \cdot \left(27 \cdot \left(\sqrt[3]{j} \cdot k\right)\right) + 4 \cdot \left(t \cdot a + x \cdot i\right)\right)\right)\\ \mathbf{elif}\;x \le 1.8041530042857012 \cdot 10^{-237}:\\ \;\;\;\;\left(\left(b \cdot c + \left(t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right) - t \cdot \left(4 \cdot a\right)\right)\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;x \le 4.16706736102893008 \cdot 10^{-133}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(x \cdot \left(18 \cdot y\right)\right) + \left(b \cdot c - \left(4 \cdot \left(t \cdot a + x \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\right)\\ \mathbf{elif}\;x \le 9.1728216570326181 \cdot 10^{-10}:\\ \;\;\;\;\left(\left(b \cdot c + \left(t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right) - t \cdot \left(4 \cdot a\right)\right)\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - \left(4 \cdot \left(t \cdot a + x \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\right) + \left(y \cdot \left(z \cdot t\right)\right) \cdot \left(x \cdot 18\right)\\ \end{array}\]
\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}\;x \le -4.0566430257111837 \cdot 10^{-47}:\\
\;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right) + \left(b \cdot c - \left(\left(\sqrt[3]{j} \cdot \sqrt[3]{j}\right) \cdot \left(27 \cdot \left(\sqrt[3]{j} \cdot k\right)\right) + 4 \cdot \left(t \cdot a + x \cdot i\right)\right)\right)\\

\mathbf{elif}\;x \le 1.8041530042857012 \cdot 10^{-237}:\\
\;\;\;\;\left(\left(b \cdot c + \left(t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right) - t \cdot \left(4 \cdot a\right)\right)\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\

\mathbf{elif}\;x \le 4.16706736102893008 \cdot 10^{-133}:\\
\;\;\;\;\left(z \cdot t\right) \cdot \left(x \cdot \left(18 \cdot y\right)\right) + \left(b \cdot c - \left(4 \cdot \left(t \cdot a + x \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\right)\\

\mathbf{elif}\;x \le 9.1728216570326181 \cdot 10^{-10}:\\
\;\;\;\;\left(\left(b \cdot c + \left(t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right) - t \cdot \left(4 \cdot a\right)\right)\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\

\mathbf{else}:\\
\;\;\;\;\left(b \cdot c - \left(4 \cdot \left(t \cdot a + x \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\right) + \left(y \cdot \left(z \cdot t\right)\right) \cdot \left(x \cdot 18\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 ((double) (((double) (((double) (((double) (((double) (((double) (((double) (((double) (x * 18.0)) * y)) * z)) * t)) - ((double) (((double) (a * 4.0)) * t)))) + ((double) (b * c)))) - ((double) (((double) (x * 4.0)) * i)))) - ((double) (((double) (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 ((x <= -4.0566430257111837e-47)) {
		VAR = ((double) (((double) (x * ((double) (18.0 * ((double) (y * ((double) (z * t)))))))) + ((double) (((double) (b * c)) - ((double) (((double) (((double) (((double) cbrt(j)) * ((double) cbrt(j)))) * ((double) (27.0 * ((double) (((double) cbrt(j)) * k)))))) + ((double) (4.0 * ((double) (((double) (t * a)) + ((double) (x * i))))))))))));
	} else {
		double VAR_1;
		if ((x <= 1.8041530042857012e-237)) {
			VAR_1 = ((double) (((double) (((double) (((double) (b * c)) + ((double) (((double) (t * ((double) (z * ((double) (y * ((double) (x * 18.0)))))))) - ((double) (t * ((double) (4.0 * a)))))))) - ((double) (i * ((double) (x * 4.0)))))) - ((double) (k * ((double) (j * 27.0))))));
		} else {
			double VAR_2;
			if ((x <= 4.16706736102893e-133)) {
				VAR_2 = ((double) (((double) (((double) (z * t)) * ((double) (x * ((double) (18.0 * y)))))) + ((double) (((double) (b * c)) - ((double) (((double) (4.0 * ((double) (((double) (t * a)) + ((double) (x * i)))))) + ((double) (j * ((double) (27.0 * k))))))))));
			} else {
				double VAR_3;
				if ((x <= 9.172821657032618e-10)) {
					VAR_3 = ((double) (((double) (((double) (((double) (b * c)) + ((double) (((double) (t * ((double) (z * ((double) (y * ((double) (x * 18.0)))))))) - ((double) (t * ((double) (4.0 * a)))))))) - ((double) (i * ((double) (x * 4.0)))))) - ((double) (k * ((double) (j * 27.0))))));
				} else {
					VAR_3 = ((double) (((double) (((double) (b * c)) - ((double) (((double) (4.0 * ((double) (((double) (t * a)) + ((double) (x * i)))))) + ((double) (j * ((double) (27.0 * k)))))))) + ((double) (((double) (y * ((double) (z * t)))) * ((double) (x * 18.0))))));
				}
				VAR_2 = VAR_3;
			}
			VAR_1 = VAR_2;
		}
		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

Target

Original5.5
Target1.4
Herbie2.1
\[\begin{array}{l} \mathbf{if}\;t \lt -1.6210815397541398 \cdot 10^{-69}:\\ \;\;\;\;\left(\left(18 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - \left(a \cdot t + i \cdot x\right) \cdot 4\right) - \left(\left(k \cdot j\right) \cdot 27 - c \cdot b\right)\\ \mathbf{elif}\;t \lt 165.680279438052224:\\ \;\;\;\;\left(\left(18 \cdot y\right) \cdot \left(x \cdot \left(z \cdot t\right)\right) - \left(a \cdot t + i \cdot x\right) \cdot 4\right) + \left(c \cdot b - 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(18 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - \left(a \cdot t + i \cdot x\right) \cdot 4\right) - \left(\left(k \cdot j\right) \cdot 27 - c \cdot b\right)\\ \end{array}\]

Derivation

  1. Split input into 4 regimes

  2. if x < -4.0566430257111837e-47

    1. Initial program 9.5

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

    2. Simplified2.2

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

    4. Applied add-cube-cbrt2.3

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

    5. Applied associate-*l*2.3

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

    6. Simplified2.2

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

    if -4.0566430257111837e-47 < x < 1.8041530042857012e-237 or 4.16706736102893008e-133 < x < 9.1728216570326181e-10

    1. Initial program 1.6

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

    if 1.8041530042857012e-237 < x < 4.16706736102893008e-133

    1. Initial program 1.8

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

    2. Simplified8.1

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

    4. Applied associate-*r*8.3

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

    6. Applied associate-*r*4.5

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

    if 9.1728216570326181e-10 < x

    1. Initial program 12.3

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

    2. Simplified1.8

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

    4. Applied associate-*r*2.0

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

  4. Final simplification2.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -4.0566430257111837 \cdot 10^{-47}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right) + \left(b \cdot c - \left(\left(\sqrt[3]{j} \cdot \sqrt[3]{j}\right) \cdot \left(27 \cdot \left(\sqrt[3]{j} \cdot k\right)\right) + 4 \cdot \left(t \cdot a + x \cdot i\right)\right)\right)\\ \mathbf{elif}\;x \le 1.8041530042857012 \cdot 10^{-237}:\\ \;\;\;\;\left(\left(b \cdot c + \left(t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right) - t \cdot \left(4 \cdot a\right)\right)\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;x \le 4.16706736102893008 \cdot 10^{-133}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(x \cdot \left(18 \cdot y\right)\right) + \left(b \cdot c - \left(4 \cdot \left(t \cdot a + x \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\right)\\ \mathbf{elif}\;x \le 9.1728216570326181 \cdot 10^{-10}:\\ \;\;\;\;\left(\left(b \cdot c + \left(t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right) - t \cdot \left(4 \cdot a\right)\right)\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - \left(4 \cdot \left(t \cdot a + x \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\right) + \left(y \cdot \left(z \cdot t\right)\right) \cdot \left(x \cdot 18\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020184 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64

  :herbie-target
  (if (< t -1.6210815397541398e-69) (- (- (* (* 18.0 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4.0)) (- (* (* k j) 27.0) (* c b))) (if (< t 165.68027943805222) (+ (- (* (* 18.0 y) (* x (* z t))) (* (+ (* a t) (* i x)) 4.0)) (- (* c b) (* 27.0 (* k j)))) (- (- (* (* 18.0 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4.0)) (- (* (* k j) 27.0) (* c b)))))

  (- (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* (* j 27.0) k)))