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

Average Accuracy: 67.8% → 74.5%

Time: 24.7s

Precision: binary64

Cost: 34120

Math

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

↓

\[\begin{array}{l} t_1 := \left(z \cdot t\right) \cdot -0.3333333333333333\\ t_2 := \frac{a}{b \cdot 3}\\ t_3 := \sqrt{x} \cdot 2\\ \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+187}:\\ \;\;\;\;\sqrt{x} \cdot \left(-2 \cdot \cos y\right) - t_2\\ \mathbf{elif}\;z \cdot t \leq 40000000:\\ \;\;\;\;t_3 \cdot \left(\cos y \cdot \cos t_1 - \sin y \cdot \sin t_1\right) - t_2\\ \mathbf{else}:\\ \;\;\;\;t_3 - 0.3333333333333333 \cdot \frac{a}{b}\\ \end{array} \]

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 (* (* z t) -0.3333333333333333))
        (t_2 (/ a (* b 3.0)))
        (t_3 (* (sqrt x) 2.0)))
   (if (<= (* z t) -5e+187)
     (- (* (sqrt x) (* -2.0 (cos y))) t_2)
     (if (<= (* z t) 40000000.0)
       (- (* t_3 (- (* (cos y) (cos t_1)) (* (sin y) (sin t_1)))) t_2)
       (- t_3 (* 0.3333333333333333 (/ a 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 = (z * t) * -0.3333333333333333;
	double t_2 = a / (b * 3.0);
	double t_3 = sqrt(x) * 2.0;
	double tmp;
	if ((z * t) <= -5e+187) {
		tmp = (sqrt(x) * (-2.0 * cos(y))) - t_2;
	} else if ((z * t) <= 40000000.0) {
		tmp = (t_3 * ((cos(y) * cos(t_1)) - (sin(y) * sin(t_1)))) - t_2;
	} else {
		tmp = t_3 - (0.3333333333333333 * (a / b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((2.0d0 * sqrt(x)) * cos((y - ((z * t) / 3.0d0)))) - (a / (b * 3.0d0))
end function

↓

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (z * t) * (-0.3333333333333333d0)
    t_2 = a / (b * 3.0d0)
    t_3 = sqrt(x) * 2.0d0
    if ((z * t) <= (-5d+187)) then
        tmp = (sqrt(x) * ((-2.0d0) * cos(y))) - t_2
    else if ((z * t) <= 40000000.0d0) then
        tmp = (t_3 * ((cos(y) * cos(t_1)) - (sin(y) * sin(t_1)))) - t_2
    else
        tmp = t_3 - (0.3333333333333333d0 * (a / b))
    end if
    code = tmp
end function

Java

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

↓

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * t) * -0.3333333333333333;
	double t_2 = a / (b * 3.0);
	double t_3 = Math.sqrt(x) * 2.0;
	double tmp;
	if ((z * t) <= -5e+187) {
		tmp = (Math.sqrt(x) * (-2.0 * Math.cos(y))) - t_2;
	} else if ((z * t) <= 40000000.0) {
		tmp = (t_3 * ((Math.cos(y) * Math.cos(t_1)) - (Math.sin(y) * Math.sin(t_1)))) - t_2;
	} else {
		tmp = t_3 - (0.3333333333333333 * (a / b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	return ((2.0 * math.sqrt(x)) * math.cos((y - ((z * t) / 3.0)))) - (a / (b * 3.0))

↓

def code(x, y, z, t, a, b):
	t_1 = (z * t) * -0.3333333333333333
	t_2 = a / (b * 3.0)
	t_3 = math.sqrt(x) * 2.0
	tmp = 0
	if (z * t) <= -5e+187:
		tmp = (math.sqrt(x) * (-2.0 * math.cos(y))) - t_2
	elif (z * t) <= 40000000.0:
		tmp = (t_3 * ((math.cos(y) * math.cos(t_1)) - (math.sin(y) * math.sin(t_1)))) - t_2
	else:
		tmp = t_3 - (0.3333333333333333 * (a / 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(Float64(z * t) * -0.3333333333333333)
	t_2 = Float64(a / Float64(b * 3.0))
	t_3 = Float64(sqrt(x) * 2.0)
	tmp = 0.0
	if (Float64(z * t) <= -5e+187)
		tmp = Float64(Float64(sqrt(x) * Float64(-2.0 * cos(y))) - t_2);
	elseif (Float64(z * t) <= 40000000.0)
		tmp = Float64(Float64(t_3 * Float64(Float64(cos(y) * cos(t_1)) - Float64(sin(y) * sin(t_1)))) - t_2);
	else
		tmp = Float64(t_3 - Float64(0.3333333333333333 * Float64(a / b)));
	end
	return tmp
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((2.0 * sqrt(x)) * cos((y - ((z * t) / 3.0)))) - (a / (b * 3.0));
end

↓

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z * t) * -0.3333333333333333;
	t_2 = a / (b * 3.0);
	t_3 = sqrt(x) * 2.0;
	tmp = 0.0;
	if ((z * t) <= -5e+187)
		tmp = (sqrt(x) * (-2.0 * cos(y))) - t_2;
	elseif ((z * t) <= 40000000.0)
		tmp = (t_3 * ((cos(y) * cos(t_1)) - (sin(y) * sin(t_1)))) - t_2;
	else
		tmp = t_3 - (0.3333333333333333 * (a / b));
	end
	tmp_2 = 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[(N[(z * t), $MachinePrecision] * -0.3333333333333333), $MachinePrecision]}, Block[{t$95$2 = N[(a / N[(b * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[Sqrt[x], $MachinePrecision] * 2.0), $MachinePrecision]}, If[LessEqual[N[(z * t), $MachinePrecision], -5e+187], N[(N[(N[Sqrt[x], $MachinePrecision] * N[(-2.0 * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 40000000.0], N[(N[(t$95$3 * N[(N[(N[Cos[y], $MachinePrecision] * N[Cos[t$95$1], $MachinePrecision]), $MachinePrecision] - N[(N[Sin[y], $MachinePrecision] * N[Sin[t$95$1], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], N[(t$95$3 - N[(0.3333333333333333 * N[(a / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Target

Original	67.8%
Target	71.0%
Herbie	74.5%

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

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -5.0000000000000001e187

   1. Initial program 23.6%

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

   2. Taylor expanded in z around 0 48.6%

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

   3. Applied egg-rr 34.9%

      \[\leadsto \color{blue}{{\left(8 \cdot {\left(\sqrt{x} \cdot \cos y\right)}^{3}\right)}^{0.3333333333333333}} - \frac{a}{b \cdot 3} \]
      Proof

      [Start] 48.6	\[ \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{a}{b \cdot 3} \]
      add-cbrt-cube [=>] 43.1	\[ \color{blue}{\sqrt[3]{\left(\left(\left(2 \cdot \sqrt{x}\right) \cdot \cos y\right) \cdot \left(\left(2 \cdot \sqrt{x}\right) \cdot \cos y\right)\right) \cdot \left(\left(2 \cdot \sqrt{x}\right) \cdot \cos y\right)}} - \frac{a}{b \cdot 3} \]
      unpow3 [<=] 43.1	\[ \sqrt[3]{\color{blue}{{\left(\left(2 \cdot \sqrt{x}\right) \cdot \cos y\right)}^{3}}} - \frac{a}{b \cdot 3} \]
      pow1/3 [=>] 34.9	\[ \color{blue}{{\left({\left(\left(2 \cdot \sqrt{x}\right) \cdot \cos y\right)}^{3}\right)}^{0.3333333333333333}} - \frac{a}{b \cdot 3} \]
      associate-*l* [=>] 34.9	\[ {\left({\color{blue}{\left(2 \cdot \left(\sqrt{x} \cdot \cos y\right)\right)}}^{3}\right)}^{0.3333333333333333} - \frac{a}{b \cdot 3} \]
      cube-prod [=>] 34.9	\[ {\color{blue}{\left({2}^{3} \cdot {\left(\sqrt{x} \cdot \cos y\right)}^{3}\right)}}^{0.3333333333333333} - \frac{a}{b \cdot 3} \]
      metadata-eval [=>] 34.9	\[ {\left(\color{blue}{8} \cdot {\left(\sqrt{x} \cdot \cos y\right)}^{3}\right)}^{0.3333333333333333} - \frac{a}{b \cdot 3} \]

   4. Simplified 43.1%

      \[\leadsto \color{blue}{\sqrt[3]{8 \cdot {\left(\sqrt{x} \cdot \cos y\right)}^{3}}} - \frac{a}{b \cdot 3} \]
      Proof

      [Start] 34.9	\[ {\left(8 \cdot {\left(\sqrt{x} \cdot \cos y\right)}^{3}\right)}^{0.3333333333333333} - \frac{a}{b \cdot 3} \]
      unpow1/3 [=>] 43.1	\[ \color{blue}{\sqrt[3]{8 \cdot {\left(\sqrt{x} \cdot \cos y\right)}^{3}}} - \frac{a}{b \cdot 3} \]

   5. Applied egg-rr 48.6%

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

      [Start] 43.1	\[ \sqrt[3]{8 \cdot {\left(\sqrt{x} \cdot \cos y\right)}^{3}} - \frac{a}{b \cdot 3} \]
      add-cube-cbrt [=>] 43.1	\[ \color{blue}{\left(\sqrt[3]{\sqrt[3]{8 \cdot {\left(\sqrt{x} \cdot \cos y\right)}^{3}}} \cdot \sqrt[3]{\sqrt[3]{8 \cdot {\left(\sqrt{x} \cdot \cos y\right)}^{3}}}\right) \cdot \sqrt[3]{\sqrt[3]{8 \cdot {\left(\sqrt{x} \cdot \cos y\right)}^{3}}}} - \frac{a}{b \cdot 3} \]
      pow3 [=>] 43.1	\[ \color{blue}{{\left(\sqrt[3]{\sqrt[3]{8 \cdot {\left(\sqrt{x} \cdot \cos y\right)}^{3}}}\right)}^{3}} - \frac{a}{b \cdot 3} \]
      cbrt-prod [=>] 43.2	\[ {\left(\sqrt[3]{\color{blue}{\sqrt[3]{8} \cdot \sqrt[3]{{\left(\sqrt{x} \cdot \cos y\right)}^{3}}}}\right)}^{3} - \frac{a}{b \cdot 3} \]
      metadata-eval [<=] 43.2	\[ {\left(\sqrt[3]{\sqrt[3]{\color{blue}{4 \cdot 2}} \cdot \sqrt[3]{{\left(\sqrt{x} \cdot \cos y\right)}^{3}}}\right)}^{3} - \frac{a}{b \cdot 3} \]
      metadata-eval [<=] 43.2	\[ {\left(\sqrt[3]{\sqrt[3]{\color{blue}{\left(2 \cdot 2\right)} \cdot 2} \cdot \sqrt[3]{{\left(\sqrt{x} \cdot \cos y\right)}^{3}}}\right)}^{3} - \frac{a}{b \cdot 3} \]
      add-cbrt-cube [<=] 43.2	\[ {\left(\sqrt[3]{\color{blue}{2} \cdot \sqrt[3]{{\left(\sqrt{x} \cdot \cos y\right)}^{3}}}\right)}^{3} - \frac{a}{b \cdot 3} \]
      rem-cbrt-cube [=>] 48.6	\[ {\left(\sqrt[3]{2 \cdot \color{blue}{\left(\sqrt{x} \cdot \cos y\right)}}\right)}^{3} - \frac{a}{b \cdot 3} \]
      *-commutative [=>] 48.6	\[ {\left(\sqrt[3]{2 \cdot \color{blue}{\left(\cos y \cdot \sqrt{x}\right)}}\right)}^{3} - \frac{a}{b \cdot 3} \]
      associate-*r* [=>] 48.6	\[ {\left(\sqrt[3]{\color{blue}{\left(2 \cdot \cos y\right) \cdot \sqrt{x}}}\right)}^{3} - \frac{a}{b \cdot 3} \]
      *-commutative [=>] 48.6	\[ {\left(\sqrt[3]{\color{blue}{\sqrt{x} \cdot \left(2 \cdot \cos y\right)}}\right)}^{3} - \frac{a}{b \cdot 3} \]
      *-commutative [=>] 48.6	\[ {\left(\sqrt[3]{\sqrt{x} \cdot \color{blue}{\left(\cos y \cdot 2\right)}}\right)}^{3} - \frac{a}{b \cdot 3} \]

   6. Taylor expanded in x around -inf 0.0%

      \[\leadsto \color{blue}{2 \cdot \left(\left({\left(\sqrt{-1}\right)}^{2} \cdot \cos y\right) \cdot \left({1}^{0.16666666666666666} \cdot \sqrt{x}\right)\right)} - \frac{a}{b \cdot 3} \]

   7. Simplified 48.8%

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

      [Start] 0.0	\[ 2 \cdot \left(\left({\left(\sqrt{-1}\right)}^{2} \cdot \cos y\right) \cdot \left({1}^{0.16666666666666666} \cdot \sqrt{x}\right)\right) - \frac{a}{b \cdot 3} \]
      associate-*r* [=>] 0.0	\[ \color{blue}{\left(2 \cdot \left({\left(\sqrt{-1}\right)}^{2} \cdot \cos y\right)\right) \cdot \left({1}^{0.16666666666666666} \cdot \sqrt{x}\right)} - \frac{a}{b \cdot 3} \]
      *-commutative [=>] 0.0	\[ \color{blue}{\left({1}^{0.16666666666666666} \cdot \sqrt{x}\right) \cdot \left(2 \cdot \left({\left(\sqrt{-1}\right)}^{2} \cdot \cos y\right)\right)} - \frac{a}{b \cdot 3} \]
      pow-base-1 [=>] 0.0	\[ \left(\color{blue}{1} \cdot \sqrt{x}\right) \cdot \left(2 \cdot \left({\left(\sqrt{-1}\right)}^{2} \cdot \cos y\right)\right) - \frac{a}{b \cdot 3} \]
      *-lft-identity [=>] 0.0	\[ \color{blue}{\sqrt{x}} \cdot \left(2 \cdot \left({\left(\sqrt{-1}\right)}^{2} \cdot \cos y\right)\right) - \frac{a}{b \cdot 3} \]
      associate-*r* [=>] 0.0	\[ \sqrt{x} \cdot \color{blue}{\left(\left(2 \cdot {\left(\sqrt{-1}\right)}^{2}\right) \cdot \cos y\right)} - \frac{a}{b \cdot 3} \]
      unpow2 [=>] 0.0	\[ \sqrt{x} \cdot \left(\left(2 \cdot \color{blue}{\left(\sqrt{-1} \cdot \sqrt{-1}\right)}\right) \cdot \cos y\right) - \frac{a}{b \cdot 3} \]
      rem-square-sqrt [=>] 48.8	\[ \sqrt{x} \cdot \left(\left(2 \cdot \color{blue}{-1}\right) \cdot \cos y\right) - \frac{a}{b \cdot 3} \]
      metadata-eval [=>] 48.8	\[ \sqrt{x} \cdot \left(\color{blue}{-2} \cdot \cos y\right) - \frac{a}{b \cdot 3} \]

   if -5.0000000000000001e187 < (*.f64 z t) < 4e7

   1. Initial program 88.6%

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

   2. Applied egg-rr 89.3%

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

      [Start] 88.6	\[ \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
      sub-neg [=>] 88.6	\[ \left(2 \cdot \sqrt{x}\right) \cdot \cos \color{blue}{\left(y + \left(-\frac{z \cdot t}{3}\right)\right)} - \frac{a}{b \cdot 3} \]
      cos-sum [=>] 89.3	\[ \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\left(\cos y \cdot \cos \left(-\frac{z \cdot t}{3}\right) - \sin y \cdot \sin \left(-\frac{z \cdot t}{3}\right)\right)} - \frac{a}{b \cdot 3} \]
      div-inv [=>] 89.3	\[ \left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \cos \left(-\color{blue}{\left(z \cdot t\right) \cdot \frac{1}{3}}\right) - \sin y \cdot \sin \left(-\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]
      distribute-rgt-neg-in [=>] 89.3	\[ \left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \cos \color{blue}{\left(\left(z \cdot t\right) \cdot \left(-\frac{1}{3}\right)\right)} - \sin y \cdot \sin \left(-\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]
      metadata-eval [=>] 89.3	\[ \left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \cos \left(\left(z \cdot t\right) \cdot \left(-\color{blue}{0.3333333333333333}\right)\right) - \sin y \cdot \sin \left(-\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]
      metadata-eval [=>] 89.3	\[ \left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \cos \left(\left(z \cdot t\right) \cdot \color{blue}{-0.3333333333333333}\right) - \sin y \cdot \sin \left(-\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]
      div-inv [=>] 89.3	\[ \left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \cos \left(\left(z \cdot t\right) \cdot -0.3333333333333333\right) - \sin y \cdot \sin \left(-\color{blue}{\left(z \cdot t\right) \cdot \frac{1}{3}}\right)\right) - \frac{a}{b \cdot 3} \]
      distribute-rgt-neg-in [=>] 89.3	\[ \left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \cos \left(\left(z \cdot t\right) \cdot -0.3333333333333333\right) - \sin y \cdot \sin \color{blue}{\left(\left(z \cdot t\right) \cdot \left(-\frac{1}{3}\right)\right)}\right) - \frac{a}{b \cdot 3} \]
      metadata-eval [=>] 89.3	\[ \left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \cos \left(\left(z \cdot t\right) \cdot -0.3333333333333333\right) - \sin y \cdot \sin \left(\left(z \cdot t\right) \cdot \left(-\color{blue}{0.3333333333333333}\right)\right)\right) - \frac{a}{b \cdot 3} \]
      metadata-eval [=>] 89.3	\[ \left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \cos \left(\left(z \cdot t\right) \cdot -0.3333333333333333\right) - \sin y \cdot \sin \left(\left(z \cdot t\right) \cdot \color{blue}{-0.3333333333333333}\right)\right) - \frac{a}{b \cdot 3} \]

   if 4e7 < (*.f64 z t)

   1. Initial program 35.1%

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

   2. Taylor expanded in z around 0 47.9%

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

   3. Taylor expanded in y around 0 48.1%

      \[\leadsto \color{blue}{2 \cdot \sqrt{x} - 0.3333333333333333 \cdot \frac{a}{b}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+187}:\\ \;\;\;\;\sqrt{x} \cdot \left(-2 \cdot \cos y\right) - \frac{a}{b \cdot 3}\\ \mathbf{elif}\;z \cdot t \leq 40000000:\\ \;\;\;\;\left(\sqrt{x} \cdot 2\right) \cdot \left(\cos y \cdot \cos \left(\left(z \cdot t\right) \cdot -0.3333333333333333\right) - \sin y \cdot \sin \left(\left(z \cdot t\right) \cdot -0.3333333333333333\right)\right) - \frac{a}{b \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot 2 - 0.3333333333333333 \cdot \frac{a}{b}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	73.5%
Cost	19776

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

Alternative 2
Accuracy	68.1%
Cost	14024

\[\begin{array}{l} t_1 := \frac{a}{b \cdot 3}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-51}:\\ \;\;\;\;\sqrt{x} \cdot 2 - t_1\\ \mathbf{elif}\;t_1 \leq 10^{-137}:\\ \;\;\;\;\sqrt{x} \cdot \left(\cos y \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(2, \sqrt{x}, \frac{\frac{a}{-3}}{b}\right)\\ \end{array} \]

Alternative 3
Accuracy	68.1%
Cost	13897

\[\begin{array}{l} t_1 := \frac{a}{b \cdot 3}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-51} \lor \neg \left(t_1 \leq 10^{-137}\right):\\ \;\;\;\;\sqrt{x} \cdot 2 - t_1\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(\cos y \cdot 2\right)\\ \end{array} \]

Alternative 4
Accuracy	73.4%
Cost	13504

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

Alternative 5
Accuracy	73.5%
Cost	13504

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

Alternative 6
Accuracy	60.7%
Cost	6976

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

Alternative 7
Accuracy	60.8%
Cost	6976

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

Alternative 8
Accuracy	43.1%
Cost	320

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

Alternative 9
Accuracy	43.1%
Cost	320

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

Alternative 10
Accuracy	43.1%
Cost	320

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

Alternative 11
Accuracy	43.2%
Cost	320

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

Reproduce

herbie shell --seed 2023135 
(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))))