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

Average Accuracy: 68.2% → 74.9%

Time: 29.7s

Precision: binary64

Cost: 87368

\[ \begin{array}{c}[z, t] = \mathsf{sort}([z, t])\\ \end{array} \]

Math

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

↓

\[\begin{array}{l} t_1 := 2 \cdot \sqrt{x}\\ t_2 := \frac{a}{3 \cdot b}\\ t_3 := \frac{z}{\frac{3}{t}}\\ t_4 := \cos y \cdot \cos t_3\\ t_5 := \sin y \cdot \sin t_3\\ \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+23}:\\ \;\;\;\;t_1 \cdot \mathsf{expm1}\left(\mathsf{fma}\left(-0.25, y \cdot y, \log 2\right)\right) - t_2\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+238}:\\ \;\;\;\;t_1 \cdot \frac{t_4 \cdot t_4 - t_5 \cdot t_5}{t_4 - t_5} - t_2\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(2, {\left(\sqrt[3]{\sqrt{x} \cdot \cos y}\right)}^{3}, \frac{\frac{a}{-3}}{b}\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (- (* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0)))) (/ a (* b 3.0))))

↓

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 2.0 (sqrt x)))
        (t_2 (/ a (* 3.0 b)))
        (t_3 (/ z (/ 3.0 t)))
        (t_4 (* (cos y) (cos t_3)))
        (t_5 (* (sin y) (sin t_3))))
   (if (<= (* z t) -5e+23)
     (- (* t_1 (expm1 (fma -0.25 (* y y) (log 2.0)))) t_2)
     (if (<= (* z t) 2e+238)
       (- (* t_1 (/ (- (* t_4 t_4) (* t_5 t_5)) (- t_4 t_5))) t_2)
       (fma 2.0 (pow (cbrt (* (sqrt x) (cos y))) 3.0) (/ (/ a -3.0) b))))))

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 t_1 = 2.0 * sqrt(x);
	double t_2 = a / (3.0 * b);
	double t_3 = z / (3.0 / t);
	double t_4 = cos(y) * cos(t_3);
	double t_5 = sin(y) * sin(t_3);
	double tmp;
	if ((z * t) <= -5e+23) {
		tmp = (t_1 * expm1(fma(-0.25, (y * y), log(2.0)))) - t_2;
	} else if ((z * t) <= 2e+238) {
		tmp = (t_1 * (((t_4 * t_4) - (t_5 * t_5)) / (t_4 - t_5))) - t_2;
	} else {
		tmp = fma(2.0, pow(cbrt((sqrt(x) * cos(y))), 3.0), ((a / -3.0) / b));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(2.0 * sqrt(x)) * cos(Float64(y - Float64(Float64(z * t) / 3.0)))) - Float64(a / Float64(b * 3.0)))
end

↓

function code(x, y, z, t, a, b)
	t_1 = Float64(2.0 * sqrt(x))
	t_2 = Float64(a / Float64(3.0 * b))
	t_3 = Float64(z / Float64(3.0 / t))
	t_4 = Float64(cos(y) * cos(t_3))
	t_5 = Float64(sin(y) * sin(t_3))
	tmp = 0.0
	if (Float64(z * t) <= -5e+23)
		tmp = Float64(Float64(t_1 * expm1(fma(-0.25, Float64(y * y), log(2.0)))) - t_2);
	elseif (Float64(z * t) <= 2e+238)
		tmp = Float64(Float64(t_1 * Float64(Float64(Float64(t_4 * t_4) - Float64(t_5 * t_5)) / Float64(t_4 - t_5))) - t_2);
	else
		tmp = fma(2.0, (cbrt(Float64(sqrt(x) * cos(y))) ^ 3.0), Float64(Float64(a / -3.0) / b));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[(a / N[(b * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z / N[(3.0 / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[Cos[y], $MachinePrecision] * N[Cos[t$95$3], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[Sin[y], $MachinePrecision] * N[Sin[t$95$3], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z * t), $MachinePrecision], -5e+23], N[(N[(t$95$1 * N[(Exp[N[(-0.25 * N[(y * y), $MachinePrecision] + N[Log[2.0], $MachinePrecision]), $MachinePrecision]] - 1), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 2e+238], N[(N[(t$95$1 * N[(N[(N[(t$95$4 * t$95$4), $MachinePrecision] - N[(t$95$5 * t$95$5), $MachinePrecision]), $MachinePrecision] / N[(t$95$4 - t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], N[(2.0 * N[Power[N[Power[N[(N[Sqrt[x], $MachinePrecision] * N[Cos[y], $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision], 3.0], $MachinePrecision] + N[(N[(a / -3.0), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]]]]]]]]

Target

Original	68.2%
Target	71.2%
Herbie	74.9%

\[\begin{array}{l} \mathbf{if}\;z < -1.3793337487235141 \cdot 10^{+129}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(\frac{1}{y} - \frac{\frac{0.3333333333333333}{z}}{t}\right) - \frac{\frac{a}{3}}{b}\\ \mathbf{elif}\;z < 3.516290613555987 \cdot 10^{+106}:\\ \;\;\;\;\left(\sqrt{x} \cdot 2\right) \cdot \cos \left(y - \frac{t}{3} \cdot z\right) - \frac{\frac{a}{3}}{b}\\ \mathbf{else}:\\ \;\;\;\;\cos \left(y - \frac{\frac{0.3333333333333333}{z}}{t}\right) \cdot \left(2 \cdot \sqrt{x}\right) - \frac{\frac{a}{b}}{3}\\ \end{array} \]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -4.9999999999999999e23

   1. Initial program 35.4%

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

   2. Simplified 35.3%

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

      [Start] 35.4	\[ \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
      associate-*l* [=>] 35.4	\[ \color{blue}{2 \cdot \left(\sqrt{x} \cdot \cos \left(y - \frac{z \cdot t}{3}\right)\right)} - \frac{a}{b \cdot 3} \]
      associate-*l* [<=] 35.4	\[ \color{blue}{\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right)} - \frac{a}{b \cdot 3} \]
      remove-double-neg [<=] 35.4	\[ \color{blue}{\left(-\left(-\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right)\right)\right)} - \frac{a}{b \cdot 3} \]
      neg-mul-1 [=>] 35.4	\[ \color{blue}{-1 \cdot \left(-\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right)\right)} - \frac{a}{b \cdot 3} \]
      neg-mul-1 [<=] 35.4	\[ \color{blue}{\left(-\left(-\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right)\right)\right)} - \frac{a}{b \cdot 3} \]
      remove-double-neg [=>] 35.4	\[ \color{blue}{\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right)} - \frac{a}{b \cdot 3} \]
      associate-*l/ [<=] 35.3	\[ \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \color{blue}{\frac{z}{3} \cdot t}\right) - \frac{a}{b \cdot 3} \]
      *-commutative [=>] 35.3	\[ \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z}{3} \cdot t\right) - \frac{a}{\color{blue}{3 \cdot b}} \]

   3. Taylor expanded in z around 0 47.3%

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

   4. Applied egg-rr 47.3%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\cos y\right)\right)} - \frac{a}{3 \cdot b} \]
      Proof

      [Start] 47.3	\[ \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{a}{3 \cdot b} \]
      expm1-log1p-u [=>] 47.3	\[ \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\cos y\right)\right)} - \frac{a}{3 \cdot b} \]

   5. Taylor expanded in y around 0 47.8%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{expm1}\left(\color{blue}{-0.25 \cdot {y}^{2} + \log 2}\right) - \frac{a}{3 \cdot b} \]

   6. Simplified 47.8%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{expm1}\left(\color{blue}{\mathsf{fma}\left(-0.25, y \cdot y, \log 2\right)}\right) - \frac{a}{3 \cdot b} \]
      Proof

      [Start] 47.8	\[ \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{expm1}\left(-0.25 \cdot {y}^{2} + \log 2\right) - \frac{a}{3 \cdot b} \]
      fma-def [=>] 47.8	\[ \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{expm1}\left(\color{blue}{\mathsf{fma}\left(-0.25, {y}^{2}, \log 2\right)}\right) - \frac{a}{3 \cdot b} \]
      unpow2 [=>] 47.8	\[ \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{expm1}\left(\mathsf{fma}\left(-0.25, \color{blue}{y \cdot y}, \log 2\right)\right) - \frac{a}{3 \cdot b} \]

   if -4.9999999999999999e23 < (*.f64 z t) < 2.0000000000000001e238

   1. Initial program 86.3%

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

   2. Simplified 86.3%

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

      [Start] 86.3	\[ \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
      associate-*l* [=>] 86.3	\[ \color{blue}{2 \cdot \left(\sqrt{x} \cdot \cos \left(y - \frac{z \cdot t}{3}\right)\right)} - \frac{a}{b \cdot 3} \]
      associate-*l* [<=] 86.3	\[ \color{blue}{\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right)} - \frac{a}{b \cdot 3} \]
      remove-double-neg [<=] 86.3	\[ \color{blue}{\left(-\left(-\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right)\right)\right)} - \frac{a}{b \cdot 3} \]
      neg-mul-1 [=>] 86.3	\[ \color{blue}{-1 \cdot \left(-\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right)\right)} - \frac{a}{b \cdot 3} \]
      neg-mul-1 [<=] 86.3	\[ \color{blue}{\left(-\left(-\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right)\right)\right)} - \frac{a}{b \cdot 3} \]
      remove-double-neg [=>] 86.3	\[ \color{blue}{\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right)} - \frac{a}{b \cdot 3} \]
      associate-*l/ [<=] 86.3	\[ \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \color{blue}{\frac{z}{3} \cdot t}\right) - \frac{a}{b \cdot 3} \]
      *-commutative [=>] 86.3	\[ \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z}{3} \cdot t\right) - \frac{a}{\color{blue}{3 \cdot b}} \]

   3. Applied egg-rr 63.0%

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

      [Start] 86.3	\[ \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z}{3} \cdot t\right) - \frac{a}{3 \cdot b} \]
      associate-*l/ [=>] 86.3	\[ \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \color{blue}{\frac{z \cdot t}{3}}\right) - \frac{a}{3 \cdot b} \]
      add-sqr-sqrt [=>] 63.0	\[ \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot \color{blue}{\left(\sqrt{t} \cdot \sqrt{t}\right)}}{3}\right) - \frac{a}{3 \cdot b} \]
      associate-*r* [=>] 63.0	\[ \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{\color{blue}{\left(z \cdot \sqrt{t}\right) \cdot \sqrt{t}}}{3}\right) - \frac{a}{3 \cdot b} \]
      associate-/l* [=>] 63.0	\[ \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \color{blue}{\frac{z \cdot \sqrt{t}}{\frac{3}{\sqrt{t}}}}\right) - \frac{a}{3 \cdot b} \]

   4. Applied egg-rr 87.5%

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

      [Start] 63.0	\[ \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot \sqrt{t}}{\frac{3}{\sqrt{t}}}\right) - \frac{a}{3 \cdot b} \]
      cos-diff [=>] 63.8	\[ \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\left(\cos y \cdot \cos \left(\frac{z \cdot \sqrt{t}}{\frac{3}{\sqrt{t}}}\right) + \sin y \cdot \sin \left(\frac{z \cdot \sqrt{t}}{\frac{3}{\sqrt{t}}}\right)\right)} - \frac{a}{3 \cdot b} \]
      flip-+ [=>] 63.8	\[ \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\frac{\left(\cos y \cdot \cos \left(\frac{z \cdot \sqrt{t}}{\frac{3}{\sqrt{t}}}\right)\right) \cdot \left(\cos y \cdot \cos \left(\frac{z \cdot \sqrt{t}}{\frac{3}{\sqrt{t}}}\right)\right) - \left(\sin y \cdot \sin \left(\frac{z \cdot \sqrt{t}}{\frac{3}{\sqrt{t}}}\right)\right) \cdot \left(\sin y \cdot \sin \left(\frac{z \cdot \sqrt{t}}{\frac{3}{\sqrt{t}}}\right)\right)}{\cos y \cdot \cos \left(\frac{z \cdot \sqrt{t}}{\frac{3}{\sqrt{t}}}\right) - \sin y \cdot \sin \left(\frac{z \cdot \sqrt{t}}{\frac{3}{\sqrt{t}}}\right)}} - \frac{a}{3 \cdot b} \]

   if 2.0000000000000001e238 < (*.f64 z t)

   1. Initial program 17.7%

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

   2. Simplified 17.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(2, \sqrt{x} \cdot \cos \left(\mathsf{fma}\left(z, t \cdot -0.3333333333333333, y\right)\right), \frac{\frac{a}{-3}}{b}\right)} \]
      Proof

      [Start] 17.7	\[ \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
      associate-*l* [=>] 17.7	\[ \color{blue}{2 \cdot \left(\sqrt{x} \cdot \cos \left(y - \frac{z \cdot t}{3}\right)\right)} - \frac{a}{b \cdot 3} \]
      fma-neg [=>] 17.7	\[ \color{blue}{\mathsf{fma}\left(2, \sqrt{x} \cdot \cos \left(y - \frac{z \cdot t}{3}\right), -\frac{a}{b \cdot 3}\right)} \]
      remove-double-neg [<=] 17.7	\[ \mathsf{fma}\left(2, \color{blue}{-\left(-\sqrt{x} \cdot \cos \left(y - \frac{z \cdot t}{3}\right)\right)}, -\frac{a}{b \cdot 3}\right) \]

   3. Taylor expanded in z around 0 51.2%

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

   4. Applied egg-rr 51.2%

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

      [Start] 51.2	\[ \mathsf{fma}\left(2, \sqrt{x} \cdot \cos y, \frac{\frac{a}{-3}}{b}\right) \]
      add-cube-cbrt [=>] 51.2	\[ \mathsf{fma}\left(2, \color{blue}{\left(\sqrt[3]{\sqrt{x} \cdot \cos y} \cdot \sqrt[3]{\sqrt{x} \cdot \cos y}\right) \cdot \sqrt[3]{\sqrt{x} \cdot \cos y}}, \frac{\frac{a}{-3}}{b}\right) \]
      pow3 [=>] 51.2	\[ \mathsf{fma}\left(2, \color{blue}{{\left(\sqrt[3]{\sqrt{x} \cdot \cos y}\right)}^{3}}, \frac{\frac{a}{-3}}{b}\right) \]

3. Recombined 3 regimes into one program.

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+23}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \mathsf{expm1}\left(\mathsf{fma}\left(-0.25, y \cdot y, \log 2\right)\right) - \frac{a}{3 \cdot b}\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+238}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \frac{\left(\cos y \cdot \cos \left(\frac{z}{\frac{3}{t}}\right)\right) \cdot \left(\cos y \cdot \cos \left(\frac{z}{\frac{3}{t}}\right)\right) - \left(\sin y \cdot \sin \left(\frac{z}{\frac{3}{t}}\right)\right) \cdot \left(\sin y \cdot \sin \left(\frac{z}{\frac{3}{t}}\right)\right)}{\cos y \cdot \cos \left(\frac{z}{\frac{3}{t}}\right) - \sin y \cdot \sin \left(\frac{z}{\frac{3}{t}}\right)} - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(2, {\left(\sqrt[3]{\sqrt{x} \cdot \cos y}\right)}^{3}, \frac{\frac{a}{-3}}{b}\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	74.9%
Cost	34120

\[\begin{array}{l} t_1 := \frac{z}{\frac{3}{t}}\\ t_2 := \frac{a}{3 \cdot b}\\ t_3 := 2 \cdot \sqrt{x}\\ \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+23}:\\ \;\;\;\;t_3 \cdot \mathsf{expm1}\left(\mathsf{fma}\left(-0.25, y \cdot y, \log 2\right)\right) - t_2\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+238}:\\ \;\;\;\;t_3 \cdot \left(\cos y \cdot \cos t_1 + \sin y \cdot \sin t_1\right) - t_2\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(2, {\left(\sqrt[3]{\sqrt{x} \cdot \cos y}\right)}^{3}, \frac{\frac{a}{-3}}{b}\right)\\ \end{array} \]

Alternative 2
Accuracy	73.5%
Cost	19776

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

Alternative 3
Accuracy	62.4%
Cost	13513

\[\begin{array}{l} \mathbf{if}\;b \leq -6.4 \cdot 10^{+231} \lor \neg \left(b \leq 7 \cdot 10^{+154}\right):\\ \;\;\;\;\sqrt{x} \cdot \left(2 \cdot \cos y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(2, \sqrt{x}, \frac{\frac{a}{-3}}{b}\right)\\ \end{array} \]

Alternative 4
Accuracy	73.4%
Cost	13504

\[\left(2 \cdot \sqrt{x}\right) \cdot \cos y + a \cdot \frac{-0.3333333333333333}{b} \]

Alternative 5
Accuracy	73.5%
Cost	13504

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

Alternative 6
Accuracy	62.4%
Cost	13385

\[\begin{array}{l} \mathbf{if}\;b \leq -1.08 \cdot 10^{+232} \lor \neg \left(b \leq 4.4 \cdot 10^{+154}\right):\\ \;\;\;\;\sqrt{x} \cdot \left(2 \cdot \cos y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{a}{3 \cdot b}\\ \end{array} \]

Alternative 7
Accuracy	61.1%
Cost	6976

\[2 \cdot \sqrt{x} + \frac{a}{b} \cdot -0.3333333333333333 \]

Alternative 8
Accuracy	61.2%
Cost	6976

\[2 \cdot \sqrt{x} - \frac{a}{3 \cdot b} \]

Alternative 9
Accuracy	44.0%
Cost	320

\[\frac{a}{b} \cdot -0.3333333333333333 \]

Alternative 10
Accuracy	44.1%
Cost	320

\[\frac{\frac{a}{-3}}{b} \]

Reproduce

herbie shell --seed 2023133 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, K"
  :precision binary64

  :herbie-target
  (if (< z -1.3793337487235141e+129) (- (* (* 2.0 (sqrt x)) (cos (- (/ 1.0 y) (/ (/ 0.3333333333333333 z) t)))) (/ (/ a 3.0) b)) (if (< z 3.516290613555987e+106) (- (* (* (sqrt x) 2.0) (cos (- y (* (/ t 3.0) z)))) (/ (/ a 3.0) b)) (- (* (cos (- y (/ (/ 0.3333333333333333 z) t))) (* 2.0 (sqrt x))) (/ (/ a b) 3.0))))

  (- (* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0)))) (/ a (* b 3.0))))