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

Average Error: 20.7 → 18.9

Time: 17.5s

Precision: 64

Math

\[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3}\]

↓

\[\begin{array}{l} \mathbf{if}\;y \le -2.5871529893740023 \cdot 10^{-49}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - 0.333333333333333315 \cdot \left(t \cdot z\right)\right) - \frac{a}{b \cdot 3}\\ \mathbf{elif}\;y \le 1.00457305858854296 \cdot 10^{-15}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \left(1 - \frac{1}{2} \cdot {y}^{2}\right) - \frac{a}{b \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \left(\left(\cos \left(\frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right) \cdot \cos \left(1 \cdot y\right) - \sin \left(1 \cdot y\right) \cdot \sin \left(-\frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)\right) \cdot \cos \left(e^{\log 0}\right) - \sin \left(\mathsf{fma}\left(1, y, -\frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)\right) \cdot \sin \left(\left(\sqrt[3]{\mathsf{fma}\left(-\frac{t}{\sqrt[3]{3}}, \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}, \frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)} \cdot \sqrt[3]{\mathsf{fma}\left(-\frac{t}{\sqrt[3]{3}}, \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}, \frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(-\frac{t}{\sqrt[3]{3}}, \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}, \frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)}\right)\right) - \frac{a}{b \cdot 3}\\ \end{array}\]

C

double code(double x, double y, double z, double t, double a, double b) {
	return (((2.0 * sqrt(x)) * cos((y - ((z * t) / 3.0)))) - (a / (b * 3.0)));
}

↓

double code(double x, double y, double z, double t, double a, double b) {
	double temp;
	if ((y <= -2.5871529893740023e-49)) {
		temp = (((2.0 * sqrt(x)) * cos((y - (0.3333333333333333 * (t * z))))) - (a / (b * 3.0)));
	} else {
		double temp_1;
		if ((y <= 1.004573058588543e-15)) {
			temp_1 = (((2.0 * sqrt(x)) * (1.0 - (0.5 * pow(y, 2.0)))) - (a / (b * 3.0)));
		} else {
			temp_1 = (((2.0 * sqrt(x)) * ((((cos(((t / cbrt(3.0)) * (z / (cbrt(3.0) * cbrt(3.0))))) * cos((1.0 * y))) - (sin((1.0 * y)) * sin(-((t / cbrt(3.0)) * (z / (cbrt(3.0) * cbrt(3.0))))))) * cos(exp(log(0.0)))) - (sin(fma(1.0, y, -((t / cbrt(3.0)) * (z / (cbrt(3.0) * cbrt(3.0)))))) * sin(((cbrt(fma(-(t / cbrt(3.0)), (z / (cbrt(3.0) * cbrt(3.0))), ((t / cbrt(3.0)) * (z / (cbrt(3.0) * cbrt(3.0)))))) * cbrt(fma(-(t / cbrt(3.0)), (z / (cbrt(3.0) * cbrt(3.0))), ((t / cbrt(3.0)) * (z / (cbrt(3.0) * cbrt(3.0))))))) * cbrt(fma(-(t / cbrt(3.0)), (z / (cbrt(3.0) * cbrt(3.0))), ((t / cbrt(3.0)) * (z / (cbrt(3.0) * cbrt(3.0))))))))))) - (a / (b * 3.0)));
		}
		temp = temp_1;
	}
	return temp;
}

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

Target

Original	20.7
Target	18.6
Herbie	18.9

\[\begin{array}{l} \mathbf{if}\;z \lt -1.379333748723514 \cdot 10^{129}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(\frac{1}{y} - \frac{\frac{0.333333333333333315}{z}}{t}\right) - \frac{\frac{a}{3}}{b}\\ \mathbf{elif}\;z \lt 3.51629061355598715 \cdot 10^{106}:\\ \;\;\;\;\left(\sqrt{x} \cdot 2\right) \cdot \cos \left(y - \frac{t}{3} \cdot z\right) - \frac{\frac{a}{3}}{b}\\ \mathbf{else}:\\ \;\;\;\;\cos \left(y - \frac{\frac{0.333333333333333315}{z}}{t}\right) \cdot \left(2 \cdot \sqrt{x}\right) - \frac{\frac{a}{b}}{3}\\ \end{array}\]

Derivation

1. Split input into 3 regimes

2. if y < -2.5871529893740023e-49

   1. Initial program 20.3

      \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3}\]

   2. Taylor expanded around inf 20.2

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos \left(y - 0.333333333333333315 \cdot \left(t \cdot z\right)\right)} - \frac{a}{b \cdot 3}\]

   if -2.5871529893740023e-49 < y < 1.004573058588543e-15

   1. Initial program 19.9

      \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3}\]

   2. Taylor expanded around 0 16.4

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\left(1 - \frac{1}{2} \cdot {y}^{2}\right)} - \frac{a}{b \cdot 3}\]

   if 1.004573058588543e-15 < y

   1. Initial program 22.6

      \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3}\]
   2. Using strategy rm

   3. Applied add-cube-cbrt 22.6

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{\color{blue}{\left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right) \cdot \sqrt[3]{3}}}\right) - \frac{a}{b \cdot 3}\]

   4. Applied times-frac 22.6

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \color{blue}{\frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}} \cdot \frac{t}{\sqrt[3]{3}}}\right) - \frac{a}{b \cdot 3}\]

   5. Applied add-sqr-sqrt 30.1

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(\color{blue}{\sqrt{y} \cdot \sqrt{y}} - \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}} \cdot \frac{t}{\sqrt[3]{3}}\right) - \frac{a}{b \cdot 3}\]

   6. Applied prod-diff 30.1

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \color{blue}{\left(\mathsf{fma}\left(\sqrt{y}, \sqrt{y}, -\frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right) + \mathsf{fma}\left(-\frac{t}{\sqrt[3]{3}}, \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}, \frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)\right)} - \frac{a}{b \cdot 3}\]

   7. Applied cos-sum 30.0

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\left(\cos \left(\mathsf{fma}\left(\sqrt{y}, \sqrt{y}, -\frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)\right) \cdot \cos \left(\mathsf{fma}\left(-\frac{t}{\sqrt[3]{3}}, \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}, \frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)\right) - \sin \left(\mathsf{fma}\left(\sqrt{y}, \sqrt{y}, -\frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)\right) \cdot \sin \left(\mathsf{fma}\left(-\frac{t}{\sqrt[3]{3}}, \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}, \frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)\right)\right)} - \frac{a}{b \cdot 3}\]

   8. Simplified 22.6

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \left(\color{blue}{\cos \left(\mathsf{fma}\left(1, y, -\frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)\right) \cdot \cos \left(\mathsf{fma}\left(-\frac{t}{\sqrt[3]{3}}, \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}, \frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)\right)} - \sin \left(\mathsf{fma}\left(\sqrt{y}, \sqrt{y}, -\frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)\right) \cdot \sin \left(\mathsf{fma}\left(-\frac{t}{\sqrt[3]{3}}, \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}, \frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)\right)\right) - \frac{a}{b \cdot 3}\]

   9. Simplified 22.6

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \left(\cos \left(\mathsf{fma}\left(1, y, -\frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)\right) \cdot \cos \left(\mathsf{fma}\left(-\frac{t}{\sqrt[3]{3}}, \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}, \frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)\right) - \color{blue}{\sin \left(\mathsf{fma}\left(1, y, -\frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)\right) \cdot \sin \left(\mathsf{fma}\left(-\frac{t}{\sqrt[3]{3}}, \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}, \frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)\right)}\right) - \frac{a}{b \cdot 3}\]
   10. Using strategy rm

   11. Applied fma-udef 22.6

       \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \left(\cos \color{blue}{\left(1 \cdot y + \left(-\frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)\right)} \cdot \cos \left(\mathsf{fma}\left(-\frac{t}{\sqrt[3]{3}}, \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}, \frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)\right) - \sin \left(\mathsf{fma}\left(1, y, -\frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)\right) \cdot \sin \left(\mathsf{fma}\left(-\frac{t}{\sqrt[3]{3}}, \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}, \frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)\right)\right) - \frac{a}{b \cdot 3}\]

   12. Applied cos-sum 21.7

       \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \left(\color{blue}{\left(\cos \left(1 \cdot y\right) \cdot \cos \left(-\frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right) - \sin \left(1 \cdot y\right) \cdot \sin \left(-\frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)\right)} \cdot \cos \left(\mathsf{fma}\left(-\frac{t}{\sqrt[3]{3}}, \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}, \frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)\right) - \sin \left(\mathsf{fma}\left(1, y, -\frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)\right) \cdot \sin \left(\mathsf{fma}\left(-\frac{t}{\sqrt[3]{3}}, \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}, \frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)\right)\right) - \frac{a}{b \cdot 3}\]

   13. Simplified 21.7

       \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \left(\left(\color{blue}{\cos \left(\frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right) \cdot \cos \left(1 \cdot y\right)} - \sin \left(1 \cdot y\right) \cdot \sin \left(-\frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)\right) \cdot \cos \left(\mathsf{fma}\left(-\frac{t}{\sqrt[3]{3}}, \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}, \frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)\right) - \sin \left(\mathsf{fma}\left(1, y, -\frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)\right) \cdot \sin \left(\mathsf{fma}\left(-\frac{t}{\sqrt[3]{3}}, \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}, \frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)\right)\right) - \frac{a}{b \cdot 3}\]
   14. Using strategy rm

   15. Applied add-cube-cbrt 21.7

       \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \left(\left(\cos \left(\frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right) \cdot \cos \left(1 \cdot y\right) - \sin \left(1 \cdot y\right) \cdot \sin \left(-\frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)\right) \cdot \cos \left(\mathsf{fma}\left(-\frac{t}{\sqrt[3]{3}}, \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}, \frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)\right) - \sin \left(\mathsf{fma}\left(1, y, -\frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)\right) \cdot \sin \color{blue}{\left(\left(\sqrt[3]{\mathsf{fma}\left(-\frac{t}{\sqrt[3]{3}}, \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}, \frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)} \cdot \sqrt[3]{\mathsf{fma}\left(-\frac{t}{\sqrt[3]{3}}, \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}, \frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(-\frac{t}{\sqrt[3]{3}}, \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}, \frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)}\right)}\right) - \frac{a}{b \cdot 3}\]
   16. Using strategy rm

   17. Applied add-exp-log 39.0

       \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \left(\left(\cos \left(\frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right) \cdot \cos \left(1 \cdot y\right) - \sin \left(1 \cdot y\right) \cdot \sin \left(-\frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)\right) \cdot \cos \color{blue}{\left(e^{\log \left(\mathsf{fma}\left(-\frac{t}{\sqrt[3]{3}}, \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}, \frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)\right)}\right)} - \sin \left(\mathsf{fma}\left(1, y, -\frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)\right) \cdot \sin \left(\left(\sqrt[3]{\mathsf{fma}\left(-\frac{t}{\sqrt[3]{3}}, \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}, \frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)} \cdot \sqrt[3]{\mathsf{fma}\left(-\frac{t}{\sqrt[3]{3}}, \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}, \frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(-\frac{t}{\sqrt[3]{3}}, \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}, \frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)}\right)\right) - \frac{a}{b \cdot 3}\]

   18. Simplified 21.7

       \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \left(\left(\cos \left(\frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right) \cdot \cos \left(1 \cdot y\right) - \sin \left(1 \cdot y\right) \cdot \sin \left(-\frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)\right) \cdot \cos \left(e^{\color{blue}{\log 0}}\right) - \sin \left(\mathsf{fma}\left(1, y, -\frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)\right) \cdot \sin \left(\left(\sqrt[3]{\mathsf{fma}\left(-\frac{t}{\sqrt[3]{3}}, \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}, \frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)} \cdot \sqrt[3]{\mathsf{fma}\left(-\frac{t}{\sqrt[3]{3}}, \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}, \frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(-\frac{t}{\sqrt[3]{3}}, \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}, \frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)}\right)\right) - \frac{a}{b \cdot 3}\]
3. Recombined 3 regimes into one program.

4. Final simplification 18.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -2.5871529893740023 \cdot 10^{-49}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - 0.333333333333333315 \cdot \left(t \cdot z\right)\right) - \frac{a}{b \cdot 3}\\ \mathbf{elif}\;y \le 1.00457305858854296 \cdot 10^{-15}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \left(1 - \frac{1}{2} \cdot {y}^{2}\right) - \frac{a}{b \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \left(\left(\cos \left(\frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right) \cdot \cos \left(1 \cdot y\right) - \sin \left(1 \cdot y\right) \cdot \sin \left(-\frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)\right) \cdot \cos \left(e^{\log 0}\right) - \sin \left(\mathsf{fma}\left(1, y, -\frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)\right) \cdot \sin \left(\left(\sqrt[3]{\mathsf{fma}\left(-\frac{t}{\sqrt[3]{3}}, \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}, \frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)} \cdot \sqrt[3]{\mathsf{fma}\left(-\frac{t}{\sqrt[3]{3}}, \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}, \frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(-\frac{t}{\sqrt[3]{3}}, \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}, \frac{t}{\sqrt[3]{3}} \cdot \frac{z}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)}\right)\right) - \frac{a}{b \cdot 3}\\ \end{array}\]

Reproduce

herbie shell --seed 2020049 +o rules:numerics
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, K"
  :precision binary64

  :herbie-target
  (if (< z -1.379333748723514e+129) (- (* (* 2 (sqrt x)) (cos (- (/ 1 y) (/ (/ 0.3333333333333333 z) t)))) (/ (/ a 3) b)) (if (< z 3.516290613555987e+106) (- (* (* (sqrt x) 2) (cos (- y (* (/ t 3) z)))) (/ (/ a 3) b)) (- (* (cos (- y (/ (/ 0.3333333333333333 z) t))) (* 2 (sqrt x))) (/ (/ a b) 3))))

  (- (* (* 2 (sqrt x)) (cos (- y (/ (* z t) 3)))) (/ a (* b 3))))