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

Percentage Accurate: 70.1% → 77.9%

Time: 27.1s

Alternatives: 10

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: 70.1% 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: 77.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \frac{a}{3 \cdot b}\\ t_2 := 2 \cdot \sqrt{x}\\ t_3 := t \cdot \left(z \cdot -0.3333333333333333\right)\\ \mathbf{if}\;\cos \left(y - \frac{z \cdot t}{3}\right) \leq 1:\\ \;\;\;\;t\_2 \cdot \left(\cos t\_3 \cdot \cos y - \sin t\_3 \cdot \sin y\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2 \cdot \cos \left(z \cdot \frac{t \cdot 0.6666666666666666}{1 + \left(1 + t \cdot 0.3333333333333333\right)}\right) - t\_1\\ \end{array} \end{array} \]

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 (/ a (* 3.0 b)))
        (t_2 (* 2.0 (sqrt x)))
        (t_3 (* t (* z -0.3333333333333333))))
   (if (<= (cos (- y (/ (* z t) 3.0))) 1.0)
     (- (* t_2 (- (* (cos t_3) (cos y)) (* (sin t_3) (sin y)))) t_1)
     (-
      (*
       t_2
       (cos
        (*
         z
         (/
          (* t 0.6666666666666666)
          (+ 1.0 (+ 1.0 (* t 0.3333333333333333)))))))
      t_1))))

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 = a / (3.0 * b);
	double t_2 = 2.0 * sqrt(x);
	double t_3 = t * (z * -0.3333333333333333);
	double tmp;
	if (cos((y - ((z * t) / 3.0))) <= 1.0) {
		tmp = (t_2 * ((cos(t_3) * cos(y)) - (sin(t_3) * sin(y)))) - t_1;
	} else {
		tmp = (t_2 * cos((z * ((t * 0.6666666666666666) / (1.0 + (1.0 + (t * 0.3333333333333333))))))) - t_1;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = a / (3.0d0 * b)
    t_2 = 2.0d0 * sqrt(x)
    t_3 = t * (z * (-0.3333333333333333d0))
    if (cos((y - ((z * t) / 3.0d0))) <= 1.0d0) then
        tmp = (t_2 * ((cos(t_3) * cos(y)) - (sin(t_3) * sin(y)))) - t_1
    else
        tmp = (t_2 * cos((z * ((t * 0.6666666666666666d0) / (1.0d0 + (1.0d0 + (t * 0.3333333333333333d0))))))) - t_1
    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 = a / (3.0 * b);
	double t_2 = 2.0 * Math.sqrt(x);
	double t_3 = t * (z * -0.3333333333333333);
	double tmp;
	if (Math.cos((y - ((z * t) / 3.0))) <= 1.0) {
		tmp = (t_2 * ((Math.cos(t_3) * Math.cos(y)) - (Math.sin(t_3) * Math.sin(y)))) - t_1;
	} else {
		tmp = (t_2 * Math.cos((z * ((t * 0.6666666666666666) / (1.0 + (1.0 + (t * 0.3333333333333333))))))) - t_1;
	}
	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 = a / (3.0 * b)
	t_2 = 2.0 * math.sqrt(x)
	t_3 = t * (z * -0.3333333333333333)
	tmp = 0
	if math.cos((y - ((z * t) / 3.0))) <= 1.0:
		tmp = (t_2 * ((math.cos(t_3) * math.cos(y)) - (math.sin(t_3) * math.sin(y)))) - t_1
	else:
		tmp = (t_2 * math.cos((z * ((t * 0.6666666666666666) / (1.0 + (1.0 + (t * 0.3333333333333333))))))) - t_1
	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(a / Float64(3.0 * b))
	t_2 = Float64(2.0 * sqrt(x))
	t_3 = Float64(t * Float64(z * -0.3333333333333333))
	tmp = 0.0
	if (cos(Float64(y - Float64(Float64(z * t) / 3.0))) <= 1.0)
		tmp = Float64(Float64(t_2 * Float64(Float64(cos(t_3) * cos(y)) - Float64(sin(t_3) * sin(y)))) - t_1);
	else
		tmp = Float64(Float64(t_2 * cos(Float64(z * Float64(Float64(t * 0.6666666666666666) / Float64(1.0 + Float64(1.0 + Float64(t * 0.3333333333333333))))))) - t_1);
	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 = a / (3.0 * b);
	t_2 = 2.0 * sqrt(x);
	t_3 = t * (z * -0.3333333333333333);
	tmp = 0.0;
	if (cos((y - ((z * t) / 3.0))) <= 1.0)
		tmp = (t_2 * ((cos(t_3) * cos(y)) - (sin(t_3) * sin(y)))) - t_1;
	else
		tmp = (t_2 * cos((z * ((t * 0.6666666666666666) / (1.0 + (1.0 + (t * 0.3333333333333333))))))) - t_1;
	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[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(z * -0.3333333333333333), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 1.0], N[(N[(t$95$2 * N[(N[(N[Cos[t$95$3], $MachinePrecision] * N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(N[Sin[t$95$3], $MachinePrecision] * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(t$95$2 * N[Cos[N[(z * N[(N[(t * 0.6666666666666666), $MachinePrecision] / N[(1.0 + N[(1.0 + N[(t * 0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64)))) < 1

   1. Initial program 74.4%

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

      1. *-commutative 74.4%

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

      2. *-commutative 74.4%

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

      3. *-commutative 74.4%

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

      4. *-commutative 74.4%

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

      5. associate-/l* 74.5%

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

      6. *-commutative 74.5%

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

   3. Simplified 74.5%

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

      1. associate-*r/ 74.4%

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

      2. div-inv 74.6%

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

      3. metadata-eval 74.6%

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

      4. metadata-eval 74.6%

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

      5. cancel-sign-sub-inv 74.6%

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

      6. metadata-eval 74.6%

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

      7. metadata-eval 74.6%

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

      8. div-inv 74.4%

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

      9. metadata-eval 74.4%

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

      10. frac-2neg 74.4%

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

      11. +-commutative 74.4%

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

      12. cos-sum 76.4%

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

      13. div-inv 76.5%

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

      14. metadata-eval 76.5%

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

      15. associate-*r* 76.1%

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

      16. *-commutative 76.1%

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

      17. associate-*r* 76.2%

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

   6. Applied egg-rr 76.1%

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

   if 1 < (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))

   1. Initial program 0.0%

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

      1. *-commutative 0.0%

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

      2. *-commutative 0.0%

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

      3. *-commutative 0.0%

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

      4. *-commutative 0.0%

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

      5. associate-/l* 0.0%

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

      6. *-commutative 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in y around 0 0.0%

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

      1. cos-neg 0.0%

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

      2. *-commutative 0.0%

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

      3. *-commutative 0.0%

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

      4. associate-*l* 0.0%

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

   7. Simplified 0.0%

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

      1. *-commutative 0.0%

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

      2. metadata-eval 0.0%

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

      3. associate-/r/ 0.0%

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

      4. add-sqr-sqrt 0.0%

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

      5. sqrt-unprod 0.0%

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

      6. clear-num 0.0%

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

      7. div-inv 0.0%

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

      8. metadata-eval 0.0%

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

      9. clear-num 0.0%

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

      10. div-inv 0.0%

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

      11. metadata-eval 0.0%

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

      12. swap-sqr 0.0%

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

      13. metadata-eval 0.0%

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

      14. metadata-eval 0.0%

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

      15. swap-sqr 0.0%

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

      16. sqrt-unprod 0.0%

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

      17. add-sqr-sqrt 0.0%

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

      18. log1p-expm1-u 0.0%

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(t \cdot -0.3333333333333333\right)\right)}\right) - \frac{a}{3 \cdot b} \]

      19. log1p-undefine 0.0%

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \color{blue}{\log \left(1 + \mathsf{expm1}\left(t \cdot -0.3333333333333333\right)\right)}\right) - \frac{a}{3 \cdot b} \]

      20. add-sqr-sqrt 0.0%

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \log \left(1 + \mathsf{expm1}\left(\color{blue}{\sqrt{t \cdot -0.3333333333333333} \cdot \sqrt{t \cdot -0.3333333333333333}}\right)\right)\right) - \frac{a}{3 \cdot b} \]

      21. sqrt-unprod 0.0%

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \log \left(1 + \mathsf{expm1}\left(\color{blue}{\sqrt{\left(t \cdot -0.3333333333333333\right) \cdot \left(t \cdot -0.3333333333333333\right)}}\right)\right)\right) - \frac{a}{3 \cdot b} \]

      22. swap-sqr 0.0%

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \log \left(1 + \mathsf{expm1}\left(\sqrt{\color{blue}{\left(t \cdot t\right) \cdot \left(-0.3333333333333333 \cdot -0.3333333333333333\right)}}\right)\right)\right) - \frac{a}{3 \cdot b} \]

      23. metadata-eval 0.0%

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \log \left(1 + \mathsf{expm1}\left(\sqrt{\left(t \cdot t\right) \cdot \color{blue}{0.1111111111111111}}\right)\right)\right) - \frac{a}{3 \cdot b} \]

      24. metadata-eval 0.0%

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \log \left(1 + \mathsf{expm1}\left(\sqrt{\left(t \cdot t\right) \cdot \color{blue}{\left(0.3333333333333333 \cdot 0.3333333333333333\right)}}\right)\right)\right) - \frac{a}{3 \cdot b} \]

      25. swap-sqr 0.0%

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \log \left(1 + \mathsf{expm1}\left(\sqrt{\color{blue}{\left(t \cdot 0.3333333333333333\right) \cdot \left(t \cdot 0.3333333333333333\right)}}\right)\right)\right) - \frac{a}{3 \cdot b} \]

      26. *-commutative 0.0%

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \log \left(1 + \mathsf{expm1}\left(\sqrt{\color{blue}{\left(0.3333333333333333 \cdot t\right)} \cdot \left(t \cdot 0.3333333333333333\right)}\right)\right)\right) - \frac{a}{3 \cdot b} \]

      27. metadata-eval 0.0%

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \log \left(1 + \mathsf{expm1}\left(\sqrt{\left(\color{blue}{\frac{1}{3}} \cdot t\right) \cdot \left(t \cdot 0.3333333333333333\right)}\right)\right)\right) - \frac{a}{3 \cdot b} \]

      28. associate-/r/ 0.0%

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \log \left(1 + \mathsf{expm1}\left(\sqrt{\color{blue}{\frac{1}{\frac{3}{t}}} \cdot \left(t \cdot 0.3333333333333333\right)}\right)\right)\right) - \frac{a}{3 \cdot b} \]

      29. *-commutative 0.0%

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \log \left(1 + \mathsf{expm1}\left(\sqrt{\frac{1}{\frac{3}{t}} \cdot \color{blue}{\left(0.3333333333333333 \cdot t\right)}}\right)\right)\right) - \frac{a}{3 \cdot b} \]

      30. metadata-eval 0.0%

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \log \left(1 + \mathsf{expm1}\left(\sqrt{\frac{1}{\frac{3}{t}} \cdot \left(\color{blue}{\frac{1}{3}} \cdot t\right)}\right)\right)\right) - \frac{a}{3 \cdot b} \]

      31. associate-/r/ 0.0%

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \log \left(1 + \mathsf{expm1}\left(\sqrt{\frac{1}{\frac{3}{t}} \cdot \color{blue}{\frac{1}{\frac{3}{t}}}}\right)\right)\right) - \frac{a}{3 \cdot b} \]

   9. Applied egg-rr 0.0%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \color{blue}{\log \left(1 + \mathsf{expm1}\left(t \cdot 0.3333333333333333\right)\right)}\right) - \frac{a}{3 \cdot b} \]
   10. Step-by-step derivation

       1. add-sqr-sqrt 0.0%

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \color{blue}{\left(\sqrt{\log \left(1 + \mathsf{expm1}\left(t \cdot 0.3333333333333333\right)\right)} \cdot \sqrt{\log \left(1 + \mathsf{expm1}\left(t \cdot 0.3333333333333333\right)\right)}\right)}\right) - \frac{a}{3 \cdot b} \]

       2. sqrt-unprod 0.0%

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \color{blue}{\sqrt{\log \left(1 + \mathsf{expm1}\left(t \cdot 0.3333333333333333\right)\right) \cdot \log \left(1 + \mathsf{expm1}\left(t \cdot 0.3333333333333333\right)\right)}}\right) - \frac{a}{3 \cdot b} \]

       3. log1p-define 0.0%

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \sqrt{\color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(t \cdot 0.3333333333333333\right)\right)} \cdot \log \left(1 + \mathsf{expm1}\left(t \cdot 0.3333333333333333\right)\right)}\right) - \frac{a}{3 \cdot b} \]

       4. log1p-expm1-u 0.0%

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \sqrt{\color{blue}{\left(t \cdot 0.3333333333333333\right)} \cdot \log \left(1 + \mathsf{expm1}\left(t \cdot 0.3333333333333333\right)\right)}\right) - \frac{a}{3 \cdot b} \]

       5. log1p-define 0.0%

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \sqrt{\left(t \cdot 0.3333333333333333\right) \cdot \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(t \cdot 0.3333333333333333\right)\right)}}\right) - \frac{a}{3 \cdot b} \]

       6. log1p-expm1-u 0.0%

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

       7. swap-sqr 0.0%

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

       8. metadata-eval 0.0%

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

       9. metadata-eval 0.0%

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

       10. swap-sqr 0.0%

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

       11. expm1-log1p-u 0.0%

           \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \sqrt{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot -0.3333333333333333\right)\right)} \cdot \left(t \cdot -0.3333333333333333\right)}\right) - \frac{a}{3 \cdot b} \]

       12. expm1-log1p-u 0.0%

           \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \sqrt{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot -0.3333333333333333\right)\right) \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot -0.3333333333333333\right)\right)}}\right) - \frac{a}{3 \cdot b} \]

       13. sqrt-unprod 0.0%

           \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \color{blue}{\left(\sqrt{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot -0.3333333333333333\right)\right)} \cdot \sqrt{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot -0.3333333333333333\right)\right)}\right)}\right) - \frac{a}{3 \cdot b} \]

       14. add-sqr-sqrt 0.0%

           \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot -0.3333333333333333\right)\right)}\right) - \frac{a}{3 \cdot b} \]

       15. expm1-undefine 0.0%

           \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(t \cdot -0.3333333333333333\right)} - 1\right)}\right) - \frac{a}{3 \cdot b} \]

       16. flip-- 0.0%

           \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \color{blue}{\frac{e^{\mathsf{log1p}\left(t \cdot -0.3333333333333333\right)} \cdot e^{\mathsf{log1p}\left(t \cdot -0.3333333333333333\right)} - 1 \cdot 1}{e^{\mathsf{log1p}\left(t \cdot -0.3333333333333333\right)} + 1}}\right) - \frac{a}{3 \cdot b} \]

   11. Applied egg-rr 0.0%

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

   12. Taylor expanded in t around 0 55.0%

       \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \frac{\color{blue}{0.6666666666666666 \cdot t}}{\left(1 + 0.3333333333333333 \cdot t\right) + 1}\right) - \frac{a}{3 \cdot b} \]
   13. Step-by-step derivation

       1. *-commutative 55.0%

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \frac{\color{blue}{t \cdot 0.6666666666666666}}{\left(1 + 0.3333333333333333 \cdot t\right) + 1}\right) - \frac{a}{3 \cdot b} \]

   14. Simplified 55.0%

       \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \frac{\color{blue}{t \cdot 0.6666666666666666}}{\left(1 + 0.3333333333333333 \cdot t\right) + 1}\right) - \frac{a}{3 \cdot b} \]
3. Recombined 2 regimes into one program.

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\cos \left(y - \frac{z \cdot t}{3}\right) \leq 1:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \left(\cos \left(t \cdot \left(z \cdot -0.3333333333333333\right)\right) \cdot \cos y - \sin \left(t \cdot \left(z \cdot -0.3333333333333333\right)\right) \cdot \sin y\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \frac{t \cdot 0.6666666666666666}{1 + \left(1 + t \cdot 0.3333333333333333\right)}\right) - \frac{a}{3 \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 77.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := 2 \cdot \sqrt{x}\\ t_2 := \frac{a}{3 \cdot b}\\ \mathbf{if}\;\cos \left(y - \frac{z \cdot t}{3}\right) \leq 1:\\ \;\;\;\;t\_1 \cdot \left(\cos y \cdot \cos \left(0.3333333333333333 \cdot \left(z \cdot t\right)\right) - \sin y \cdot \sin \left(z \cdot \left(t \cdot -0.3333333333333333\right)\right)\right) - t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1 \cdot \cos \left(z \cdot \frac{t \cdot 0.6666666666666666}{1 + \left(1 + t \cdot 0.3333333333333333\right)}\right) - t\_2\\ \end{array} \end{array} \]

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))) 1.0)
     (-
      (*
       t_1
       (-
        (* (cos y) (cos (* 0.3333333333333333 (* z t))))
        (* (sin y) (sin (* z (* t -0.3333333333333333))))))
      t_2)
     (-
      (*
       t_1
       (cos
        (*
         z
         (/
          (* t 0.6666666666666666)
          (+ 1.0 (+ 1.0 (* t 0.3333333333333333)))))))
      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))) <= 1.0) {
		tmp = (t_1 * ((cos(y) * cos((0.3333333333333333 * (z * t)))) - (sin(y) * sin((z * (t * -0.3333333333333333)))))) - t_2;
	} else {
		tmp = (t_1 * cos((z * ((t * 0.6666666666666666) / (1.0 + (1.0 + (t * 0.3333333333333333))))))) - 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))) <= 1.0d0) then
        tmp = (t_1 * ((cos(y) * cos((0.3333333333333333d0 * (z * t)))) - (sin(y) * sin((z * (t * (-0.3333333333333333d0))))))) - t_2
    else
        tmp = (t_1 * cos((z * ((t * 0.6666666666666666d0) / (1.0d0 + (1.0d0 + (t * 0.3333333333333333d0))))))) - 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))) <= 1.0) {
		tmp = (t_1 * ((Math.cos(y) * Math.cos((0.3333333333333333 * (z * t)))) - (Math.sin(y) * Math.sin((z * (t * -0.3333333333333333)))))) - t_2;
	} else {
		tmp = (t_1 * Math.cos((z * ((t * 0.6666666666666666) / (1.0 + (1.0 + (t * 0.3333333333333333))))))) - 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))) <= 1.0:
		tmp = (t_1 * ((math.cos(y) * math.cos((0.3333333333333333 * (z * t)))) - (math.sin(y) * math.sin((z * (t * -0.3333333333333333)))))) - t_2
	else:
		tmp = (t_1 * math.cos((z * ((t * 0.6666666666666666) / (1.0 + (1.0 + (t * 0.3333333333333333))))))) - 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))) <= 1.0)
		tmp = Float64(Float64(t_1 * Float64(Float64(cos(y) * cos(Float64(0.3333333333333333 * Float64(z * t)))) - Float64(sin(y) * sin(Float64(z * Float64(t * -0.3333333333333333)))))) - t_2);
	else
		tmp = Float64(Float64(t_1 * cos(Float64(z * Float64(Float64(t * 0.6666666666666666) / Float64(1.0 + Float64(1.0 + Float64(t * 0.3333333333333333))))))) - 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))) <= 1.0)
		tmp = (t_1 * ((cos(y) * cos((0.3333333333333333 * (z * t)))) - (sin(y) * sin((z * (t * -0.3333333333333333)))))) - t_2;
	else
		tmp = (t_1 * cos((z * ((t * 0.6666666666666666) / (1.0 + (1.0 + (t * 0.3333333333333333))))))) - 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], 1.0], N[(N[(t$95$1 * N[(N[(N[Cos[y], $MachinePrecision] * N[Cos[N[(0.3333333333333333 * N[(z * t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[(N[Sin[y], $MachinePrecision] * N[Sin[N[(z * N[(t * -0.3333333333333333), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], N[(N[(t$95$1 * N[Cos[N[(z * N[(N[(t * 0.6666666666666666), $MachinePrecision] / N[(1.0 + N[(1.0 + N[(t * 0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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)))) < 1

   1. Initial program 74.4%

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

      1. *-commutative 74.4%

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

      2. *-commutative 74.4%

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

      3. *-commutative 74.4%

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

      4. *-commutative 74.4%

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

      5. associate-/l* 74.5%

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

      6. *-commutative 74.5%

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

   3. Simplified 74.5%

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

   6. Applied egg-rr 76.1%

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

      1. fma-define 76.1%

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

      2. *-rgt-identity 76.1%

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

      3. fma-neg 76.1%

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

      4. *-rgt-identity 76.1%

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

      5. associate-*l* 76.0%

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

      6. *-commutative 76.0%

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

      7. associate-*r* 76.3%

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

      8. *-commutative 76.3%

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

      9. metadata-eval 76.3%

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

      10. *-commutative 76.3%

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

      11. distribute-lft-neg-in 76.3%

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

      12. cos-neg 76.3%

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

      13. *-commutative 76.3%

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

      14. *-commutative 76.3%

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

      15. associate-*l* 76.0%

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

      16. associate-*l* 76.1%

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

      17. *-commutative 76.1%

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

   8. Simplified 76.1%

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

   9. Taylor expanded in z around inf 76.4%

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

   if 1 < (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))

   1. Initial program 0.0%

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

      1. *-commutative 0.0%

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

      2. *-commutative 0.0%

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

      3. *-commutative 0.0%

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

      4. *-commutative 0.0%

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

      5. associate-/l* 0.0%

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

      6. *-commutative 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in y around 0 0.0%

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

      1. cos-neg 0.0%

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

      2. *-commutative 0.0%

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

      3. *-commutative 0.0%

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

      4. associate-*l* 0.0%

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

   7. Simplified 0.0%

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

      1. *-commutative 0.0%

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

      2. metadata-eval 0.0%

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

      3. associate-/r/ 0.0%

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

      4. add-sqr-sqrt 0.0%

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

      5. sqrt-unprod 0.0%

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

      6. clear-num 0.0%

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

      7. div-inv 0.0%

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

      8. metadata-eval 0.0%

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

      9. clear-num 0.0%

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

      10. div-inv 0.0%

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

      11. metadata-eval 0.0%

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

      12. swap-sqr 0.0%

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

      13. metadata-eval 0.0%

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

      14. metadata-eval 0.0%

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

      15. swap-sqr 0.0%

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

      16. sqrt-unprod 0.0%

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

      17. add-sqr-sqrt 0.0%

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

      18. log1p-expm1-u 0.0%

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(t \cdot -0.3333333333333333\right)\right)}\right) - \frac{a}{3 \cdot b} \]

      19. log1p-undefine 0.0%

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \color{blue}{\log \left(1 + \mathsf{expm1}\left(t \cdot -0.3333333333333333\right)\right)}\right) - \frac{a}{3 \cdot b} \]

      20. add-sqr-sqrt 0.0%

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \log \left(1 + \mathsf{expm1}\left(\color{blue}{\sqrt{t \cdot -0.3333333333333333} \cdot \sqrt{t \cdot -0.3333333333333333}}\right)\right)\right) - \frac{a}{3 \cdot b} \]

      21. sqrt-unprod 0.0%

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \log \left(1 + \mathsf{expm1}\left(\color{blue}{\sqrt{\left(t \cdot -0.3333333333333333\right) \cdot \left(t \cdot -0.3333333333333333\right)}}\right)\right)\right) - \frac{a}{3 \cdot b} \]

      22. swap-sqr 0.0%

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \log \left(1 + \mathsf{expm1}\left(\sqrt{\color{blue}{\left(t \cdot t\right) \cdot \left(-0.3333333333333333 \cdot -0.3333333333333333\right)}}\right)\right)\right) - \frac{a}{3 \cdot b} \]

      23. metadata-eval 0.0%

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \log \left(1 + \mathsf{expm1}\left(\sqrt{\left(t \cdot t\right) \cdot \color{blue}{0.1111111111111111}}\right)\right)\right) - \frac{a}{3 \cdot b} \]

      24. metadata-eval 0.0%

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \log \left(1 + \mathsf{expm1}\left(\sqrt{\left(t \cdot t\right) \cdot \color{blue}{\left(0.3333333333333333 \cdot 0.3333333333333333\right)}}\right)\right)\right) - \frac{a}{3 \cdot b} \]

      25. swap-sqr 0.0%

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \log \left(1 + \mathsf{expm1}\left(\sqrt{\color{blue}{\left(t \cdot 0.3333333333333333\right) \cdot \left(t \cdot 0.3333333333333333\right)}}\right)\right)\right) - \frac{a}{3 \cdot b} \]

      26. *-commutative 0.0%

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \log \left(1 + \mathsf{expm1}\left(\sqrt{\color{blue}{\left(0.3333333333333333 \cdot t\right)} \cdot \left(t \cdot 0.3333333333333333\right)}\right)\right)\right) - \frac{a}{3 \cdot b} \]

      27. metadata-eval 0.0%

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \log \left(1 + \mathsf{expm1}\left(\sqrt{\left(\color{blue}{\frac{1}{3}} \cdot t\right) \cdot \left(t \cdot 0.3333333333333333\right)}\right)\right)\right) - \frac{a}{3 \cdot b} \]

      28. associate-/r/ 0.0%

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \log \left(1 + \mathsf{expm1}\left(\sqrt{\color{blue}{\frac{1}{\frac{3}{t}}} \cdot \left(t \cdot 0.3333333333333333\right)}\right)\right)\right) - \frac{a}{3 \cdot b} \]

      29. *-commutative 0.0%

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \log \left(1 + \mathsf{expm1}\left(\sqrt{\frac{1}{\frac{3}{t}} \cdot \color{blue}{\left(0.3333333333333333 \cdot t\right)}}\right)\right)\right) - \frac{a}{3 \cdot b} \]

      30. metadata-eval 0.0%

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \log \left(1 + \mathsf{expm1}\left(\sqrt{\frac{1}{\frac{3}{t}} \cdot \left(\color{blue}{\frac{1}{3}} \cdot t\right)}\right)\right)\right) - \frac{a}{3 \cdot b} \]

      31. associate-/r/ 0.0%

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \log \left(1 + \mathsf{expm1}\left(\sqrt{\frac{1}{\frac{3}{t}} \cdot \color{blue}{\frac{1}{\frac{3}{t}}}}\right)\right)\right) - \frac{a}{3 \cdot b} \]

   9. Applied egg-rr 0.0%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \color{blue}{\log \left(1 + \mathsf{expm1}\left(t \cdot 0.3333333333333333\right)\right)}\right) - \frac{a}{3 \cdot b} \]
   10. Step-by-step derivation

       1. add-sqr-sqrt 0.0%

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \color{blue}{\left(\sqrt{\log \left(1 + \mathsf{expm1}\left(t \cdot 0.3333333333333333\right)\right)} \cdot \sqrt{\log \left(1 + \mathsf{expm1}\left(t \cdot 0.3333333333333333\right)\right)}\right)}\right) - \frac{a}{3 \cdot b} \]

       2. sqrt-unprod 0.0%

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \color{blue}{\sqrt{\log \left(1 + \mathsf{expm1}\left(t \cdot 0.3333333333333333\right)\right) \cdot \log \left(1 + \mathsf{expm1}\left(t \cdot 0.3333333333333333\right)\right)}}\right) - \frac{a}{3 \cdot b} \]

       3. log1p-define 0.0%

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \sqrt{\color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(t \cdot 0.3333333333333333\right)\right)} \cdot \log \left(1 + \mathsf{expm1}\left(t \cdot 0.3333333333333333\right)\right)}\right) - \frac{a}{3 \cdot b} \]

       4. log1p-expm1-u 0.0%

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \sqrt{\color{blue}{\left(t \cdot 0.3333333333333333\right)} \cdot \log \left(1 + \mathsf{expm1}\left(t \cdot 0.3333333333333333\right)\right)}\right) - \frac{a}{3 \cdot b} \]

       5. log1p-define 0.0%

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \sqrt{\left(t \cdot 0.3333333333333333\right) \cdot \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(t \cdot 0.3333333333333333\right)\right)}}\right) - \frac{a}{3 \cdot b} \]

       6. log1p-expm1-u 0.0%

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

       7. swap-sqr 0.0%

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

       8. metadata-eval 0.0%

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

       9. metadata-eval 0.0%

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

       10. swap-sqr 0.0%

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

       11. expm1-log1p-u 0.0%

           \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \sqrt{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot -0.3333333333333333\right)\right)} \cdot \left(t \cdot -0.3333333333333333\right)}\right) - \frac{a}{3 \cdot b} \]

       12. expm1-log1p-u 0.0%

           \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \sqrt{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot -0.3333333333333333\right)\right) \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot -0.3333333333333333\right)\right)}}\right) - \frac{a}{3 \cdot b} \]

       13. sqrt-unprod 0.0%

           \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \color{blue}{\left(\sqrt{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot -0.3333333333333333\right)\right)} \cdot \sqrt{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot -0.3333333333333333\right)\right)}\right)}\right) - \frac{a}{3 \cdot b} \]

       14. add-sqr-sqrt 0.0%

           \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot -0.3333333333333333\right)\right)}\right) - \frac{a}{3 \cdot b} \]

       15. expm1-undefine 0.0%

           \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(t \cdot -0.3333333333333333\right)} - 1\right)}\right) - \frac{a}{3 \cdot b} \]

       16. flip-- 0.0%

           \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \color{blue}{\frac{e^{\mathsf{log1p}\left(t \cdot -0.3333333333333333\right)} \cdot e^{\mathsf{log1p}\left(t \cdot -0.3333333333333333\right)} - 1 \cdot 1}{e^{\mathsf{log1p}\left(t \cdot -0.3333333333333333\right)} + 1}}\right) - \frac{a}{3 \cdot b} \]

   11. Applied egg-rr 0.0%

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

   12. Taylor expanded in t around 0 55.0%

       \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \frac{\color{blue}{0.6666666666666666 \cdot t}}{\left(1 + 0.3333333333333333 \cdot t\right) + 1}\right) - \frac{a}{3 \cdot b} \]
   13. Step-by-step derivation

       1. *-commutative 55.0%

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \frac{\color{blue}{t \cdot 0.6666666666666666}}{\left(1 + 0.3333333333333333 \cdot t\right) + 1}\right) - \frac{a}{3 \cdot b} \]

   14. Simplified 55.0%

       \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \frac{\color{blue}{t \cdot 0.6666666666666666}}{\left(1 + 0.3333333333333333 \cdot t\right) + 1}\right) - \frac{a}{3 \cdot b} \]
3. Recombined 2 regimes into one program.

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\cos \left(y - \frac{z \cdot t}{3}\right) \leq 1:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \cos \left(0.3333333333333333 \cdot \left(z \cdot t\right)\right) - \sin y \cdot \sin \left(z \cdot \left(t \cdot -0.3333333333333333\right)\right)\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(z \cdot \frac{t \cdot 0.6666666666666666}{1 + \left(1 + t \cdot 0.3333333333333333\right)}\right) - \frac{a}{3 \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 66.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{+201} \lor \neg \left(b \leq 3.8 \cdot 10^{+83}\right):\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \cos y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{a}{3 \cdot b}\\ \end{array} \end{array} \]

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
 (if (or (<= b -7e+201) (not (<= b 3.8e+83)))
   (* 2.0 (* (sqrt x) (cos y)))
   (- (* 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) {
	double tmp;
	if ((b <= -7e+201) || !(b <= 3.8e+83)) {
		tmp = 2.0 * (sqrt(x) * cos(y));
	} else {
		tmp = (2.0 * sqrt(x)) - (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) :: tmp
    if ((b <= (-7d+201)) .or. (.not. (b <= 3.8d+83))) then
        tmp = 2.0d0 * (sqrt(x) * cos(y))
    else
        tmp = (2.0d0 * sqrt(x)) - (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 tmp;
	if ((b <= -7e+201) || !(b <= 3.8e+83)) {
		tmp = 2.0 * (Math.sqrt(x) * Math.cos(y));
	} else {
		tmp = (2.0 * Math.sqrt(x)) - (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):
	tmp = 0
	if (b <= -7e+201) or not (b <= 3.8e+83):
		tmp = 2.0 * (math.sqrt(x) * math.cos(y))
	else:
		tmp = (2.0 * math.sqrt(x)) - (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)
	tmp = 0.0
	if ((b <= -7e+201) || !(b <= 3.8e+83))
		tmp = Float64(2.0 * Float64(sqrt(x) * cos(y)));
	else
		tmp = Float64(Float64(2.0 * sqrt(x)) - 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)
	tmp = 0.0;
	if ((b <= -7e+201) || ~((b <= 3.8e+83)))
		tmp = 2.0 * (sqrt(x) * cos(y));
	else
		tmp = (2.0 * sqrt(x)) - (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_] := If[Or[LessEqual[b, -7e+201], N[Not[LessEqual[b, 3.8e+83]], $MachinePrecision]], N[(2.0 * N[(N[Sqrt[x], $MachinePrecision] * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] - N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -7.0000000000000004e201 or 3.8000000000000002e83 < b

   1. Initial program 54.8%

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

      1. *-commutative 54.8%

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

      2. *-commutative 54.8%

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

      3. *-commutative 54.8%

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

      4. *-commutative 54.8%

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

      5. associate-/l* 55.0%

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

      6. *-commutative 55.0%

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

   3. Simplified 55.0%

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

   5. Taylor expanded in z around 0 54.9%

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

   6. Taylor expanded in a around 0 54.9%

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

      1. metadata-eval 54.9%

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

      2. times-frac 54.9%

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

      3. associate-*l/ 54.9%

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

      4. associate-/r/ 54.9%

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

      5. associate-*r/ 54.8%

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

      6. associate-/r* 54.8%

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

      7. metadata-eval 54.8%

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

   8. Simplified 54.8%

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

   9. Taylor expanded in x around inf 49.6%

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

   if -7.0000000000000004e201 < b < 3.8000000000000002e83

   1. Initial program 70.2%

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

      1. *-commutative 70.2%

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

      2. *-commutative 70.2%

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

      3. *-commutative 70.2%

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

      4. *-commutative 70.2%

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

      5. associate-/l* 70.2%

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

      6. *-commutative 70.2%

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

   3. Simplified 70.2%

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

   5. Taylor expanded in z around 0 78.1%

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

   6. Taylor expanded in y around 0 75.4%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{+201} \lor \neg \left(b \leq 3.8 \cdot 10^{+83}\right):\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \cos y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{a}{3 \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{0.3333333333333333}{\frac{b}{a}} \end{array} \]

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
 (- (* (* 2.0 (sqrt x)) (cos y)) (/ 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 ((2.0 * sqrt(x)) * cos(y)) - (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 = ((2.0d0 * sqrt(x)) * cos(y)) - (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 ((2.0 * Math.sqrt(x)) * Math.cos(y)) - (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 ((2.0 * math.sqrt(x)) * math.cos(y)) - (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(Float64(Float64(2.0 * sqrt(x)) * cos(y)) - 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 = ((2.0 * sqrt(x)) * cos(y)) - (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[(N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(0.3333333333333333 / N[(b / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 66.0%

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

   1. *-commutative 66.0%

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

   2. *-commutative 66.0%

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

   3. *-commutative 66.0%

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

   4. *-commutative 66.0%

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

   5. associate-/l* 66.0%

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

   6. *-commutative 66.0%

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

3. Simplified 66.0%

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

5. Taylor expanded in z around 0 71.7%

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

6. Taylor expanded in a around 0 71.7%

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

   1. metadata-eval 71.7%

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

   2. times-frac 71.7%

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

   3. associate-*l/ 71.7%

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

   4. associate-/r/ 71.7%

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

   5. associate-*r/ 71.7%

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

   6. associate-/r* 71.7%

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

   7. metadata-eval 71.7%

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

8. Simplified 71.7%

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

9. Final simplification 71.7%

   \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{0.3333333333333333}{\frac{b}{a}} \]
10. Add Preprocessing

Alternative 5: 76.8% 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 66.0%

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

   1. *-commutative 66.0%

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

   2. *-commutative 66.0%

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

   3. *-commutative 66.0%

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

   4. *-commutative 66.0%

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

   5. associate-/l* 66.0%

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

   6. *-commutative 66.0%

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

3. Simplified 66.0%

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

5. Taylor expanded in z around 0 71.7%

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

6. Final simplification 71.7%

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

Alternative 6: 66.4% 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 66.0%

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

   1. *-commutative 66.0%

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

   2. *-commutative 66.0%

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

   3. *-commutative 66.0%

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

   4. *-commutative 66.0%

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

   5. associate-/l* 66.0%

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

   6. *-commutative 66.0%

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

3. Simplified 66.0%

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

5. Taylor expanded in z around 0 71.7%

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

6. Taylor expanded in y around 0 62.5%

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

7. Final simplification 62.5%

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

Alternative 7: 51.2% 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 66.0%

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

   1. *-commutative 66.0%

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

   2. *-commutative 66.0%

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

   3. *-commutative 66.0%

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

   4. *-commutative 66.0%

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

   5. associate-/l* 66.0%

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

   6. *-commutative 66.0%

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

3. Simplified 66.0%

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

5. Taylor expanded in z around 0 71.7%

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

6. Taylor expanded in a around inf 48.2%

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

7. Final simplification 48.2%

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

Alternative 8: 51.2% 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 66.0%

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

   1. *-commutative 66.0%

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

   2. *-commutative 66.0%

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

   3. *-commutative 66.0%

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

   4. *-commutative 66.0%

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

   5. associate-/l* 66.0%

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

   6. *-commutative 66.0%

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

3. Simplified 66.0%

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

5. Taylor expanded in z around 0 71.7%

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

6. Taylor expanded in a around inf 48.2%

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

   1. clear-num 48.2%

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

   2. un-div-inv 48.2%

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

8. Applied egg-rr 48.2%

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

9. Final simplification 48.2%

   \[\leadsto \frac{-0.3333333333333333}{\frac{b}{a}} \]
10. Add Preprocessing

Alternative 9: 51.3% accurate, 43.4× speedup

Math

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

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 (/ a (* b -3.0)))

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 a / (b * -3.0);
}

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 = a / (b * (-3.0d0))
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 a / (b * -3.0);
}

Python

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

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	return Float64(a / Float64(b * -3.0))
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 = a / (b * -3.0);
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[(a / N[(b * -3.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 66.0%

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

   1. *-commutative 66.0%

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

   2. *-commutative 66.0%

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

   3. *-commutative 66.0%

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

   4. *-commutative 66.0%

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

   5. associate-/l* 66.0%

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

   6. *-commutative 66.0%

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

3. Simplified 66.0%

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

5. Taylor expanded in z around 0 71.7%

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

6. Taylor expanded in a around inf 48.2%

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

   1. clear-num 48.2%

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

   2. un-div-inv 48.2%

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

8. Applied egg-rr 48.2%

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

   1. associate-/r/ 48.1%

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

10. Simplified 48.1%

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

    1. *-commutative 48.1%

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

    2. clear-num 48.1%

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

    3. un-div-inv 48.2%

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

    4. div-inv 48.2%

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

    5. metadata-eval 48.2%

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

12. Applied egg-rr 48.2%

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

13. Final simplification 48.2%

    \[\leadsto \frac{a}{b \cdot -3} \]
14. Add Preprocessing

Alternative 10: 51.3% accurate, 43.4× speedup

Math

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

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 (/ (/ 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 (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 = (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 (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 (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(a / -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 = (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[(a / -3.0), $MachinePrecision] / b), $MachinePrecision]

Derivation

1. Initial program 66.0%

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

   1. *-commutative 66.0%

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

   2. *-commutative 66.0%

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

   3. *-commutative 66.0%

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

   4. *-commutative 66.0%

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

   5. associate-/l* 66.0%

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

   6. *-commutative 66.0%

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

3. Simplified 66.0%

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

5. Taylor expanded in z around 0 71.7%

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

6. Taylor expanded in a around inf 48.2%

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

   1. metadata-eval 48.2%

      \[\leadsto \color{blue}{\frac{1}{-3}} \cdot \frac{a}{b} \]

   2. times-frac 48.2%

      \[\leadsto \color{blue}{\frac{1 \cdot a}{-3 \cdot b}} \]

   3. *-lft-identity 48.2%

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

   4. associate-/r* 48.2%

      \[\leadsto \color{blue}{\frac{\frac{a}{-3}}{b}} \]

8. Simplified 48.2%

   \[\leadsto \color{blue}{\frac{\frac{a}{-3}}{b}} \]

9. Final simplification 48.2%

   \[\leadsto \frac{\frac{a}{-3}}{b} \]
10. Add Preprocessing

Developer target: 74.6% 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 2024060 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, K"
  :precision binary64

  :alt
  (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))))