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

Percentage Accurate: 70.0% → 77.1%

Time: 22.4s

Alternatives: 8

Speedup: 1.0×

Specification

Math

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

FPCore

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

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));
}

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

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));
}

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))

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

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

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]

Initial Program: 70.0% accurate, 1.0× speedup

Math

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

FPCore

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

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));
}

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

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));
}

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))

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

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

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]

Alternative 1: 77.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := 2 \cdot \sqrt{x}\\ t_2 := \frac{a}{3 \cdot b}\\ \mathbf{if}\;\cos \left(y - \frac{z \cdot t}{3}\right) \leq 0.75:\\ \;\;\;\;t\_1 \cdot \left(\cos y \cdot \cos \left(z \cdot \left(t \cdot -0.3333333333333333\right)\right) + \sin y \cdot \sin \left(z \cdot \frac{t}{3}\right)\right) - t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1 \cdot \left|\cos y\right| - t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 2.0 (sqrt x))) (t_2 (/ a (* 3.0 b))))
   (if (<= (cos (- y (/ (* z t) 3.0))) 0.75)
     (-
      (*
       t_1
       (+
        (* (cos y) (cos (* z (* t -0.3333333333333333))))
        (* (sin y) (sin (* z (/ t 3.0))))))
      t_2)
     (- (* t_1 (fabs (cos y))) t_2))))

C

assert(x < y && y < z && z < t && t < a && a < b);
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 tmp;
	if (cos((y - ((z * t) / 3.0))) <= 0.75) {
		tmp = (t_1 * ((cos(y) * cos((z * (t * -0.3333333333333333)))) + (sin(y) * sin((z * (t / 3.0)))))) - t_2;
	} else {
		tmp = (t_1 * fabs(cos(y))) - t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this 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) :: tmp
    t_1 = 2.0d0 * sqrt(x)
    t_2 = a / (3.0d0 * b)
    if (cos((y - ((z * t) / 3.0d0))) <= 0.75d0) then
        tmp = (t_1 * ((cos(y) * cos((z * (t * (-0.3333333333333333d0))))) + (sin(y) * sin((z * (t / 3.0d0)))))) - t_2
    else
        tmp = (t_1 * abs(cos(y))) - t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 2.0 * Math.sqrt(x);
	double t_2 = a / (3.0 * b);
	double tmp;
	if (Math.cos((y - ((z * t) / 3.0))) <= 0.75) {
		tmp = (t_1 * ((Math.cos(y) * Math.cos((z * (t * -0.3333333333333333)))) + (Math.sin(y) * Math.sin((z * (t / 3.0)))))) - t_2;
	} else {
		tmp = (t_1 * Math.abs(Math.cos(y))) - t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = 2.0 * math.sqrt(x)
	t_2 = a / (3.0 * b)
	tmp = 0
	if math.cos((y - ((z * t) / 3.0))) <= 0.75:
		tmp = (t_1 * ((math.cos(y) * math.cos((z * (t * -0.3333333333333333)))) + (math.sin(y) * math.sin((z * (t / 3.0)))))) - t_2
	else:
		tmp = (t_1 * math.fabs(math.cos(y))) - t_2
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(2.0 * sqrt(x))
	t_2 = Float64(a / Float64(3.0 * b))
	tmp = 0.0
	if (cos(Float64(y - Float64(Float64(z * t) / 3.0))) <= 0.75)
		tmp = Float64(Float64(t_1 * Float64(Float64(cos(y) * cos(Float64(z * Float64(t * -0.3333333333333333)))) + Float64(sin(y) * sin(Float64(z * Float64(t / 3.0)))))) - t_2);
	else
		tmp = Float64(Float64(t_1 * abs(cos(y))) - t_2);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 2.0 * sqrt(x);
	t_2 = a / (3.0 * b);
	tmp = 0.0;
	if (cos((y - ((z * t) / 3.0))) <= 0.75)
		tmp = (t_1 * ((cos(y) * cos((z * (t * -0.3333333333333333)))) + (sin(y) * sin((z * (t / 3.0)))))) - t_2;
	else
		tmp = (t_1 * abs(cos(y))) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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]}, If[LessEqual[N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 0.75], N[(N[(t$95$1 * N[(N[(N[Cos[y], $MachinePrecision] * N[Cos[N[(z * N[(t * -0.3333333333333333), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + N[(N[Sin[y], $MachinePrecision] * N[Sin[N[(z * N[(t / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], N[(N[(t$95$1 * N[Abs[N[Cos[y], $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64)))) < 0.75

   1. Initial program 71.6%

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

      1. *-commutative 71.6%

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

      2. *-commutative 71.6%

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

      3. *-commutative 71.6%

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

      4. *-commutative 71.6%

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

      5. associate-/l* 71.6%

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

      6. *-commutative 71.6%

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

   3. Simplified 71.6%

      \[\leadsto \color{blue}{\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - z \cdot \frac{t}{3}\right) - \frac{a}{3 \cdot b}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. add-sqr-sqrt 45.8%

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

      2. pow2 45.8%

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

      3. associate-*r/ 45.7%

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

      4. associate-*r/ 45.8%

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

      5. add-sqr-sqrt 45.8%

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

      6. sqrt-unprod 56.9%

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

      7. associate-*r/ 56.9%

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

      8. associate-*r/ 56.9%

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

      9. frac-times 57.1%

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

      10. metadata-eval 57.1%

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - {\left(\sqrt{\sqrt{\frac{\left(z \cdot t\right) \cdot \left(z \cdot t\right)}{\color{blue}{9}}}}\right)}^{2}\right) - \frac{a}{3 \cdot b} \]

      11. metadata-eval 57.1%

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

      12. frac-times 56.9%

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

      13. sqrt-unprod 36.3%

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

      14. add-sqr-sqrt 36.3%

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

      15. associate-/l* 36.1%

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

      16. div-inv 36.3%

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

      17. metadata-eval 36.3%

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

   6. Applied egg-rr 36.3%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \color{blue}{{\left(\sqrt{z \cdot \left(t \cdot -0.3333333333333333\right)}\right)}^{2}}\right) - \frac{a}{3 \cdot b} \]
   7. Step-by-step derivation

      1. cos-diff 36.6%

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

      2. unpow2 36.6%

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

      3. add-sqr-sqrt 36.0%

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

      4. unpow2 36.0%

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

      5. add-sqr-sqrt 72.1%

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

   8. Applied egg-rr 72.1%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\left(\cos y \cdot \cos \left(z \cdot \left(t \cdot -0.3333333333333333\right)\right) + \sin y \cdot \sin \left(z \cdot \left(t \cdot -0.3333333333333333\right)\right)\right)} - \frac{a}{3 \cdot b} \]
   9. Step-by-step derivation

      1. add-sqr-sqrt 36.7%

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

      2. sqrt-unprod 57.4%

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

      3. swap-sqr 57.5%

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

      4. metadata-eval 57.5%

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \cos \left(z \cdot \left(t \cdot -0.3333333333333333\right)\right) + \sin y \cdot \sin \left(z \cdot \sqrt{\left(t \cdot t\right) \cdot \color{blue}{0.1111111111111111}}\right)\right) - \frac{a}{3 \cdot b} \]

      5. metadata-eval 57.5%

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

      6. metadata-eval 57.5%

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

      7. metadata-eval 57.5%

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

      8. swap-sqr 57.4%

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

      9. metadata-eval 57.4%

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

      10. metadata-eval 57.4%

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \cos \left(z \cdot \left(t \cdot -0.3333333333333333\right)\right) + \sin y \cdot \sin \left(z \cdot \sqrt{\left(t \cdot \color{blue}{\frac{1}{3}}\right) \cdot \left(t \cdot \left(--0.3333333333333333\right)\right)}\right)\right) - \frac{a}{3 \cdot b} \]

      11. div-inv 57.6%

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

      12. metadata-eval 57.6%

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

      13. metadata-eval 57.6%

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \cos \left(z \cdot \left(t \cdot -0.3333333333333333\right)\right) + \sin y \cdot \sin \left(z \cdot \sqrt{\frac{t}{3} \cdot \left(t \cdot \color{blue}{\frac{1}{3}}\right)}\right)\right) - \frac{a}{3 \cdot b} \]

      14. div-inv 57.6%

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

      15. sqrt-unprod 37.3%

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

      16. add-sqr-sqrt 74.0%

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

   10. Applied egg-rr 74.0%

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

   if 0.75 < (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))

   1. Initial program 65.1%

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

      1. *-commutative 65.1%

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

      2. *-commutative 65.1%

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

      3. *-commutative 65.1%

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

      4. *-commutative 65.1%

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

      5. associate-/l* 65.1%

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

      6. *-commutative 65.1%

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

   3. Simplified 65.1%

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

   5. Taylor expanded in z around 0 78.4%

      \[\leadsto \color{blue}{2 \cdot \left(\sqrt{x} \cdot \cos y\right)} - \frac{a}{3 \cdot b} \]
   6. Step-by-step derivation

      1. associate-*r* 78.4%

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

      2. *-commutative 78.4%

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

      3. *-commutative 78.4%

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

   7. Simplified 78.4%

      \[\leadsto \color{blue}{\cos y \cdot \left(\sqrt{x} \cdot 2\right)} - \frac{a}{3 \cdot b} \]
   8. Step-by-step derivation

      1. add-sqr-sqrt 73.7%

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

      2. sqrt-unprod 78.7%

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

      3. pow2 78.7%

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

   9. Applied egg-rr 78.7%

      \[\leadsto \color{blue}{\sqrt{{\cos y}^{2}}} \cdot \left(\sqrt{x} \cdot 2\right) - \frac{a}{3 \cdot b} \]
   10. Step-by-step derivation

       1. unpow2 78.7%

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

       2. rem-sqrt-square 78.7%

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

   11. Simplified 78.7%

       \[\leadsto \color{blue}{\left|\cos y\right|} \cdot \left(\sqrt{x} \cdot 2\right) - \frac{a}{3 \cdot b} \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\cos \left(y - \frac{z \cdot t}{3}\right) \leq 0.75:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \cos \left(z \cdot \left(t \cdot -0.3333333333333333\right)\right) + \sin y \cdot \sin \left(z \cdot \frac{t}{3}\right)\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \left|\cos y\right| - \frac{a}{3 \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 76.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \left(2 \cdot \sqrt{x}\right) \cdot \cos y - {\left(3 \cdot \frac{b}{a}\right)}^{-1} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (- (* (* 2.0 (sqrt x)) (cos y)) (pow (* 3.0 (/ b a)) -1.0)))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	return ((2.0 * sqrt(x)) * cos(y)) - pow((3.0 * (b / a)), -1.0);
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this 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
    code = ((2.0d0 * sqrt(x)) * cos(y)) - ((3.0d0 * (b / a)) ** (-1.0d0))
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
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)) - Math.pow((3.0 * (b / a)), -1.0);
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	return ((2.0 * math.sqrt(x)) * math.cos(y)) - math.pow((3.0 * (b / a)), -1.0)

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(2.0 * sqrt(x)) * cos(y)) - (Float64(3.0 * Float64(b / a)) ^ -1.0))
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = ((2.0 * sqrt(x)) * cos(y)) - ((3.0 * (b / a)) ^ -1.0);
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[Power[N[(3.0 * N[(b / a), $MachinePrecision]), $MachinePrecision], -1.0], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 68.2%

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

   1. *-commutative 68.2%

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

   2. *-commutative 68.2%

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

   3. *-commutative 68.2%

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

   4. *-commutative 68.2%

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

   5. associate-/l* 68.3%

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

   6. *-commutative 68.3%

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

3. Simplified 68.3%

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

5. Taylor expanded in z around 0 74.9%

   \[\leadsto \color{blue}{2 \cdot \left(\sqrt{x} \cdot \cos y\right)} - \frac{a}{3 \cdot b} \]
6. Step-by-step derivation

   1. associate-*r* 74.9%

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

   2. *-commutative 74.9%

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

   3. *-commutative 74.9%

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

7. Simplified 74.9%

   \[\leadsto \color{blue}{\cos y \cdot \left(\sqrt{x} \cdot 2\right)} - \frac{a}{3 \cdot b} \]
8. Step-by-step derivation

   1. *-commutative 74.9%

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

   2. clear-num 74.9%

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

   3. inv-pow 74.9%

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

   4. *-commutative 74.9%

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

   5. *-un-lft-identity 74.9%

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

   6. times-frac 75.0%

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

   7. metadata-eval 75.0%

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

9. Applied egg-rr 75.0%

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

10. Final simplification 75.0%

    \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - {\left(3 \cdot \frac{b}{a}\right)}^{-1} \]
11. Add Preprocessing

Alternative 3: 65.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := 2 \cdot \sqrt{x}\\ \mathbf{if}\;b \leq -8.2 \cdot 10^{+183}:\\ \;\;\;\;t\_1 \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;t\_1 - {\left(3 \cdot \frac{b}{a}\right)}^{-1}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 2.0 (sqrt x))))
   (if (<= b -8.2e+183) (* t_1 (cos y)) (- t_1 (pow (* 3.0 (/ b a)) -1.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 2.0 * sqrt(x);
	double tmp;
	if (b <= -8.2e+183) {
		tmp = t_1 * cos(y);
	} else {
		tmp = t_1 - pow((3.0 * (b / a)), -1.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this 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) :: tmp
    t_1 = 2.0d0 * sqrt(x)
    if (b <= (-8.2d+183)) then
        tmp = t_1 * cos(y)
    else
        tmp = t_1 - ((3.0d0 * (b / a)) ** (-1.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 2.0 * Math.sqrt(x);
	double tmp;
	if (b <= -8.2e+183) {
		tmp = t_1 * Math.cos(y);
	} else {
		tmp = t_1 - Math.pow((3.0 * (b / a)), -1.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = 2.0 * math.sqrt(x)
	tmp = 0
	if b <= -8.2e+183:
		tmp = t_1 * math.cos(y)
	else:
		tmp = t_1 - math.pow((3.0 * (b / a)), -1.0)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(2.0 * sqrt(x))
	tmp = 0.0
	if (b <= -8.2e+183)
		tmp = Float64(t_1 * cos(y));
	else
		tmp = Float64(t_1 - (Float64(3.0 * Float64(b / a)) ^ -1.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 2.0 * sqrt(x);
	tmp = 0.0;
	if (b <= -8.2e+183)
		tmp = t_1 * cos(y);
	else
		tmp = t_1 - ((3.0 * (b / a)) ^ -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8.2e+183], N[(t$95$1 * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[Power[N[(3.0 * N[(b / a), $MachinePrecision]), $MachinePrecision], -1.0], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -8.20000000000000029e183

   1. Initial program 59.6%

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

      1. *-commutative 59.6%

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

      2. *-commutative 59.6%

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

      3. *-commutative 59.6%

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

      4. *-commutative 59.6%

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

      5. associate-/l* 60.5%

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

      6. *-commutative 60.5%

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

   3. Simplified 60.5%

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

   5. Taylor expanded in z around 0 61.5%

      \[\leadsto \color{blue}{2 \cdot \left(\sqrt{x} \cdot \cos y\right)} - \frac{a}{3 \cdot b} \]
   6. Step-by-step derivation

      1. associate-*r* 61.5%

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

      2. *-commutative 61.5%

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

      3. *-commutative 61.5%

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

   7. Simplified 61.5%

      \[\leadsto \color{blue}{\cos y \cdot \left(\sqrt{x} \cdot 2\right)} - \frac{a}{3 \cdot b} \]
   8. Step-by-step derivation

      1. *-commutative 61.5%

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

      2. clear-num 61.5%

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

      3. inv-pow 61.5%

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

      4. *-commutative 61.5%

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

      5. *-un-lft-identity 61.5%

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

      6. times-frac 61.5%

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

      7. metadata-eval 61.5%

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

   9. Applied egg-rr 61.5%

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

   10. Taylor expanded in x around inf 55.7%

       \[\leadsto \color{blue}{2 \cdot \left(\sqrt{x} \cdot \cos y\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 55.7%

          \[\leadsto \color{blue}{\left(2 \cdot \sqrt{x}\right) \cdot \cos y} \]

       2. *-commutative 55.7%

          \[\leadsto \color{blue}{\left(\sqrt{x} \cdot 2\right)} \cdot \cos y \]

       3. *-commutative 55.7%

          \[\leadsto \color{blue}{\cos y \cdot \left(\sqrt{x} \cdot 2\right)} \]

       4. *-commutative 55.7%

          \[\leadsto \cos y \cdot \color{blue}{\left(2 \cdot \sqrt{x}\right)} \]

   12. Simplified 55.7%

       \[\leadsto \color{blue}{\cos y \cdot \left(2 \cdot \sqrt{x}\right)} \]

   if -8.20000000000000029e183 < b

   1. Initial program 69.5%

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

      1. *-commutative 69.5%

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

      2. *-commutative 69.5%

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

      3. *-commutative 69.5%

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

      4. *-commutative 69.5%

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

      5. associate-/l* 69.4%

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

      6. *-commutative 69.4%

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

   3. Simplified 69.4%

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

   5. Taylor expanded in z around 0 76.9%

      \[\leadsto \color{blue}{2 \cdot \left(\sqrt{x} \cdot \cos y\right)} - \frac{a}{3 \cdot b} \]
   6. Step-by-step derivation

      1. associate-*r* 76.9%

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

      2. *-commutative 76.9%

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

      3. *-commutative 76.9%

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

   7. Simplified 76.9%

      \[\leadsto \color{blue}{\cos y \cdot \left(\sqrt{x} \cdot 2\right)} - \frac{a}{3 \cdot b} \]
   8. Step-by-step derivation

      1. *-commutative 76.9%

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

      2. clear-num 76.8%

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

      3. inv-pow 76.8%

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

      4. *-commutative 76.8%

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

      5. *-un-lft-identity 76.8%

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

      6. times-frac 76.9%

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

      7. metadata-eval 76.9%

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

   9. Applied egg-rr 76.9%

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

   10. Taylor expanded in y around 0 67.3%

       \[\leadsto \color{blue}{2 \cdot \sqrt{x}} - {\left(3 \cdot \frac{b}{a}\right)}^{-1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.2 \cdot 10^{+183}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x} - {\left(3 \cdot \frac{b}{a}\right)}^{-1}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{a}{3 \cdot b} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (- (* (* 2.0 (sqrt x)) (cos y)) (/ a (* 3.0 b))))

C

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

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this 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
    code = ((2.0d0 * sqrt(x)) * cos(y)) - (a / (3.0d0 * b))
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
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)) - (a / (3.0 * b));
}

Python

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

Julia

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

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = ((2.0 * sqrt(x)) * cos(y)) - (a / (3.0 * b));
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 68.2%

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

   1. *-commutative 68.2%

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

   2. *-commutative 68.2%

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

   3. *-commutative 68.2%

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

   4. *-commutative 68.2%

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

   5. associate-/l* 68.3%

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

   6. *-commutative 68.3%

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

3. Simplified 68.3%

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

5. Taylor expanded in z around 0 74.9%

   \[\leadsto \color{blue}{2 \cdot \left(\sqrt{x} \cdot \cos y\right)} - \frac{a}{3 \cdot b} \]
6. Step-by-step derivation

   1. associate-*r* 74.9%

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

   2. *-commutative 74.9%

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

   3. *-commutative 74.9%

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

7. Simplified 74.9%

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

8. Final simplification 74.9%

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

Alternative 5: 65.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := 2 \cdot \sqrt{x}\\ \mathbf{if}\;b \leq -3.8 \cdot 10^{+183}:\\ \;\;\;\;t\_1 \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;t\_1 - \frac{a}{3 \cdot b}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 2.0 (sqrt x))))
   (if (<= b -3.8e+183) (* t_1 (cos y)) (- t_1 (/ a (* 3.0 b))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 2.0 * sqrt(x);
	double tmp;
	if (b <= -3.8e+183) {
		tmp = t_1 * cos(y);
	} else {
		tmp = t_1 - (a / (3.0 * b));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this 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) :: tmp
    t_1 = 2.0d0 * sqrt(x)
    if (b <= (-3.8d+183)) then
        tmp = t_1 * cos(y)
    else
        tmp = t_1 - (a / (3.0d0 * b))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 2.0 * Math.sqrt(x);
	double tmp;
	if (b <= -3.8e+183) {
		tmp = t_1 * Math.cos(y);
	} else {
		tmp = t_1 - (a / (3.0 * b));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = 2.0 * math.sqrt(x)
	tmp = 0
	if b <= -3.8e+183:
		tmp = t_1 * math.cos(y)
	else:
		tmp = t_1 - (a / (3.0 * b))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(2.0 * sqrt(x))
	tmp = 0.0
	if (b <= -3.8e+183)
		tmp = Float64(t_1 * cos(y));
	else
		tmp = Float64(t_1 - Float64(a / Float64(3.0 * b)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 2.0 * sqrt(x);
	tmp = 0.0;
	if (b <= -3.8e+183)
		tmp = t_1 * cos(y);
	else
		tmp = t_1 - (a / (3.0 * b));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.8e+183], N[(t$95$1 * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -3.80000000000000001e183

   1. Initial program 59.6%

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

      1. *-commutative 59.6%

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

      2. *-commutative 59.6%

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

      3. *-commutative 59.6%

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

      4. *-commutative 59.6%

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

      5. associate-/l* 60.5%

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

      6. *-commutative 60.5%

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

   3. Simplified 60.5%

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

   5. Taylor expanded in z around 0 61.5%

      \[\leadsto \color{blue}{2 \cdot \left(\sqrt{x} \cdot \cos y\right)} - \frac{a}{3 \cdot b} \]
   6. Step-by-step derivation

      1. associate-*r* 61.5%

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

      2. *-commutative 61.5%

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

      3. *-commutative 61.5%

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

   7. Simplified 61.5%

      \[\leadsto \color{blue}{\cos y \cdot \left(\sqrt{x} \cdot 2\right)} - \frac{a}{3 \cdot b} \]
   8. Step-by-step derivation

      1. *-commutative 61.5%

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

      2. clear-num 61.5%

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

      3. inv-pow 61.5%

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

      4. *-commutative 61.5%

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

      5. *-un-lft-identity 61.5%

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

      6. times-frac 61.5%

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

      7. metadata-eval 61.5%

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

   9. Applied egg-rr 61.5%

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

   10. Taylor expanded in x around inf 55.7%

       \[\leadsto \color{blue}{2 \cdot \left(\sqrt{x} \cdot \cos y\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 55.7%

          \[\leadsto \color{blue}{\left(2 \cdot \sqrt{x}\right) \cdot \cos y} \]

       2. *-commutative 55.7%

          \[\leadsto \color{blue}{\left(\sqrt{x} \cdot 2\right)} \cdot \cos y \]

       3. *-commutative 55.7%

          \[\leadsto \color{blue}{\cos y \cdot \left(\sqrt{x} \cdot 2\right)} \]

       4. *-commutative 55.7%

          \[\leadsto \cos y \cdot \color{blue}{\left(2 \cdot \sqrt{x}\right)} \]

   12. Simplified 55.7%

       \[\leadsto \color{blue}{\cos y \cdot \left(2 \cdot \sqrt{x}\right)} \]

   if -3.80000000000000001e183 < b

   1. Initial program 69.5%

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

      1. *-commutative 69.5%

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

      2. *-commutative 69.5%

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

      3. *-commutative 69.5%

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

      4. *-commutative 69.5%

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

      5. associate-/l* 69.4%

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

      6. *-commutative 69.4%

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

   3. Simplified 69.4%

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

   5. Taylor expanded in z around 0 76.9%

      \[\leadsto \color{blue}{2 \cdot \left(\sqrt{x} \cdot \cos y\right)} - \frac{a}{3 \cdot b} \]
   6. Step-by-step derivation

      1. associate-*r* 76.9%

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

      2. *-commutative 76.9%

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

      3. *-commutative 76.9%

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

   7. Simplified 76.9%

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

   8. Taylor expanded in y around 0 67.3%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{+183}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{a}{3 \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 65.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ 2 \cdot \sqrt{x} - \frac{a}{3 \cdot b} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b) :precision binary64 (- (* 2.0 (sqrt x)) (/ a (* 3.0 b))))

C

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

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this 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
    code = (2.0d0 * sqrt(x)) - (a / (3.0d0 * b))
end function

Java

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

Python

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

Julia

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

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = (2.0 * sqrt(x)) - (a / (3.0 * b));
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] - N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 68.2%

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

   1. *-commutative 68.2%

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

   2. *-commutative 68.2%

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

   3. *-commutative 68.2%

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

   4. *-commutative 68.2%

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

   5. associate-/l* 68.3%

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

   6. *-commutative 68.3%

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

3. Simplified 68.3%

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

5. Taylor expanded in z around 0 74.9%

   \[\leadsto \color{blue}{2 \cdot \left(\sqrt{x} \cdot \cos y\right)} - \frac{a}{3 \cdot b} \]
6. Step-by-step derivation

   1. associate-*r* 74.9%

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

   2. *-commutative 74.9%

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

   3. *-commutative 74.9%

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

7. Simplified 74.9%

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

8. Taylor expanded in y around 0 63.9%

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

Alternative 7: 49.9% accurate, 43.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \frac{-0.3333333333333333}{\frac{b}{a}} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b) :precision binary64 (/ -0.3333333333333333 (/ b a)))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	return -0.3333333333333333 / (b / a);
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this 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
    code = (-0.3333333333333333d0) / (b / a)
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	return -0.3333333333333333 / (b / a);
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	return -0.3333333333333333 / (b / a)

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	return Float64(-0.3333333333333333 / Float64(b / a))
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = -0.3333333333333333 / (b / a);
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(-0.3333333333333333 / N[(b / a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 68.2%

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

3. Simplified 68.4%

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

5. Taylor expanded in a around inf 53.8%

   \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{a}{b}} \]
6. Step-by-step derivation

   1. clear-num 53.8%

      \[\leadsto -0.3333333333333333 \cdot \color{blue}{\frac{1}{\frac{b}{a}}} \]

   2. un-div-inv 53.8%

      \[\leadsto \color{blue}{\frac{-0.3333333333333333}{\frac{b}{a}}} \]

7. Applied egg-rr 53.8%

   \[\leadsto \color{blue}{\frac{-0.3333333333333333}{\frac{b}{a}}} \]
8. Add Preprocessing

Alternative 8: 49.9% accurate, 43.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ -0.3333333333333333 \cdot \frac{a}{b} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b) :precision binary64 (* -0.3333333333333333 (/ a b)))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	return -0.3333333333333333 * (a / b);
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this 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
    code = (-0.3333333333333333d0) * (a / b)
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	return -0.3333333333333333 * (a / b);
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	return -0.3333333333333333 * (a / b)

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	return Float64(-0.3333333333333333 * Float64(a / b))
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = -0.3333333333333333 * (a / b);
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(-0.3333333333333333 * N[(a / b), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 68.2%

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

3. Simplified 68.4%

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

5. Taylor expanded in a around inf 53.8%

   \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{a}{b}} \]
6. Add Preprocessing

Developer Target 1: 73.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{0.3333333333333333}{z}}{t}\\ t_2 := \frac{\frac{a}{3}}{b}\\ t_3 := 2 \cdot \sqrt{x}\\ \mathbf{if}\;z < -1.3793337487235141 \cdot 10^{+129}:\\ \;\;\;\;t\_3 \cdot \cos \left(\frac{1}{y} - t\_1\right) - t\_2\\ \mathbf{elif}\;z < 3.516290613555987 \cdot 10^{+106}:\\ \;\;\;\;\left(\sqrt{x} \cdot 2\right) \cdot \cos \left(y - \frac{t}{3} \cdot z\right) - t\_2\\ \mathbf{else}:\\ \;\;\;\;\cos \left(y - t\_1\right) \cdot t\_3 - \frac{\frac{a}{b}}{3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ 0.3333333333333333 z) t))
        (t_2 (/ (/ a 3.0) b))
        (t_3 (* 2.0 (sqrt x))))
   (if (< z -1.3793337487235141e+129)
     (- (* t_3 (cos (- (/ 1.0 y) t_1))) t_2)
     (if (< z 3.516290613555987e+106)
       (- (* (* (sqrt x) 2.0) (cos (- y (* (/ t 3.0) z)))) t_2)
       (- (* (cos (- y t_1)) t_3) (/ (/ a b) 3.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (0.3333333333333333 / z) / t;
	double t_2 = (a / 3.0) / b;
	double t_3 = 2.0 * sqrt(x);
	double tmp;
	if (z < -1.3793337487235141e+129) {
		tmp = (t_3 * cos(((1.0 / y) - t_1))) - t_2;
	} else if (z < 3.516290613555987e+106) {
		tmp = ((sqrt(x) * 2.0) * cos((y - ((t / 3.0) * z)))) - t_2;
	} else {
		tmp = (cos((y - t_1)) * t_3) - ((a / b) / 3.0);
	}
	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
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (0.3333333333333333d0 / z) / t
    t_2 = (a / 3.0d0) / b
    t_3 = 2.0d0 * sqrt(x)
    if (z < (-1.3793337487235141d+129)) then
        tmp = (t_3 * cos(((1.0d0 / y) - t_1))) - t_2
    else if (z < 3.516290613555987d+106) then
        tmp = ((sqrt(x) * 2.0d0) * cos((y - ((t / 3.0d0) * z)))) - t_2
    else
        tmp = (cos((y - t_1)) * t_3) - ((a / b) / 3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (0.3333333333333333 / z) / t;
	double t_2 = (a / 3.0) / b;
	double t_3 = 2.0 * Math.sqrt(x);
	double tmp;
	if (z < -1.3793337487235141e+129) {
		tmp = (t_3 * Math.cos(((1.0 / y) - t_1))) - t_2;
	} else if (z < 3.516290613555987e+106) {
		tmp = ((Math.sqrt(x) * 2.0) * Math.cos((y - ((t / 3.0) * z)))) - t_2;
	} else {
		tmp = (Math.cos((y - t_1)) * t_3) - ((a / b) / 3.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (0.3333333333333333 / z) / t
	t_2 = (a / 3.0) / b
	t_3 = 2.0 * math.sqrt(x)
	tmp = 0
	if z < -1.3793337487235141e+129:
		tmp = (t_3 * math.cos(((1.0 / y) - t_1))) - t_2
	elif z < 3.516290613555987e+106:
		tmp = ((math.sqrt(x) * 2.0) * math.cos((y - ((t / 3.0) * z)))) - t_2
	else:
		tmp = (math.cos((y - t_1)) * t_3) - ((a / b) / 3.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(0.3333333333333333 / z) / t)
	t_2 = Float64(Float64(a / 3.0) / b)
	t_3 = Float64(2.0 * sqrt(x))
	tmp = 0.0
	if (z < -1.3793337487235141e+129)
		tmp = Float64(Float64(t_3 * cos(Float64(Float64(1.0 / y) - t_1))) - t_2);
	elseif (z < 3.516290613555987e+106)
		tmp = Float64(Float64(Float64(sqrt(x) * 2.0) * cos(Float64(y - Float64(Float64(t / 3.0) * z)))) - t_2);
	else
		tmp = Float64(Float64(cos(Float64(y - t_1)) * t_3) - Float64(Float64(a / b) / 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (0.3333333333333333 / z) / t;
	t_2 = (a / 3.0) / b;
	t_3 = 2.0 * sqrt(x);
	tmp = 0.0;
	if (z < -1.3793337487235141e+129)
		tmp = (t_3 * cos(((1.0 / y) - t_1))) - t_2;
	elseif (z < 3.516290613555987e+106)
		tmp = ((sqrt(x) * 2.0) * cos((y - ((t / 3.0) * z)))) - t_2;
	else
		tmp = (cos((y - t_1)) * t_3) - ((a / b) / 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(0.3333333333333333 / z), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a / 3.0), $MachinePrecision] / b), $MachinePrecision]}, Block[{t$95$3 = N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, If[Less[z, -1.3793337487235141e+129], N[(N[(t$95$3 * N[Cos[N[(N[(1.0 / y), $MachinePrecision] - t$95$1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], If[Less[z, 3.516290613555987e+106], N[(N[(N[(N[Sqrt[x], $MachinePrecision] * 2.0), $MachinePrecision] * N[Cos[N[(y - N[(N[(t / 3.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], N[(N[(N[Cos[N[(y - t$95$1), $MachinePrecision]], $MachinePrecision] * t$95$3), $MachinePrecision] - N[(N[(a / b), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]]]]]]

Reproduce

herbie shell --seed 2024172 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, K"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -1379333748723514100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* (* 2 (sqrt x)) (cos (- (/ 1 y) (/ (/ 3333333333333333/10000000000000000 z) t)))) (/ (/ a 3) b)) (if (< z 35162906135559870000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* (* (sqrt x) 2) (cos (- y (* (/ t 3) z)))) (/ (/ a 3) b)) (- (* (cos (- y (/ (/ 3333333333333333/10000000000000000 z) t))) (* 2 (sqrt x))) (/ (/ a b) 3)))))

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