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

Average Error: 20.6 → 16.2

Time: 40.2s

Precision: binary64

Cost: 119880

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

Math

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

↓

\[\begin{array}{l} t_1 := \frac{t}{\frac{3}{z}}\\ t_2 := \cos t_1\\ t_3 := \sin y \cdot \sin t_1\\ t_4 := \cos y \cdot t_2\\ \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{+283}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{\frac{a}{b}}{3}\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+271}:\\ \;\;\;\;\frac{\sqrt{x} \cdot \left(2 \cdot \left({t_4}^{3} + {t_3}^{3}\right)\right)}{\mathsf{fma}\left(\cos y, t_2 \cdot t_4, t_3 \cdot \left(t_3 - t_4\right)\right)} - \frac{a}{b \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(2, \sqrt{x}, \frac{\frac{a}{-3}}{b}\right)\\ \end{array} \]

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 (/ t (/ 3.0 z)))
        (t_2 (cos t_1))
        (t_3 (* (sin y) (sin t_1)))
        (t_4 (* (cos y) t_2)))
   (if (<= (* z t) -2e+283)
     (- (* 2.0 (sqrt x)) (/ (/ a b) 3.0))
     (if (<= (* z t) 5e+271)
       (-
        (/
         (* (sqrt x) (* 2.0 (+ (pow t_4 3.0) (pow t_3 3.0))))
         (fma (cos y) (* t_2 t_4) (* t_3 (- t_3 t_4))))
        (/ a (* b 3.0)))
       (fma 2.0 (sqrt x) (/ (/ 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 = t / (3.0 / z);
	double t_2 = cos(t_1);
	double t_3 = sin(y) * sin(t_1);
	double t_4 = cos(y) * t_2;
	double tmp;
	if ((z * t) <= -2e+283) {
		tmp = (2.0 * sqrt(x)) - ((a / b) / 3.0);
	} else if ((z * t) <= 5e+271) {
		tmp = ((sqrt(x) * (2.0 * (pow(t_4, 3.0) + pow(t_3, 3.0)))) / fma(cos(y), (t_2 * t_4), (t_3 * (t_3 - t_4)))) - (a / (b * 3.0));
	} else {
		tmp = fma(2.0, sqrt(x), ((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(t / Float64(3.0 / z))
	t_2 = cos(t_1)
	t_3 = Float64(sin(y) * sin(t_1))
	t_4 = Float64(cos(y) * t_2)
	tmp = 0.0
	if (Float64(z * t) <= -2e+283)
		tmp = Float64(Float64(2.0 * sqrt(x)) - Float64(Float64(a / b) / 3.0));
	elseif (Float64(z * t) <= 5e+271)
		tmp = Float64(Float64(Float64(sqrt(x) * Float64(2.0 * Float64((t_4 ^ 3.0) + (t_3 ^ 3.0)))) / fma(cos(y), Float64(t_2 * t_4), Float64(t_3 * Float64(t_3 - t_4)))) - Float64(a / Float64(b * 3.0)));
	else
		tmp = fma(2.0, sqrt(x), 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[(t / N[(3.0 / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[Cos[t$95$1], $MachinePrecision]}, Block[{t$95$3 = N[(N[Sin[y], $MachinePrecision] * N[Sin[t$95$1], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[Cos[y], $MachinePrecision] * t$95$2), $MachinePrecision]}, If[LessEqual[N[(z * t), $MachinePrecision], -2e+283], N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] - N[(N[(a / b), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 5e+271], N[(N[(N[(N[Sqrt[x], $MachinePrecision] * N[(2.0 * N[(N[Power[t$95$4, 3.0], $MachinePrecision] + N[Power[t$95$3, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[Cos[y], $MachinePrecision] * N[(t$95$2 * t$95$4), $MachinePrecision] + N[(t$95$3 * N[(t$95$3 - t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / N[(b * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[Sqrt[x], $MachinePrecision] + N[(N[(a / -3.0), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]]]]]]]

Target

Original	20.6
Target	18.7
Herbie	16.2

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

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -1.99999999999999991e283

   1. Initial program 59.8

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

   2. Taylor expanded in z around 0 34.6

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

   3. Applied egg-rr 34.6

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

   4. Simplified 34.6

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

      [Start] 34.6	\[ \left(\left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{a}{b \cdot 3}\right) \cdot 1 \]
      *-rgt-identity [=>] 34.6	\[ \color{blue}{\left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{a}{b \cdot 3}} \]
      associate-*l* [=>] 34.6	\[ \color{blue}{2 \cdot \left(\sqrt{x} \cdot \cos y\right)} - \frac{a}{b \cdot 3} \]
      associate-/r* [=>] 34.6	\[ 2 \cdot \left(\sqrt{x} \cdot \cos y\right) - \color{blue}{\frac{\frac{a}{b}}{3}} \]

   5. Taylor expanded in y around 0 34.7

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

   if -1.99999999999999991e283 < (*.f64 z t) < 5.0000000000000003e271

   1. Initial program 13.6

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

   2. Simplified 13.5

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

      [Start] 13.6	\[ \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
      associate-*l* [=>] 13.6	\[ \color{blue}{2 \cdot \left(\sqrt{x} \cdot \cos \left(y - \frac{z \cdot t}{3}\right)\right)} - \frac{a}{b \cdot 3} \]
      associate-*l* [<=] 13.6	\[ \color{blue}{\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right)} - \frac{a}{b \cdot 3} \]
      remove-double-neg [<=] 13.6	\[ \color{blue}{\left(-\left(-\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right)\right)\right)} - \frac{a}{b \cdot 3} \]
      neg-mul-1 [=>] 13.6	\[ \color{blue}{-1 \cdot \left(-\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right)\right)} - \frac{a}{b \cdot 3} \]
      neg-mul-1 [<=] 13.6	\[ \color{blue}{\left(-\left(-\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right)\right)\right)} - \frac{a}{b \cdot 3} \]
      remove-double-neg [=>] 13.6	\[ \color{blue}{\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right)} - \frac{a}{b \cdot 3} \]
      associate-*l/ [<=] 13.5	\[ \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \color{blue}{\frac{z}{3} \cdot t}\right) - \frac{a}{b \cdot 3} \]
      *-commutative [=>] 13.5	\[ \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z}{3} \cdot t\right) - \frac{a}{\color{blue}{3 \cdot b}} \]

   3. Applied egg-rr 13.0

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

   4. Simplified 13.0

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

      [Start] 13.0

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

      *-commutative [=>] 13.0

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

   if 5.0000000000000003e271 < (*.f64 z t)

   1. Initial program 58.0

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

   2. Simplified 57.9

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

      [Start] 58.0	\[ \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
      associate-*l* [=>] 58.0	\[ \color{blue}{2 \cdot \left(\sqrt{x} \cdot \cos \left(y - \frac{z \cdot t}{3}\right)\right)} - \frac{a}{b \cdot 3} \]
      fma-neg [=>] 58.0	\[ \color{blue}{\mathsf{fma}\left(2, \sqrt{x} \cdot \cos \left(y - \frac{z \cdot t}{3}\right), -\frac{a}{b \cdot 3}\right)} \]
      remove-double-neg [<=] 58.0	\[ \mathsf{fma}\left(2, \color{blue}{-\left(-\sqrt{x} \cdot \cos \left(y - \frac{z \cdot t}{3}\right)\right)}, -\frac{a}{b \cdot 3}\right) \]

   3. Taylor expanded in z around 0 32.7

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

   4. Taylor expanded in y around 0 32.6

      \[\leadsto \mathsf{fma}\left(2, \color{blue}{\sqrt{x}}, \frac{\frac{a}{-3}}{b}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 16.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{+283}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{\frac{a}{b}}{3}\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+271}:\\ \;\;\;\;\frac{\sqrt{x} \cdot \left(2 \cdot \left({\left(\cos y \cdot \cos \left(\frac{t}{\frac{3}{z}}\right)\right)}^{3} + {\left(\sin y \cdot \sin \left(\frac{t}{\frac{3}{z}}\right)\right)}^{3}\right)\right)}{\mathsf{fma}\left(\cos y, \cos \left(\frac{t}{\frac{3}{z}}\right) \cdot \left(\cos y \cdot \cos \left(\frac{t}{\frac{3}{z}}\right)\right), \left(\sin y \cdot \sin \left(\frac{t}{\frac{3}{z}}\right)\right) \cdot \left(\sin y \cdot \sin \left(\frac{t}{\frac{3}{z}}\right) - \cos y \cdot \cos \left(\frac{t}{\frac{3}{z}}\right)\right)\right)} - \frac{a}{b \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(2, \sqrt{x}, \frac{\frac{a}{-3}}{b}\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	16.2
Cost	93640

\[\begin{array}{l} t_1 := \frac{t}{\frac{3}{z}}\\ t_2 := \cos t_1\\ t_3 := \sin y \cdot \sin t_1\\ t_4 := \cos y \cdot t_2 - t_3\\ \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{+283}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{\frac{a}{b}}{3}\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+271}:\\ \;\;\;\;2 \cdot \left(t_4 \cdot \frac{\mathsf{fma}\left(\cos y, t_2, t_3\right)}{\frac{t_4}{\sqrt{x}}}\right) - \frac{a}{b \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(2, \sqrt{x}, \frac{\frac{a}{-3}}{b}\right)\\ \end{array} \]

Alternative 2
Error	16.2
Cost	34120

\[\begin{array}{l} t_1 := \frac{z}{\frac{3}{t}}\\ \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{+283}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{\frac{a}{b}}{3}\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+271}:\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \left(\sin y \cdot \sin t_1 + \cos y \cdot \cos t_1\right)\right) - \frac{a}{b \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(2, \sqrt{x}, \frac{\frac{a}{-3}}{b}\right)\\ \end{array} \]

Alternative 3
Error	16.3
Cost	34120

\[\begin{array}{l} \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{+283}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{\frac{a}{b}}{3}\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+230}:\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \left(\cos y \cdot \cos \left(\left(z \cdot t\right) \cdot 0.3333333333333333\right) - \sin y \cdot \sin \left(t \cdot \left(z \cdot -0.3333333333333333\right)\right)\right)\right) - \frac{a}{b \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(2, \sqrt{x}, \frac{\frac{a}{-3}}{b}\right)\\ \end{array} \]

Alternative 4
Error	16.2
Cost	34120

\[\begin{array}{l} t_1 := \left(z \cdot t\right) \cdot -0.3333333333333333\\ t_2 := 2 \cdot \sqrt{x}\\ \mathbf{if}\;z \cdot t \leq -4 \cdot 10^{+202}:\\ \;\;\;\;t_2 - \frac{\frac{a}{b}}{3}\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+230}:\\ \;\;\;\;t_2 \cdot \left(\cos y \cdot \cos t_1 - \sin y \cdot \sin t_1\right) - \frac{a}{b \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(2, \sqrt{x}, \frac{\frac{a}{-3}}{b}\right)\\ \end{array} \]

Alternative 5
Error	16.9
Cost	19776

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

Alternative 6
Error	20.1
Cost	14024

\[\begin{array}{l} t_1 := \frac{a}{b \cdot 3}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-79}:\\ \;\;\;\;2 \cdot \sqrt{x} - t_1\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{-94}:\\ \;\;\;\;\sqrt{x} \cdot \left(2 \cdot \cos y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(2, \sqrt{x}, \frac{\frac{a}{-3}}{b}\right)\\ \end{array} \]

Alternative 7
Error	20.2
Cost	13896

\[\begin{array}{l} t_1 := \frac{a}{b \cdot 3}\\ t_2 := 2 \cdot \sqrt{x}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-79}:\\ \;\;\;\;t_2 - t_1\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{-94}:\\ \;\;\;\;\sqrt{x} \cdot \left(2 \cdot \cos y\right)\\ \mathbf{else}:\\ \;\;\;\;t_2 - \frac{\frac{a}{b}}{3}\\ \end{array} \]

Alternative 8
Error	17.0
Cost	13504

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

Alternative 9
Error	17.0
Cost	13504

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

Alternative 10
Error	25.1
Cost	6976

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

Alternative 11
Error	25.0
Cost	6976

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

Alternative 12
Error	25.0
Cost	6976

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

Alternative 13
Error	35.8
Cost	320

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

Alternative 14
Error	35.8
Cost	320

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

Alternative 15
Error	35.7
Cost	320

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

Alternative 16
Error	35.7
Cost	320

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

Reproduce

herbie shell --seed 2023031 
(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))))