Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, J

Average Error: 20.5 → 8.0

Time: 8.8s

Precision: 64

Math

\[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\]

↓

\[\begin{array}{l} \mathbf{if}\;\left(x \cdot 9\right) \cdot y \le -5.2031824371176434 \cdot 10^{281}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\right) - 4 \cdot \left(\left(a \cdot \left(\sqrt[3]{t} \cdot \left(\sqrt[3]{\sqrt[3]{t}} \cdot \sqrt[3]{\sqrt[3]{t}}\right)\right)\right) \cdot \left(\sqrt[3]{\sqrt[3]{t}} \cdot \frac{\sqrt[3]{t}}{c}\right)\right)\\ \mathbf{elif}\;\left(x \cdot 9\right) \cdot y \le -4.44461852404034349 \cdot 10^{-84}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;\left(x \cdot 9\right) \cdot y \le 6.32049670678102 \cdot 10^{-96}:\\ \;\;\;\;\left(\frac{\frac{b}{c}}{z} + 9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\right) - 4 \cdot \left(\left(a \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right) \cdot \frac{\sqrt[3]{t}}{c}\right)\\ \mathbf{elif}\;\left(x \cdot 9\right) \cdot y \le 1.2680964165413392 \cdot 10^{182}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x}{\frac{c}{y} \cdot z}\right) - 4 \cdot \left(\left(a \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right) \cdot \frac{\sqrt[3]{t}}{c}\right)\\ \end{array}\]

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((double) (((double) (((double) (((double) (((double) (x * 9.0)) * y)) - ((double) (((double) (((double) (z * 4.0)) * t)) * a)))) + b)) / ((double) (z * c))));
}

↓

double code(double x, double y, double z, double t, double a, double b, double c) {
	double VAR;
	if ((((double) (((double) (x * 9.0)) * y)) <= -5.2031824371176434e+281)) {
		VAR = ((double) (((double) (((double) (b / ((double) (z * c)))) + ((double) (9.0 * ((double) (((double) (y / c)) * ((double) (x / z)))))))) - ((double) (4.0 * ((double) (((double) (a * ((double) (((double) cbrt(t)) * ((double) (((double) cbrt(((double) cbrt(t)))) * ((double) cbrt(((double) cbrt(t)))))))))) * ((double) (((double) cbrt(((double) cbrt(t)))) * ((double) (((double) cbrt(t)) / c))))))))));
	} else {
		double VAR_1;
		if ((((double) (((double) (x * 9.0)) * y)) <= -4.4446185240403435e-84)) {
			VAR_1 = ((double) (((double) (((double) (b / ((double) (z * c)))) + ((double) (9.0 * ((double) (((double) (x * y)) / ((double) (z * c)))))))) - ((double) (4.0 * ((double) (a / ((double) (c / t))))))));
		} else {
			double VAR_2;
			if ((((double) (((double) (x * 9.0)) * y)) <= 6.32049670678102e-96)) {
				VAR_2 = ((double) (((double) (((double) (((double) (b / c)) / z)) + ((double) (9.0 * ((double) (((double) (y / c)) * ((double) (x / z)))))))) - ((double) (4.0 * ((double) (((double) (a * ((double) (((double) cbrt(t)) * ((double) cbrt(t)))))) * ((double) (((double) cbrt(t)) / c))))))));
			} else {
				double VAR_3;
				if ((((double) (((double) (x * 9.0)) * y)) <= 1.2680964165413392e+182)) {
					VAR_3 = ((double) (((double) (((double) (b / ((double) (z * c)))) + ((double) (9.0 * ((double) (((double) (x * y)) / ((double) (z * c)))))))) - ((double) (4.0 * ((double) (a / ((double) (c / t))))))));
				} else {
					VAR_3 = ((double) (((double) (((double) (b / ((double) (z * c)))) + ((double) (9.0 * ((double) (x / ((double) (((double) (c / y)) * z)))))))) - ((double) (4.0 * ((double) (((double) (a * ((double) (((double) cbrt(t)) * ((double) cbrt(t)))))) * ((double) (((double) cbrt(t)) / c))))))));
				}
				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

Target

Original	20.5
Target	14.4
Herbie	8.0

\[\begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt -1.10015674080410512 \cdot 10^{-171}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt -0.0:\\ \;\;\;\;\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt 1.17088779117474882 \cdot 10^{-53}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt 2.8768236795461372 \cdot 10^{130}:\\ \;\;\;\;\left(\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt 1.3838515042456319 \cdot 10^{158}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot \left(\frac{y}{c \cdot z} \cdot x\right) + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \end{array}\]

Derivation

1. Split input into 4 regimes

2. if (* (* x 9.0) y) < -5.2031824371176434e+281

   1. Initial program 55.3

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\]

   2. Taylor expanded around 0 52.4

      \[\leadsto \color{blue}{\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \frac{a \cdot t}{c}}\]
   3. Using strategy rm

   4. Applied *-un-lft-identity 52.4

      \[\leadsto \left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \frac{a \cdot t}{\color{blue}{1 \cdot c}}\]

   5. Applied add-cube-cbrt 52.4

      \[\leadsto \left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \frac{a \cdot \color{blue}{\left(\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}\right)}}{1 \cdot c}\]

   6. Applied associate-*r* 52.4

      \[\leadsto \left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \frac{\color{blue}{\left(a \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right) \cdot \sqrt[3]{t}}}{1 \cdot c}\]

   7. Applied times-frac 52.2

      \[\leadsto \left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \color{blue}{\left(\frac{a \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)}{1} \cdot \frac{\sqrt[3]{t}}{c}\right)}\]

   8. Simplified 52.2

      \[\leadsto \left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \left(\color{blue}{\left(a \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right)} \cdot \frac{\sqrt[3]{t}}{c}\right)\]
   9. Using strategy rm

   10. Applied *-commutative 52.2

       \[\leadsto \left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{\color{blue}{c \cdot z}}\right) - 4 \cdot \left(\left(a \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right) \cdot \frac{\sqrt[3]{t}}{c}\right)\]

   11. Applied *-commutative 52.2

       \[\leadsto \left(\frac{b}{z \cdot c} + 9 \cdot \frac{\color{blue}{y \cdot x}}{c \cdot z}\right) - 4 \cdot \left(\left(a \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right) \cdot \frac{\sqrt[3]{t}}{c}\right)\]

   12. Applied times-frac 11.9

       \[\leadsto \left(\frac{b}{z \cdot c} + 9 \cdot \color{blue}{\left(\frac{y}{c} \cdot \frac{x}{z}\right)}\right) - 4 \cdot \left(\left(a \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right) \cdot \frac{\sqrt[3]{t}}{c}\right)\]
   13. Using strategy rm

   14. Applied add-cube-cbrt 11.9

       \[\leadsto \left(\frac{b}{z \cdot c} + 9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\right) - 4 \cdot \left(\left(a \cdot \left(\sqrt[3]{t} \cdot \color{blue}{\left(\left(\sqrt[3]{\sqrt[3]{t}} \cdot \sqrt[3]{\sqrt[3]{t}}\right) \cdot \sqrt[3]{\sqrt[3]{t}}\right)}\right)\right) \cdot \frac{\sqrt[3]{t}}{c}\right)\]

   15. Applied associate-*r* 11.9

       \[\leadsto \left(\frac{b}{z \cdot c} + 9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\right) - 4 \cdot \left(\left(a \cdot \color{blue}{\left(\left(\sqrt[3]{t} \cdot \left(\sqrt[3]{\sqrt[3]{t}} \cdot \sqrt[3]{\sqrt[3]{t}}\right)\right) \cdot \sqrt[3]{\sqrt[3]{t}}\right)}\right) \cdot \frac{\sqrt[3]{t}}{c}\right)\]

   16. Applied associate-*r* 11.9

       \[\leadsto \left(\frac{b}{z \cdot c} + 9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\right) - 4 \cdot \left(\color{blue}{\left(\left(a \cdot \left(\sqrt[3]{t} \cdot \left(\sqrt[3]{\sqrt[3]{t}} \cdot \sqrt[3]{\sqrt[3]{t}}\right)\right)\right) \cdot \sqrt[3]{\sqrt[3]{t}}\right)} \cdot \frac{\sqrt[3]{t}}{c}\right)\]

   17. Applied associate-*l* 10.8

       \[\leadsto \left(\frac{b}{z \cdot c} + 9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\right) - 4 \cdot \color{blue}{\left(\left(a \cdot \left(\sqrt[3]{t} \cdot \left(\sqrt[3]{\sqrt[3]{t}} \cdot \sqrt[3]{\sqrt[3]{t}}\right)\right)\right) \cdot \left(\sqrt[3]{\sqrt[3]{t}} \cdot \frac{\sqrt[3]{t}}{c}\right)\right)}\]

   if -5.2031824371176434e+281 < (* (* x 9.0) y) < -4.4446185240403435e-84 or 6.32049670678102e-96 < (* (* x 9.0) y) < 1.2680964165413392e+182

   1. Initial program 17.7

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\]

   2. Taylor expanded around 0 8.1

      \[\leadsto \color{blue}{\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \frac{a \cdot t}{c}}\]
   3. Using strategy rm

   4. Applied associate-/l* 6.8

      \[\leadsto \left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \color{blue}{\frac{a}{\frac{c}{t}}}\]

   if -4.4446185240403435e-84 < (* (* x 9.0) y) < 6.32049670678102e-96

   1. Initial program 16.7

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\]

   2. Taylor expanded around 0 7.8

      \[\leadsto \color{blue}{\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \frac{a \cdot t}{c}}\]
   3. Using strategy rm

   4. Applied *-un-lft-identity 7.8

      \[\leadsto \left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \frac{a \cdot t}{\color{blue}{1 \cdot c}}\]

   5. Applied add-cube-cbrt 8.3

      \[\leadsto \left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \frac{a \cdot \color{blue}{\left(\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}\right)}}{1 \cdot c}\]

   6. Applied associate-*r* 8.3

      \[\leadsto \left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \frac{\color{blue}{\left(a \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right) \cdot \sqrt[3]{t}}}{1 \cdot c}\]

   7. Applied times-frac 7.3

      \[\leadsto \left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \color{blue}{\left(\frac{a \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)}{1} \cdot \frac{\sqrt[3]{t}}{c}\right)}\]

   8. Simplified 7.3

      \[\leadsto \left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \left(\color{blue}{\left(a \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right)} \cdot \frac{\sqrt[3]{t}}{c}\right)\]
   9. Using strategy rm

   10. Applied *-commutative 7.3

       \[\leadsto \left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{\color{blue}{c \cdot z}}\right) - 4 \cdot \left(\left(a \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right) \cdot \frac{\sqrt[3]{t}}{c}\right)\]

   11. Applied *-commutative 7.3

       \[\leadsto \left(\frac{b}{z \cdot c} + 9 \cdot \frac{\color{blue}{y \cdot x}}{c \cdot z}\right) - 4 \cdot \left(\left(a \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right) \cdot \frac{\sqrt[3]{t}}{c}\right)\]

   12. Applied times-frac 8.8

       \[\leadsto \left(\frac{b}{z \cdot c} + 9 \cdot \color{blue}{\left(\frac{y}{c} \cdot \frac{x}{z}\right)}\right) - 4 \cdot \left(\left(a \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right) \cdot \frac{\sqrt[3]{t}}{c}\right)\]
   13. Using strategy rm

   14. Applied *-commutative 8.8

       \[\leadsto \left(\frac{b}{\color{blue}{c \cdot z}} + 9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\right) - 4 \cdot \left(\left(a \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right) \cdot \frac{\sqrt[3]{t}}{c}\right)\]

   15. Applied associate-/r* 8.4

       \[\leadsto \left(\color{blue}{\frac{\frac{b}{c}}{z}} + 9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\right) - 4 \cdot \left(\left(a \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right) \cdot \frac{\sqrt[3]{t}}{c}\right)\]

   if 1.2680964165413392e+182 < (* (* x 9.0) y)

   1. Initial program 36.8

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\]

   2. Taylor expanded around 0 32.0

      \[\leadsto \color{blue}{\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \frac{a \cdot t}{c}}\]
   3. Using strategy rm

   4. Applied *-un-lft-identity 32.0

      \[\leadsto \left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \frac{a \cdot t}{\color{blue}{1 \cdot c}}\]

   5. Applied add-cube-cbrt 32.1

      \[\leadsto \left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \frac{a \cdot \color{blue}{\left(\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}\right)}}{1 \cdot c}\]

   6. Applied associate-*r* 32.1

      \[\leadsto \left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \frac{\color{blue}{\left(a \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right) \cdot \sqrt[3]{t}}}{1 \cdot c}\]

   7. Applied times-frac 31.3

      \[\leadsto \left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \color{blue}{\left(\frac{a \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)}{1} \cdot \frac{\sqrt[3]{t}}{c}\right)}\]

   8. Simplified 31.3

      \[\leadsto \left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \left(\color{blue}{\left(a \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right)} \cdot \frac{\sqrt[3]{t}}{c}\right)\]
   9. Using strategy rm

   10. Applied *-commutative 31.3

       \[\leadsto \left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{\color{blue}{c \cdot z}}\right) - 4 \cdot \left(\left(a \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right) \cdot \frac{\sqrt[3]{t}}{c}\right)\]

   11. Applied *-commutative 31.3

       \[\leadsto \left(\frac{b}{z \cdot c} + 9 \cdot \frac{\color{blue}{y \cdot x}}{c \cdot z}\right) - 4 \cdot \left(\left(a \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right) \cdot \frac{\sqrt[3]{t}}{c}\right)\]

   12. Applied times-frac 12.9

       \[\leadsto \left(\frac{b}{z \cdot c} + 9 \cdot \color{blue}{\left(\frac{y}{c} \cdot \frac{x}{z}\right)}\right) - 4 \cdot \left(\left(a \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right) \cdot \frac{\sqrt[3]{t}}{c}\right)\]
   13. Using strategy rm

   14. Applied clear-num 13.2

       \[\leadsto \left(\frac{b}{z \cdot c} + 9 \cdot \left(\color{blue}{\frac{1}{\frac{c}{y}}} \cdot \frac{x}{z}\right)\right) - 4 \cdot \left(\left(a \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right) \cdot \frac{\sqrt[3]{t}}{c}\right)\]

   15. Applied frac-times 11.2

       \[\leadsto \left(\frac{b}{z \cdot c} + 9 \cdot \color{blue}{\frac{1 \cdot x}{\frac{c}{y} \cdot z}}\right) - 4 \cdot \left(\left(a \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right) \cdot \frac{\sqrt[3]{t}}{c}\right)\]

   16. Simplified 11.2

       \[\leadsto \left(\frac{b}{z \cdot c} + 9 \cdot \frac{\color{blue}{x}}{\frac{c}{y} \cdot z}\right) - 4 \cdot \left(\left(a \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right) \cdot \frac{\sqrt[3]{t}}{c}\right)\]
3. Recombined 4 regimes into one program.

4. Final simplification 8.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot 9\right) \cdot y \le -5.2031824371176434 \cdot 10^{281}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\right) - 4 \cdot \left(\left(a \cdot \left(\sqrt[3]{t} \cdot \left(\sqrt[3]{\sqrt[3]{t}} \cdot \sqrt[3]{\sqrt[3]{t}}\right)\right)\right) \cdot \left(\sqrt[3]{\sqrt[3]{t}} \cdot \frac{\sqrt[3]{t}}{c}\right)\right)\\ \mathbf{elif}\;\left(x \cdot 9\right) \cdot y \le -4.44461852404034349 \cdot 10^{-84}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;\left(x \cdot 9\right) \cdot y \le 6.32049670678102 \cdot 10^{-96}:\\ \;\;\;\;\left(\frac{\frac{b}{c}}{z} + 9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\right) - 4 \cdot \left(\left(a \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right) \cdot \frac{\sqrt[3]{t}}{c}\right)\\ \mathbf{elif}\;\left(x \cdot 9\right) \cdot y \le 1.2680964165413392 \cdot 10^{182}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x}{\frac{c}{y} \cdot z}\right) - 4 \cdot \left(\left(a \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right) \cdot \frac{\sqrt[3]{t}}{c}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020114 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, J"
  :precision binary64

  :herbie-target
  (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) -1.1001567408041051e-171) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) -0.0) (/ (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) z) c) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 1.1708877911747488e-53) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 2.876823679546137e+130) (- (+ (* (* 9 (/ y c)) (/ x z)) (/ b (* c z))) (* 4 (/ (* a t) c))) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 1.3838515042456319e+158) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (- (+ (* 9 (* (/ y (* c z)) x)) (/ b (* c z))) (* 4 (/ (* a t) c))))))))

  (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)))