Codec.Picture.Jpg.FastDct:referenceDct from JuicyPixels-3.2.6.1

Percentage Accurate: 28.1% → 32.2%

Time: 16.2s

Alternatives: 5

Speedup: 225.0×

Specification

Math

\[\begin{array}{l} \\ \left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right) \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (*
  (* x (cos (/ (* (* (+ (* y 2.0) 1.0) z) t) 16.0)))
  (cos (/ (* (* (+ (* a 2.0) 1.0) b) t) 16.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x * cos((((((y * 2.0) + 1.0) * z) * t) / 16.0))) * cos((((((a * 2.0) + 1.0) * b) * t) / 16.0));
}

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 = (x * cos((((((y * 2.0d0) + 1.0d0) * z) * t) / 16.0d0))) * cos((((((a * 2.0d0) + 1.0d0) * b) * t) / 16.0d0))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x * Math.cos((((((y * 2.0) + 1.0) * z) * t) / 16.0))) * Math.cos((((((a * 2.0) + 1.0) * b) * t) / 16.0));
}

Python

def code(x, y, z, t, a, b):
	return (x * math.cos((((((y * 2.0) + 1.0) * z) * t) / 16.0))) * math.cos((((((a * 2.0) + 1.0) * b) * t) / 16.0))

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x * cos(Float64(Float64(Float64(Float64(Float64(y * 2.0) + 1.0) * z) * t) / 16.0))) * cos(Float64(Float64(Float64(Float64(Float64(a * 2.0) + 1.0) * b) * t) / 16.0)))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x * cos((((((y * 2.0) + 1.0) * z) * t) / 16.0))) * cos((((((a * 2.0) + 1.0) * b) * t) / 16.0));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x * N[Cos[N[(N[(N[(N[(N[(y * 2.0), $MachinePrecision] + 1.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] / 16.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Cos[N[(N[(N[(N[(N[(a * 2.0), $MachinePrecision] + 1.0), $MachinePrecision] * b), $MachinePrecision] * t), $MachinePrecision] / 16.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Initial Program: 28.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right) \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (*
  (* x (cos (/ (* (* (+ (* y 2.0) 1.0) z) t) 16.0)))
  (cos (/ (* (* (+ (* a 2.0) 1.0) b) t) 16.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x * cos((((((y * 2.0) + 1.0) * z) * t) / 16.0))) * cos((((((a * 2.0) + 1.0) * b) * t) / 16.0));
}

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 = (x * cos((((((y * 2.0d0) + 1.0d0) * z) * t) / 16.0d0))) * cos((((((a * 2.0d0) + 1.0d0) * b) * t) / 16.0d0))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x * Math.cos((((((y * 2.0) + 1.0) * z) * t) / 16.0))) * Math.cos((((((a * 2.0) + 1.0) * b) * t) / 16.0));
}

Python

def code(x, y, z, t, a, b):
	return (x * math.cos((((((y * 2.0) + 1.0) * z) * t) / 16.0))) * math.cos((((((a * 2.0) + 1.0) * b) * t) / 16.0))

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x * cos(Float64(Float64(Float64(Float64(Float64(y * 2.0) + 1.0) * z) * t) / 16.0))) * cos(Float64(Float64(Float64(Float64(Float64(a * 2.0) + 1.0) * b) * t) / 16.0)))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x * cos((((((y * 2.0) + 1.0) * z) * t) / 16.0))) * cos((((((a * 2.0) + 1.0) * b) * t) / 16.0));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x * N[Cos[N[(N[(N[(N[(N[(y * 2.0), $MachinePrecision] + 1.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] / 16.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Cos[N[(N[(N[(N[(N[(a * 2.0), $MachinePrecision] + 1.0), $MachinePrecision] * b), $MachinePrecision] * t), $MachinePrecision] / 16.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Alternative 1: 32.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{t}{16}\\ t_2 := z \cdot \left(t \cdot \left(y \cdot 0.125\right)\right)\\ t_3 := \cos t\_1 \cdot \cos t\_2\\ t_4 := \sin t\_1 \cdot \sin t\_2\\ \mathbf{if}\;\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{t \cdot \left(\left(1 + 2 \cdot a\right) \cdot b\right)}{16}\right) \leq 5 \cdot 10^{+306}:\\ \;\;\;\;\frac{{t\_3}^{3} - {t\_4}^{3}}{t\_3 \cdot t\_3 + \left(t\_4 \cdot t\_4 + t\_3 \cdot t\_4\right)} \cdot \left(x \cdot \cos \left(\left(t \cdot b\right) \cdot \left(0.0625 + a \cdot 0.125\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (/ t 16.0)))
        (t_2 (* z (* t (* y 0.125))))
        (t_3 (* (cos t_1) (cos t_2)))
        (t_4 (* (sin t_1) (sin t_2))))
   (if (<=
        (*
         (* x (cos (/ (* (* (+ (* y 2.0) 1.0) z) t) 16.0)))
         (cos (/ (* t (* (+ 1.0 (* 2.0 a)) b)) 16.0)))
        5e+306)
     (*
      (/
       (- (pow t_3 3.0) (pow t_4 3.0))
       (+ (* t_3 t_3) (+ (* t_4 t_4) (* t_3 t_4))))
      (* x (cos (* (* t b) (+ 0.0625 (* a 0.125))))))
     x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t / 16.0);
	double t_2 = z * (t * (y * 0.125));
	double t_3 = cos(t_1) * cos(t_2);
	double t_4 = sin(t_1) * sin(t_2);
	double tmp;
	if (((x * cos((((((y * 2.0) + 1.0) * z) * t) / 16.0))) * cos(((t * ((1.0 + (2.0 * a)) * b)) / 16.0))) <= 5e+306) {
		tmp = ((pow(t_3, 3.0) - pow(t_4, 3.0)) / ((t_3 * t_3) + ((t_4 * t_4) + (t_3 * t_4)))) * (x * cos(((t * b) * (0.0625 + (a * 0.125)))));
	} else {
		tmp = x;
	}
	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) :: t_4
    real(8) :: tmp
    t_1 = z * (t / 16.0d0)
    t_2 = z * (t * (y * 0.125d0))
    t_3 = cos(t_1) * cos(t_2)
    t_4 = sin(t_1) * sin(t_2)
    if (((x * cos((((((y * 2.0d0) + 1.0d0) * z) * t) / 16.0d0))) * cos(((t * ((1.0d0 + (2.0d0 * a)) * b)) / 16.0d0))) <= 5d+306) then
        tmp = (((t_3 ** 3.0d0) - (t_4 ** 3.0d0)) / ((t_3 * t_3) + ((t_4 * t_4) + (t_3 * t_4)))) * (x * cos(((t * b) * (0.0625d0 + (a * 0.125d0)))))
    else
        tmp = x
    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 = z * (t / 16.0);
	double t_2 = z * (t * (y * 0.125));
	double t_3 = Math.cos(t_1) * Math.cos(t_2);
	double t_4 = Math.sin(t_1) * Math.sin(t_2);
	double tmp;
	if (((x * Math.cos((((((y * 2.0) + 1.0) * z) * t) / 16.0))) * Math.cos(((t * ((1.0 + (2.0 * a)) * b)) / 16.0))) <= 5e+306) {
		tmp = ((Math.pow(t_3, 3.0) - Math.pow(t_4, 3.0)) / ((t_3 * t_3) + ((t_4 * t_4) + (t_3 * t_4)))) * (x * Math.cos(((t * b) * (0.0625 + (a * 0.125)))));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (t / 16.0)
	t_2 = z * (t * (y * 0.125))
	t_3 = math.cos(t_1) * math.cos(t_2)
	t_4 = math.sin(t_1) * math.sin(t_2)
	tmp = 0
	if ((x * math.cos((((((y * 2.0) + 1.0) * z) * t) / 16.0))) * math.cos(((t * ((1.0 + (2.0 * a)) * b)) / 16.0))) <= 5e+306:
		tmp = ((math.pow(t_3, 3.0) - math.pow(t_4, 3.0)) / ((t_3 * t_3) + ((t_4 * t_4) + (t_3 * t_4)))) * (x * math.cos(((t * b) * (0.0625 + (a * 0.125)))))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(t / 16.0))
	t_2 = Float64(z * Float64(t * Float64(y * 0.125)))
	t_3 = Float64(cos(t_1) * cos(t_2))
	t_4 = Float64(sin(t_1) * sin(t_2))
	tmp = 0.0
	if (Float64(Float64(x * cos(Float64(Float64(Float64(Float64(Float64(y * 2.0) + 1.0) * z) * t) / 16.0))) * cos(Float64(Float64(t * Float64(Float64(1.0 + Float64(2.0 * a)) * b)) / 16.0))) <= 5e+306)
		tmp = Float64(Float64(Float64((t_3 ^ 3.0) - (t_4 ^ 3.0)) / Float64(Float64(t_3 * t_3) + Float64(Float64(t_4 * t_4) + Float64(t_3 * t_4)))) * Float64(x * cos(Float64(Float64(t * b) * Float64(0.0625 + Float64(a * 0.125))))));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (t / 16.0);
	t_2 = z * (t * (y * 0.125));
	t_3 = cos(t_1) * cos(t_2);
	t_4 = sin(t_1) * sin(t_2);
	tmp = 0.0;
	if (((x * cos((((((y * 2.0) + 1.0) * z) * t) / 16.0))) * cos(((t * ((1.0 + (2.0 * a)) * b)) / 16.0))) <= 5e+306)
		tmp = (((t_3 ^ 3.0) - (t_4 ^ 3.0)) / ((t_3 * t_3) + ((t_4 * t_4) + (t_3 * t_4)))) * (x * cos(((t * b) * (0.0625 + (a * 0.125)))));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(t / 16.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(t * N[(y * 0.125), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[Cos[t$95$1], $MachinePrecision] * N[Cos[t$95$2], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[Sin[t$95$1], $MachinePrecision] * N[Sin[t$95$2], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(x * N[Cos[N[(N[(N[(N[(N[(y * 2.0), $MachinePrecision] + 1.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] / 16.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Cos[N[(N[(t * N[(N[(1.0 + N[(2.0 * a), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] / 16.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 5e+306], N[(N[(N[(N[Power[t$95$3, 3.0], $MachinePrecision] - N[Power[t$95$4, 3.0], $MachinePrecision]), $MachinePrecision] / N[(N[(t$95$3 * t$95$3), $MachinePrecision] + N[(N[(t$95$4 * t$95$4), $MachinePrecision] + N[(t$95$3 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x * N[Cos[N[(N[(t * b), $MachinePrecision] * N[(0.0625 + N[(a * 0.125), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 x (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y #s(literal 2 binary64)) #s(literal 1 binary64)) z) t) #s(literal 16 binary64)))) (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 a #s(literal 2 binary64)) #s(literal 1 binary64)) b) t) #s(literal 16 binary64)))) < 4.99999999999999993e306

   1. Initial program 50.4%

      \[\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right) \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right) \cdot x\right) \cdot \cos \color{blue}{\left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)} \]

      2. associate-*l* N/A

         \[\leadsto \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right) \cdot \color{blue}{\left(x \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right), \color{blue}{\left(x \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right)}\right) \]

   3. Simplified 50.9%

      \[\leadsto \color{blue}{\cos \left(\left(z \cdot t\right) \cdot \left(0.0625 + y \cdot 0.125\right)\right) \cdot \left(x \cdot \cos \left(\left(t \cdot b\right) \cdot \left(0.0625 + a \cdot 0.125\right)\right)\right)} \]
   4. Add Preprocessing

   6. Applied egg-rr 51.7%

      \[\leadsto \color{blue}{\frac{{\left(\cos \left(z \cdot \frac{t}{16}\right) \cdot \cos \left(z \cdot \left(t \cdot \left(y \cdot 0.125\right)\right)\right)\right)}^{3} - {\left(\sin \left(z \cdot \frac{t}{16}\right) \cdot \sin \left(z \cdot \left(t \cdot \left(y \cdot 0.125\right)\right)\right)\right)}^{3}}{\left(\cos \left(z \cdot \frac{t}{16}\right) \cdot \cos \left(z \cdot \left(t \cdot \left(y \cdot 0.125\right)\right)\right)\right) \cdot \left(\cos \left(z \cdot \frac{t}{16}\right) \cdot \cos \left(z \cdot \left(t \cdot \left(y \cdot 0.125\right)\right)\right)\right) + \left(\left(\sin \left(z \cdot \frac{t}{16}\right) \cdot \sin \left(z \cdot \left(t \cdot \left(y \cdot 0.125\right)\right)\right)\right) \cdot \left(\sin \left(z \cdot \frac{t}{16}\right) \cdot \sin \left(z \cdot \left(t \cdot \left(y \cdot 0.125\right)\right)\right)\right) + \left(\cos \left(z \cdot \frac{t}{16}\right) \cdot \cos \left(z \cdot \left(t \cdot \left(y \cdot 0.125\right)\right)\right)\right) \cdot \left(\sin \left(z \cdot \frac{t}{16}\right) \cdot \sin \left(z \cdot \left(t \cdot \left(y \cdot 0.125\right)\right)\right)\right)\right)}} \cdot \left(x \cdot \cos \left(\left(t \cdot b\right) \cdot \left(0.0625 + a \cdot 0.125\right)\right)\right) \]

   if 4.99999999999999993e306 < (*.f64 (*.f64 x (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y #s(literal 2 binary64)) #s(literal 1 binary64)) z) t) #s(literal 16 binary64)))) (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 a #s(literal 2 binary64)) #s(literal 1 binary64)) b) t) #s(literal 16 binary64))))

   1. Initial program 0.0%

      \[\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right) \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right) \cdot x\right) \cdot \cos \color{blue}{\left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)} \]

      2. associate-*l* N/A

         \[\leadsto \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right) \cdot \color{blue}{\left(x \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right), \color{blue}{\left(x \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right)}\right) \]

   3. Simplified 2.1%

      \[\leadsto \color{blue}{\cos \left(\left(z \cdot t\right) \cdot \left(0.0625 + y \cdot 0.125\right)\right) \cdot \left(x \cdot \cos \left(\left(t \cdot b\right) \cdot \left(0.0625 + a \cdot 0.125\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x} \]
   6. Step-by-step derivation

   7. Simplified 10.6%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 35.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{t \cdot \left(\left(1 + 2 \cdot a\right) \cdot b\right)}{16}\right) \leq 5 \cdot 10^{+306}:\\ \;\;\;\;\frac{{\left(\cos \left(z \cdot \frac{t}{16}\right) \cdot \cos \left(z \cdot \left(t \cdot \left(y \cdot 0.125\right)\right)\right)\right)}^{3} - {\left(\sin \left(z \cdot \frac{t}{16}\right) \cdot \sin \left(z \cdot \left(t \cdot \left(y \cdot 0.125\right)\right)\right)\right)}^{3}}{\left(\cos \left(z \cdot \frac{t}{16}\right) \cdot \cos \left(z \cdot \left(t \cdot \left(y \cdot 0.125\right)\right)\right)\right) \cdot \left(\cos \left(z \cdot \frac{t}{16}\right) \cdot \cos \left(z \cdot \left(t \cdot \left(y \cdot 0.125\right)\right)\right)\right) + \left(\left(\sin \left(z \cdot \frac{t}{16}\right) \cdot \sin \left(z \cdot \left(t \cdot \left(y \cdot 0.125\right)\right)\right)\right) \cdot \left(\sin \left(z \cdot \frac{t}{16}\right) \cdot \sin \left(z \cdot \left(t \cdot \left(y \cdot 0.125\right)\right)\right)\right) + \left(\cos \left(z \cdot \frac{t}{16}\right) \cdot \cos \left(z \cdot \left(t \cdot \left(y \cdot 0.125\right)\right)\right)\right) \cdot \left(\sin \left(z \cdot \frac{t}{16}\right) \cdot \sin \left(z \cdot \left(t \cdot \left(y \cdot 0.125\right)\right)\right)\right)\right)} \cdot \left(x \cdot \cos \left(\left(t \cdot b\right) \cdot \left(0.0625 + a \cdot 0.125\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 32.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{t}{16}\\ t_2 := z \cdot \left(t \cdot \left(y \cdot 0.125\right)\right)\\ \mathbf{if}\;\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{t \cdot \left(\left(1 + 2 \cdot a\right) \cdot b\right)}{16}\right) \leq 5 \cdot 10^{+306}:\\ \;\;\;\;\left(x \cdot \cos \left(\left(t \cdot b\right) \cdot \left(0.0625 + a \cdot 0.125\right)\right)\right) \cdot \left(\cos t\_1 \cdot \cos t\_2 - \sin t\_1 \cdot \sin t\_2\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (/ t 16.0))) (t_2 (* z (* t (* y 0.125)))))
   (if (<=
        (*
         (* x (cos (/ (* (* (+ (* y 2.0) 1.0) z) t) 16.0)))
         (cos (/ (* t (* (+ 1.0 (* 2.0 a)) b)) 16.0)))
        5e+306)
     (*
      (* x (cos (* (* t b) (+ 0.0625 (* a 0.125)))))
      (- (* (cos t_1) (cos t_2)) (* (sin t_1) (sin t_2))))
     x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t / 16.0);
	double t_2 = z * (t * (y * 0.125));
	double tmp;
	if (((x * cos((((((y * 2.0) + 1.0) * z) * t) / 16.0))) * cos(((t * ((1.0 + (2.0 * a)) * b)) / 16.0))) <= 5e+306) {
		tmp = (x * cos(((t * b) * (0.0625 + (a * 0.125))))) * ((cos(t_1) * cos(t_2)) - (sin(t_1) * sin(t_2)));
	} else {
		tmp = x;
	}
	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) :: tmp
    t_1 = z * (t / 16.0d0)
    t_2 = z * (t * (y * 0.125d0))
    if (((x * cos((((((y * 2.0d0) + 1.0d0) * z) * t) / 16.0d0))) * cos(((t * ((1.0d0 + (2.0d0 * a)) * b)) / 16.0d0))) <= 5d+306) then
        tmp = (x * cos(((t * b) * (0.0625d0 + (a * 0.125d0))))) * ((cos(t_1) * cos(t_2)) - (sin(t_1) * sin(t_2)))
    else
        tmp = x
    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 = z * (t / 16.0);
	double t_2 = z * (t * (y * 0.125));
	double tmp;
	if (((x * Math.cos((((((y * 2.0) + 1.0) * z) * t) / 16.0))) * Math.cos(((t * ((1.0 + (2.0 * a)) * b)) / 16.0))) <= 5e+306) {
		tmp = (x * Math.cos(((t * b) * (0.0625 + (a * 0.125))))) * ((Math.cos(t_1) * Math.cos(t_2)) - (Math.sin(t_1) * Math.sin(t_2)));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (t / 16.0)
	t_2 = z * (t * (y * 0.125))
	tmp = 0
	if ((x * math.cos((((((y * 2.0) + 1.0) * z) * t) / 16.0))) * math.cos(((t * ((1.0 + (2.0 * a)) * b)) / 16.0))) <= 5e+306:
		tmp = (x * math.cos(((t * b) * (0.0625 + (a * 0.125))))) * ((math.cos(t_1) * math.cos(t_2)) - (math.sin(t_1) * math.sin(t_2)))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(t / 16.0))
	t_2 = Float64(z * Float64(t * Float64(y * 0.125)))
	tmp = 0.0
	if (Float64(Float64(x * cos(Float64(Float64(Float64(Float64(Float64(y * 2.0) + 1.0) * z) * t) / 16.0))) * cos(Float64(Float64(t * Float64(Float64(1.0 + Float64(2.0 * a)) * b)) / 16.0))) <= 5e+306)
		tmp = Float64(Float64(x * cos(Float64(Float64(t * b) * Float64(0.0625 + Float64(a * 0.125))))) * Float64(Float64(cos(t_1) * cos(t_2)) - Float64(sin(t_1) * sin(t_2))));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (t / 16.0);
	t_2 = z * (t * (y * 0.125));
	tmp = 0.0;
	if (((x * cos((((((y * 2.0) + 1.0) * z) * t) / 16.0))) * cos(((t * ((1.0 + (2.0 * a)) * b)) / 16.0))) <= 5e+306)
		tmp = (x * cos(((t * b) * (0.0625 + (a * 0.125))))) * ((cos(t_1) * cos(t_2)) - (sin(t_1) * sin(t_2)));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(t / 16.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(t * N[(y * 0.125), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(x * N[Cos[N[(N[(N[(N[(N[(y * 2.0), $MachinePrecision] + 1.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] / 16.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Cos[N[(N[(t * N[(N[(1.0 + N[(2.0 * a), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] / 16.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 5e+306], N[(N[(x * N[Cos[N[(N[(t * b), $MachinePrecision] * N[(0.0625 + N[(a * 0.125), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(N[(N[Cos[t$95$1], $MachinePrecision] * N[Cos[t$95$2], $MachinePrecision]), $MachinePrecision] - N[(N[Sin[t$95$1], $MachinePrecision] * N[Sin[t$95$2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 x (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y #s(literal 2 binary64)) #s(literal 1 binary64)) z) t) #s(literal 16 binary64)))) (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 a #s(literal 2 binary64)) #s(literal 1 binary64)) b) t) #s(literal 16 binary64)))) < 4.99999999999999993e306

   1. Initial program 50.4%

      \[\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right) \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right) \cdot x\right) \cdot \cos \color{blue}{\left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)} \]

      2. associate-*l* N/A

         \[\leadsto \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right) \cdot \color{blue}{\left(x \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right), \color{blue}{\left(x \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right)}\right) \]

   3. Simplified 50.9%

      \[\leadsto \color{blue}{\cos \left(\left(z \cdot t\right) \cdot \left(0.0625 + y \cdot 0.125\right)\right) \cdot \left(x \cdot \cos \left(\left(t \cdot b\right) \cdot \left(0.0625 + a \cdot 0.125\right)\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. distribute-lft-in N/A

         \[\leadsto \mathsf{*.f64}\left(\cos \left(\left(z \cdot t\right) \cdot \frac{1}{16} + \left(z \cdot t\right) \cdot \left(y \cdot \frac{1}{8}\right)\right), \mathsf{*.f64}\left(x, \mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, b\right), \mathsf{+.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(a, \frac{1}{8}\right)\right)\right)\right)\right)\right) \]

      2. cos-sum N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\cos \left(\left(z \cdot t\right) \cdot \frac{1}{16}\right) \cdot \cos \left(\left(z \cdot t\right) \cdot \left(y \cdot \frac{1}{8}\right)\right) - \sin \left(\left(z \cdot t\right) \cdot \frac{1}{16}\right) \cdot \sin \left(\left(z \cdot t\right) \cdot \left(y \cdot \frac{1}{8}\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{x}, \mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, b\right), \mathsf{+.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(a, \frac{1}{8}\right)\right)\right)\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\cos \left(\left(z \cdot t\right) \cdot \frac{1}{16}\right) \cdot \cos \left(\left(z \cdot t\right) \cdot \left(y \cdot \frac{1}{8}\right)\right)\right), \left(\sin \left(\left(z \cdot t\right) \cdot \frac{1}{16}\right) \cdot \sin \left(\left(z \cdot t\right) \cdot \left(y \cdot \frac{1}{8}\right)\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{x}, \mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, b\right), \mathsf{+.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(a, \frac{1}{8}\right)\right)\right)\right)\right)\right) \]

   6. Applied egg-rr 51.7%

      \[\leadsto \color{blue}{\left(\cos \left(z \cdot \frac{t}{16}\right) \cdot \cos \left(z \cdot \left(t \cdot \left(y \cdot 0.125\right)\right)\right) - \sin \left(z \cdot \frac{t}{16}\right) \cdot \sin \left(z \cdot \left(t \cdot \left(y \cdot 0.125\right)\right)\right)\right)} \cdot \left(x \cdot \cos \left(\left(t \cdot b\right) \cdot \left(0.0625 + a \cdot 0.125\right)\right)\right) \]

   if 4.99999999999999993e306 < (*.f64 (*.f64 x (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y #s(literal 2 binary64)) #s(literal 1 binary64)) z) t) #s(literal 16 binary64)))) (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 a #s(literal 2 binary64)) #s(literal 1 binary64)) b) t) #s(literal 16 binary64))))

   1. Initial program 0.0%

      \[\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right) \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right) \cdot x\right) \cdot \cos \color{blue}{\left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)} \]

      2. associate-*l* N/A

         \[\leadsto \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right) \cdot \color{blue}{\left(x \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right), \color{blue}{\left(x \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right)}\right) \]

   3. Simplified 2.1%

      \[\leadsto \color{blue}{\cos \left(\left(z \cdot t\right) \cdot \left(0.0625 + y \cdot 0.125\right)\right) \cdot \left(x \cdot \cos \left(\left(t \cdot b\right) \cdot \left(0.0625 + a \cdot 0.125\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x} \]
   6. Step-by-step derivation

   7. Simplified 10.6%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 35.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{t \cdot \left(\left(1 + 2 \cdot a\right) \cdot b\right)}{16}\right) \leq 5 \cdot 10^{+306}:\\ \;\;\;\;\left(x \cdot \cos \left(\left(t \cdot b\right) \cdot \left(0.0625 + a \cdot 0.125\right)\right)\right) \cdot \left(\cos \left(z \cdot \frac{t}{16}\right) \cdot \cos \left(z \cdot \left(t \cdot \left(y \cdot 0.125\right)\right)\right) - \sin \left(z \cdot \frac{t}{16}\right) \cdot \sin \left(z \cdot \left(t \cdot \left(y \cdot 0.125\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 32.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{t \cdot \left(\left(1 + 2 \cdot a\right) \cdot b\right)}{16}\right) \leq 5 \cdot 10^{+306}:\\ \;\;\;\;\left(x \cdot \cos \left(\left(t \cdot b\right) \cdot \left(0.0625 + a \cdot 0.125\right)\right)\right) \cdot \cos \left(\frac{z \cdot t}{-1} \cdot \left(y \cdot \left(0 - \left(0.125 + \frac{0.0625}{y}\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<=
      (*
       (* x (cos (/ (* (* (+ (* y 2.0) 1.0) z) t) 16.0)))
       (cos (/ (* t (* (+ 1.0 (* 2.0 a)) b)) 16.0)))
      5e+306)
   (*
    (* x (cos (* (* t b) (+ 0.0625 (* a 0.125)))))
    (cos (* (/ (* z t) -1.0) (* y (- 0.0 (+ 0.125 (/ 0.0625 y)))))))
   x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((x * cos((((((y * 2.0) + 1.0) * z) * t) / 16.0))) * cos(((t * ((1.0 + (2.0 * a)) * b)) / 16.0))) <= 5e+306) {
		tmp = (x * cos(((t * b) * (0.0625 + (a * 0.125))))) * cos((((z * t) / -1.0) * (y * (0.0 - (0.125 + (0.0625 / y))))));
	} else {
		tmp = x;
	}
	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) :: tmp
    if (((x * cos((((((y * 2.0d0) + 1.0d0) * z) * t) / 16.0d0))) * cos(((t * ((1.0d0 + (2.0d0 * a)) * b)) / 16.0d0))) <= 5d+306) then
        tmp = (x * cos(((t * b) * (0.0625d0 + (a * 0.125d0))))) * cos((((z * t) / (-1.0d0)) * (y * (0.0d0 - (0.125d0 + (0.0625d0 / y))))))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((x * Math.cos((((((y * 2.0) + 1.0) * z) * t) / 16.0))) * Math.cos(((t * ((1.0 + (2.0 * a)) * b)) / 16.0))) <= 5e+306) {
		tmp = (x * Math.cos(((t * b) * (0.0625 + (a * 0.125))))) * Math.cos((((z * t) / -1.0) * (y * (0.0 - (0.125 + (0.0625 / y))))));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((x * math.cos((((((y * 2.0) + 1.0) * z) * t) / 16.0))) * math.cos(((t * ((1.0 + (2.0 * a)) * b)) / 16.0))) <= 5e+306:
		tmp = (x * math.cos(((t * b) * (0.0625 + (a * 0.125))))) * math.cos((((z * t) / -1.0) * (y * (0.0 - (0.125 + (0.0625 / y))))))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(x * cos(Float64(Float64(Float64(Float64(Float64(y * 2.0) + 1.0) * z) * t) / 16.0))) * cos(Float64(Float64(t * Float64(Float64(1.0 + Float64(2.0 * a)) * b)) / 16.0))) <= 5e+306)
		tmp = Float64(Float64(x * cos(Float64(Float64(t * b) * Float64(0.0625 + Float64(a * 0.125))))) * cos(Float64(Float64(Float64(z * t) / -1.0) * Float64(y * Float64(0.0 - Float64(0.125 + Float64(0.0625 / y)))))));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((x * cos((((((y * 2.0) + 1.0) * z) * t) / 16.0))) * cos(((t * ((1.0 + (2.0 * a)) * b)) / 16.0))) <= 5e+306)
		tmp = (x * cos(((t * b) * (0.0625 + (a * 0.125))))) * cos((((z * t) / -1.0) * (y * (0.0 - (0.125 + (0.0625 / y))))));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(x * N[Cos[N[(N[(N[(N[(N[(y * 2.0), $MachinePrecision] + 1.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] / 16.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Cos[N[(N[(t * N[(N[(1.0 + N[(2.0 * a), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] / 16.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 5e+306], N[(N[(x * N[Cos[N[(N[(t * b), $MachinePrecision] * N[(0.0625 + N[(a * 0.125), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Cos[N[(N[(N[(z * t), $MachinePrecision] / -1.0), $MachinePrecision] * N[(y * N[(0.0 - N[(0.125 + N[(0.0625 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 x (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y #s(literal 2 binary64)) #s(literal 1 binary64)) z) t) #s(literal 16 binary64)))) (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 a #s(literal 2 binary64)) #s(literal 1 binary64)) b) t) #s(literal 16 binary64)))) < 4.99999999999999993e306

   1. Initial program 50.4%

      \[\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right) \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right) \cdot x\right) \cdot \cos \color{blue}{\left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)} \]

      2. associate-*l* N/A

         \[\leadsto \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right) \cdot \color{blue}{\left(x \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right), \color{blue}{\left(x \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right)}\right) \]

   3. Simplified 50.9%

      \[\leadsto \color{blue}{\cos \left(\left(z \cdot t\right) \cdot \left(0.0625 + y \cdot 0.125\right)\right) \cdot \left(x \cdot \cos \left(\left(t \cdot b\right) \cdot \left(0.0625 + a \cdot 0.125\right)\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. flip3-+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{cos.f64}\left(\left(\left(z \cdot t\right) \cdot \frac{{\frac{1}{16}}^{3} + {\left(y \cdot \frac{1}{8}\right)}^{3}}{\frac{1}{16} \cdot \frac{1}{16} + \left(\left(y \cdot \frac{1}{8}\right) \cdot \left(y \cdot \frac{1}{8}\right) - \frac{1}{16} \cdot \left(y \cdot \frac{1}{8}\right)\right)}\right)\right), \mathsf{*.f64}\left(x, \mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, b\right), \mathsf{+.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(a, \frac{1}{8}\right)\right)\right)\right)\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{cos.f64}\left(\left(\left(z \cdot t\right) \cdot \frac{1}{\frac{\frac{1}{16} \cdot \frac{1}{16} + \left(\left(y \cdot \frac{1}{8}\right) \cdot \left(y \cdot \frac{1}{8}\right) - \frac{1}{16} \cdot \left(y \cdot \frac{1}{8}\right)\right)}{{\frac{1}{16}}^{3} + {\left(y \cdot \frac{1}{8}\right)}^{3}}}\right)\right), \mathsf{*.f64}\left(x, \mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, b\right), \mathsf{+.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(a, \frac{1}{8}\right)\right)\right)\right)\right)\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{cos.f64}\left(\left(\frac{z \cdot t}{\frac{\frac{1}{16} \cdot \frac{1}{16} + \left(\left(y \cdot \frac{1}{8}\right) \cdot \left(y \cdot \frac{1}{8}\right) - \frac{1}{16} \cdot \left(y \cdot \frac{1}{8}\right)\right)}{{\frac{1}{16}}^{3} + {\left(y \cdot \frac{1}{8}\right)}^{3}}}\right)\right), \mathsf{*.f64}\left(x, \mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, b\right), \mathsf{+.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(a, \frac{1}{8}\right)\right)\right)\right)\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{cos.f64}\left(\mathsf{/.f64}\left(\left(z \cdot t\right), \left(\frac{\frac{1}{16} \cdot \frac{1}{16} + \left(\left(y \cdot \frac{1}{8}\right) \cdot \left(y \cdot \frac{1}{8}\right) - \frac{1}{16} \cdot \left(y \cdot \frac{1}{8}\right)\right)}{{\frac{1}{16}}^{3} + {\left(y \cdot \frac{1}{8}\right)}^{3}}\right)\right)\right), \mathsf{*.f64}\left(x, \mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, b\right), \mathsf{+.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(a, \frac{1}{8}\right)\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{cos.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), \left(\frac{\frac{1}{16} \cdot \frac{1}{16} + \left(\left(y \cdot \frac{1}{8}\right) \cdot \left(y \cdot \frac{1}{8}\right) - \frac{1}{16} \cdot \left(y \cdot \frac{1}{8}\right)\right)}{{\frac{1}{16}}^{3} + {\left(y \cdot \frac{1}{8}\right)}^{3}}\right)\right)\right), \mathsf{*.f64}\left(x, \mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, b\right), \mathsf{+.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(a, \frac{1}{8}\right)\right)\right)\right)\right)\right) \]

      6. clear-num N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{cos.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), \left(\frac{1}{\frac{{\frac{1}{16}}^{3} + {\left(y \cdot \frac{1}{8}\right)}^{3}}{\frac{1}{16} \cdot \frac{1}{16} + \left(\left(y \cdot \frac{1}{8}\right) \cdot \left(y \cdot \frac{1}{8}\right) - \frac{1}{16} \cdot \left(y \cdot \frac{1}{8}\right)\right)}}\right)\right)\right), \mathsf{*.f64}\left(x, \mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, b\right), \mathsf{+.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(a, \frac{1}{8}\right)\right)\right)\right)\right)\right) \]

      7. flip3-+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{cos.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), \left(\frac{1}{\frac{1}{16} + y \cdot \frac{1}{8}}\right)\right)\right), \mathsf{*.f64}\left(x, \mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, b\right), \mathsf{+.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(a, \frac{1}{8}\right)\right)\right)\right)\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{cos.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), \mathsf{/.f64}\left(1, \left(\frac{1}{16} + y \cdot \frac{1}{8}\right)\right)\right)\right), \mathsf{*.f64}\left(x, \mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, b\right), \mathsf{+.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(a, \frac{1}{8}\right)\right)\right)\right)\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{cos.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\frac{1}{16}, \left(y \cdot \frac{1}{8}\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x, \mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, b\right), \mathsf{+.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(a, \frac{1}{8}\right)\right)\right)\right)\right)\right) \]

      10. *-lowering-*.f64 50.8%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{cos.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(y, \frac{1}{8}\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x, \mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, b\right), \mathsf{+.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(a, \frac{1}{8}\right)\right)\right)\right)\right)\right) \]

   6. Applied egg-rr 50.8%

      \[\leadsto \cos \color{blue}{\left(\frac{z \cdot t}{\frac{1}{0.0625 + y \cdot 0.125}}\right)} \cdot \left(x \cdot \cos \left(\left(t \cdot b\right) \cdot \left(0.0625 + a \cdot 0.125\right)\right)\right) \]
   7. Step-by-step derivation

      1. div-inv N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{cos.f64}\left(\left(\left(z \cdot t\right) \cdot \frac{1}{\frac{1}{\frac{1}{16} + y \cdot \frac{1}{8}}}\right)\right), \mathsf{*.f64}\left(x, \mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, b\right), \mathsf{+.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(a, \frac{1}{8}\right)\right)\right)\right)\right)\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{cos.f64}\left(\left(\frac{\left(z \cdot t\right) \cdot 1}{\frac{1}{\frac{1}{16} + y \cdot \frac{1}{8}}}\right)\right), \mathsf{*.f64}\left(x, \mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, b\right), \mathsf{+.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(a, \frac{1}{8}\right)\right)\right)\right)\right)\right) \]

      3. frac-2neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{cos.f64}\left(\left(\frac{\left(z \cdot t\right) \cdot 1}{\frac{\mathsf{neg}\left(1\right)}{\mathsf{neg}\left(\left(\frac{1}{16} + y \cdot \frac{1}{8}\right)\right)}}\right)\right), \mathsf{*.f64}\left(x, \mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, b\right), \mathsf{+.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(a, \frac{1}{8}\right)\right)\right)\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{cos.f64}\left(\left(\frac{\left(z \cdot t\right) \cdot 1}{\frac{-1}{\mathsf{neg}\left(\left(\frac{1}{16} + y \cdot \frac{1}{8}\right)\right)}}\right)\right), \mathsf{*.f64}\left(x, \mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, b\right), \mathsf{+.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(a, \frac{1}{8}\right)\right)\right)\right)\right)\right) \]

      5. div-inv N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{cos.f64}\left(\left(\frac{\left(z \cdot t\right) \cdot 1}{-1 \cdot \frac{1}{\mathsf{neg}\left(\left(\frac{1}{16} + y \cdot \frac{1}{8}\right)\right)}}\right)\right), \mathsf{*.f64}\left(x, \mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, b\right), \mathsf{+.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(a, \frac{1}{8}\right)\right)\right)\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{cos.f64}\left(\left(\frac{\left(z \cdot t\right) \cdot 1}{-1 \cdot \frac{\mathsf{neg}\left(-1\right)}{\mathsf{neg}\left(\left(\frac{1}{16} + y \cdot \frac{1}{8}\right)\right)}}\right)\right), \mathsf{*.f64}\left(x, \mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, b\right), \mathsf{+.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(a, \frac{1}{8}\right)\right)\right)\right)\right)\right) \]

      7. distribute-neg-frac N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{cos.f64}\left(\left(\frac{\left(z \cdot t\right) \cdot 1}{-1 \cdot \left(\mathsf{neg}\left(\frac{-1}{\mathsf{neg}\left(\left(\frac{1}{16} + y \cdot \frac{1}{8}\right)\right)}\right)\right)}\right)\right), \mathsf{*.f64}\left(x, \mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, b\right), \mathsf{+.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(a, \frac{1}{8}\right)\right)\right)\right)\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{cos.f64}\left(\left(\frac{\left(z \cdot t\right) \cdot 1}{-1 \cdot \left(\mathsf{neg}\left(\frac{\mathsf{neg}\left(1\right)}{\mathsf{neg}\left(\left(\frac{1}{16} + y \cdot \frac{1}{8}\right)\right)}\right)\right)}\right)\right), \mathsf{*.f64}\left(x, \mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, b\right), \mathsf{+.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(a, \frac{1}{8}\right)\right)\right)\right)\right)\right) \]

      9. frac-2neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{cos.f64}\left(\left(\frac{\left(z \cdot t\right) \cdot 1}{-1 \cdot \left(\mathsf{neg}\left(\frac{1}{\frac{1}{16} + y \cdot \frac{1}{8}}\right)\right)}\right)\right), \mathsf{*.f64}\left(x, \mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, b\right), \mathsf{+.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(a, \frac{1}{8}\right)\right)\right)\right)\right)\right) \]

      10. times-frac N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{cos.f64}\left(\left(\frac{z \cdot t}{-1} \cdot \frac{1}{\mathsf{neg}\left(\frac{1}{\frac{1}{16} + y \cdot \frac{1}{8}}\right)}\right)\right), \mathsf{*.f64}\left(x, \mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, b\right), \mathsf{+.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(a, \frac{1}{8}\right)\right)\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{cos.f64}\left(\mathsf{*.f64}\left(\left(\frac{z \cdot t}{-1}\right), \left(\frac{1}{\mathsf{neg}\left(\frac{1}{\frac{1}{16} + y \cdot \frac{1}{8}}\right)}\right)\right)\right), \mathsf{*.f64}\left(x, \mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, b\right), \mathsf{+.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(a, \frac{1}{8}\right)\right)\right)\right)\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(z \cdot t\right), -1\right), \left(\frac{1}{\mathsf{neg}\left(\frac{1}{\frac{1}{16} + y \cdot \frac{1}{8}}\right)}\right)\right)\right), \mathsf{*.f64}\left(x, \mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, b\right), \mathsf{+.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(a, \frac{1}{8}\right)\right)\right)\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(t \cdot z\right), -1\right), \left(\frac{1}{\mathsf{neg}\left(\frac{1}{\frac{1}{16} + y \cdot \frac{1}{8}}\right)}\right)\right)\right), \mathsf{*.f64}\left(x, \mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, b\right), \mathsf{+.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(a, \frac{1}{8}\right)\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(t, z\right), -1\right), \left(\frac{1}{\mathsf{neg}\left(\frac{1}{\frac{1}{16} + y \cdot \frac{1}{8}}\right)}\right)\right)\right), \mathsf{*.f64}\left(x, \mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, b\right), \mathsf{+.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(a, \frac{1}{8}\right)\right)\right)\right)\right)\right) \]

      15. frac-2neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(t, z\right), -1\right), \left(\frac{\mathsf{neg}\left(1\right)}{\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{1}{\frac{1}{16} + y \cdot \frac{1}{8}}\right)\right)\right)}\right)\right)\right), \mathsf{*.f64}\left(x, \mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, b\right), \mathsf{+.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(a, \frac{1}{8}\right)\right)\right)\right)\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(t, z\right), -1\right), \left(\frac{-1}{\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{1}{\frac{1}{16} + y \cdot \frac{1}{8}}\right)\right)\right)}\right)\right)\right), \mathsf{*.f64}\left(x, \mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, b\right), \mathsf{+.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(a, \frac{1}{8}\right)\right)\right)\right)\right)\right) \]

      17. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(t, z\right), -1\right), \left(\frac{-1}{\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{1}{\frac{1}{16} + \frac{1}{8} \cdot y}\right)\right)\right)}\right)\right)\right), \mathsf{*.f64}\left(x, \mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, b\right), \mathsf{+.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(a, \frac{1}{8}\right)\right)\right)\right)\right)\right) \]

      18. distribute-neg-frac N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(t, z\right), -1\right), \left(\frac{-1}{\mathsf{neg}\left(\frac{\mathsf{neg}\left(1\right)}{\frac{1}{16} + \frac{1}{8} \cdot y}\right)}\right)\right)\right), \mathsf{*.f64}\left(x, \mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, b\right), \mathsf{+.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(a, \frac{1}{8}\right)\right)\right)\right)\right)\right) \]

   8. Applied egg-rr 50.9%

      \[\leadsto \cos \color{blue}{\left(\frac{t \cdot z}{-1} \cdot \frac{-1}{\frac{1}{0.0625 + 0.125 \cdot y}}\right)} \cdot \left(x \cdot \cos \left(\left(t \cdot b\right) \cdot \left(0.0625 + a \cdot 0.125\right)\right)\right) \]

   9. Taylor expanded in y around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(t, z\right), -1\right), \color{blue}{\left(-1 \cdot \left(y \cdot \left(\frac{1}{8} + \frac{1}{16} \cdot \frac{1}{y}\right)\right)\right)}\right)\right), \mathsf{*.f64}\left(x, \mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, b\right), \mathsf{+.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(a, \frac{1}{8}\right)\right)\right)\right)\right)\right) \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(t, z\right), -1\right), \left(\mathsf{neg}\left(y \cdot \left(\frac{1}{8} + \frac{1}{16} \cdot \frac{1}{y}\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x, \mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, b\right), \mathsf{+.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(a, \frac{1}{8}\right)\right)\right)\right)\right)\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(t, z\right), -1\right), \left(\mathsf{neg}\left(\left(\frac{1}{8} + \frac{1}{16} \cdot \frac{1}{y}\right) \cdot y\right)\right)\right)\right), \mathsf{*.f64}\left(x, \mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, b\right), \mathsf{+.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(a, \frac{1}{8}\right)\right)\right)\right)\right)\right) \]

       3. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(t, z\right), -1\right), \left(\left(\frac{1}{8} + \frac{1}{16} \cdot \frac{1}{y}\right) \cdot \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x, \mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, b\right), \mathsf{+.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(a, \frac{1}{8}\right)\right)\right)\right)\right)\right) \]

       4. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(t, z\right), -1\right), \left(\left(\frac{1}{8} + \frac{1}{16} \cdot \frac{1}{y}\right) \cdot \left(-1 \cdot y\right)\right)\right)\right), \mathsf{*.f64}\left(x, \mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, b\right), \mathsf{+.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(a, \frac{1}{8}\right)\right)\right)\right)\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(t, z\right), -1\right), \mathsf{*.f64}\left(\left(\frac{1}{8} + \frac{1}{16} \cdot \frac{1}{y}\right), \left(-1 \cdot y\right)\right)\right)\right), \mathsf{*.f64}\left(x, \mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, b\right), \mathsf{+.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(a, \frac{1}{8}\right)\right)\right)\right)\right)\right) \]

       6. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(t, z\right), -1\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(\frac{1}{8}, \left(\frac{1}{16} \cdot \frac{1}{y}\right)\right), \left(-1 \cdot y\right)\right)\right)\right), \mathsf{*.f64}\left(x, \mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, b\right), \mathsf{+.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(a, \frac{1}{8}\right)\right)\right)\right)\right)\right) \]

       7. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(t, z\right), -1\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(\frac{1}{8}, \left(\frac{\frac{1}{16} \cdot 1}{y}\right)\right), \left(-1 \cdot y\right)\right)\right)\right), \mathsf{*.f64}\left(x, \mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, b\right), \mathsf{+.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(a, \frac{1}{8}\right)\right)\right)\right)\right)\right) \]

       8. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(t, z\right), -1\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(\frac{1}{8}, \left(\frac{\frac{1}{16}}{y}\right)\right), \left(-1 \cdot y\right)\right)\right)\right), \mathsf{*.f64}\left(x, \mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, b\right), \mathsf{+.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(a, \frac{1}{8}\right)\right)\right)\right)\right)\right) \]

       9. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(t, z\right), -1\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(\frac{1}{8}, \mathsf{/.f64}\left(\frac{1}{16}, y\right)\right), \left(-1 \cdot y\right)\right)\right)\right), \mathsf{*.f64}\left(x, \mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, b\right), \mathsf{+.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(a, \frac{1}{8}\right)\right)\right)\right)\right)\right) \]

       10. mul-1-neg N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(t, z\right), -1\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(\frac{1}{8}, \mathsf{/.f64}\left(\frac{1}{16}, y\right)\right), \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x, \mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, b\right), \mathsf{+.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(a, \frac{1}{8}\right)\right)\right)\right)\right)\right) \]

       11. neg-lowering-neg.f64 51.2%

           \[\leadsto \mathsf{*.f64}\left(\mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(t, z\right), -1\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(\frac{1}{8}, \mathsf{/.f64}\left(\frac{1}{16}, y\right)\right), \mathsf{neg.f64}\left(y\right)\right)\right)\right), \mathsf{*.f64}\left(x, \mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, b\right), \mathsf{+.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(a, \frac{1}{8}\right)\right)\right)\right)\right)\right) \]

   11. Simplified 51.2%

       \[\leadsto \cos \left(\frac{t \cdot z}{-1} \cdot \color{blue}{\left(\left(0.125 + \frac{0.0625}{y}\right) \cdot \left(-y\right)\right)}\right) \cdot \left(x \cdot \cos \left(\left(t \cdot b\right) \cdot \left(0.0625 + a \cdot 0.125\right)\right)\right) \]

   if 4.99999999999999993e306 < (*.f64 (*.f64 x (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y #s(literal 2 binary64)) #s(literal 1 binary64)) z) t) #s(literal 16 binary64)))) (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 a #s(literal 2 binary64)) #s(literal 1 binary64)) b) t) #s(literal 16 binary64))))

   1. Initial program 0.0%

      \[\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right) \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right) \cdot x\right) \cdot \cos \color{blue}{\left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)} \]

      2. associate-*l* N/A

         \[\leadsto \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right) \cdot \color{blue}{\left(x \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right), \color{blue}{\left(x \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right)}\right) \]

   3. Simplified 2.1%

      \[\leadsto \color{blue}{\cos \left(\left(z \cdot t\right) \cdot \left(0.0625 + y \cdot 0.125\right)\right) \cdot \left(x \cdot \cos \left(\left(t \cdot b\right) \cdot \left(0.0625 + a \cdot 0.125\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x} \]
   6. Step-by-step derivation

   7. Simplified 10.6%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 34.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{t \cdot \left(\left(1 + 2 \cdot a\right) \cdot b\right)}{16}\right) \leq 5 \cdot 10^{+306}:\\ \;\;\;\;\left(x \cdot \cos \left(\left(t \cdot b\right) \cdot \left(0.0625 + a \cdot 0.125\right)\right)\right) \cdot \cos \left(\frac{z \cdot t}{-1} \cdot \left(y \cdot \left(0 - \left(0.125 + \frac{0.0625}{y}\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 32.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{t \cdot \left(\left(1 + 2 \cdot a\right) \cdot b\right)}{16}\right) \leq 5 \cdot 10^{+306}:\\ \;\;\;\;\left(x \cdot \cos \left(\left(t \cdot b\right) \cdot \left(0.0625 + a \cdot 0.125\right)\right)\right) \cdot \cos \left(\left(z \cdot t\right) \cdot \left(y \cdot 0.125 + 0.0625\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<=
      (*
       (* x (cos (/ (* (* (+ (* y 2.0) 1.0) z) t) 16.0)))
       (cos (/ (* t (* (+ 1.0 (* 2.0 a)) b)) 16.0)))
      5e+306)
   (*
    (* x (cos (* (* t b) (+ 0.0625 (* a 0.125)))))
    (cos (* (* z t) (+ (* y 0.125) 0.0625))))
   x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((x * cos((((((y * 2.0) + 1.0) * z) * t) / 16.0))) * cos(((t * ((1.0 + (2.0 * a)) * b)) / 16.0))) <= 5e+306) {
		tmp = (x * cos(((t * b) * (0.0625 + (a * 0.125))))) * cos(((z * t) * ((y * 0.125) + 0.0625)));
	} else {
		tmp = x;
	}
	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) :: tmp
    if (((x * cos((((((y * 2.0d0) + 1.0d0) * z) * t) / 16.0d0))) * cos(((t * ((1.0d0 + (2.0d0 * a)) * b)) / 16.0d0))) <= 5d+306) then
        tmp = (x * cos(((t * b) * (0.0625d0 + (a * 0.125d0))))) * cos(((z * t) * ((y * 0.125d0) + 0.0625d0)))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((x * Math.cos((((((y * 2.0) + 1.0) * z) * t) / 16.0))) * Math.cos(((t * ((1.0 + (2.0 * a)) * b)) / 16.0))) <= 5e+306) {
		tmp = (x * Math.cos(((t * b) * (0.0625 + (a * 0.125))))) * Math.cos(((z * t) * ((y * 0.125) + 0.0625)));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((x * math.cos((((((y * 2.0) + 1.0) * z) * t) / 16.0))) * math.cos(((t * ((1.0 + (2.0 * a)) * b)) / 16.0))) <= 5e+306:
		tmp = (x * math.cos(((t * b) * (0.0625 + (a * 0.125))))) * math.cos(((z * t) * ((y * 0.125) + 0.0625)))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(x * cos(Float64(Float64(Float64(Float64(Float64(y * 2.0) + 1.0) * z) * t) / 16.0))) * cos(Float64(Float64(t * Float64(Float64(1.0 + Float64(2.0 * a)) * b)) / 16.0))) <= 5e+306)
		tmp = Float64(Float64(x * cos(Float64(Float64(t * b) * Float64(0.0625 + Float64(a * 0.125))))) * cos(Float64(Float64(z * t) * Float64(Float64(y * 0.125) + 0.0625))));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((x * cos((((((y * 2.0) + 1.0) * z) * t) / 16.0))) * cos(((t * ((1.0 + (2.0 * a)) * b)) / 16.0))) <= 5e+306)
		tmp = (x * cos(((t * b) * (0.0625 + (a * 0.125))))) * cos(((z * t) * ((y * 0.125) + 0.0625)));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(x * N[Cos[N[(N[(N[(N[(N[(y * 2.0), $MachinePrecision] + 1.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] / 16.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Cos[N[(N[(t * N[(N[(1.0 + N[(2.0 * a), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] / 16.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 5e+306], N[(N[(x * N[Cos[N[(N[(t * b), $MachinePrecision] * N[(0.0625 + N[(a * 0.125), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Cos[N[(N[(z * t), $MachinePrecision] * N[(N[(y * 0.125), $MachinePrecision] + 0.0625), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 x (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y #s(literal 2 binary64)) #s(literal 1 binary64)) z) t) #s(literal 16 binary64)))) (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 a #s(literal 2 binary64)) #s(literal 1 binary64)) b) t) #s(literal 16 binary64)))) < 4.99999999999999993e306

   1. Initial program 50.4%

      \[\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right) \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right) \cdot x\right) \cdot \cos \color{blue}{\left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)} \]

      2. associate-*l* N/A

         \[\leadsto \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right) \cdot \color{blue}{\left(x \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right), \color{blue}{\left(x \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right)}\right) \]

   3. Simplified 50.9%

      \[\leadsto \color{blue}{\cos \left(\left(z \cdot t\right) \cdot \left(0.0625 + y \cdot 0.125\right)\right) \cdot \left(x \cdot \cos \left(\left(t \cdot b\right) \cdot \left(0.0625 + a \cdot 0.125\right)\right)\right)} \]
   4. Add Preprocessing

   if 4.99999999999999993e306 < (*.f64 (*.f64 x (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y #s(literal 2 binary64)) #s(literal 1 binary64)) z) t) #s(literal 16 binary64)))) (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 a #s(literal 2 binary64)) #s(literal 1 binary64)) b) t) #s(literal 16 binary64))))

   1. Initial program 0.0%

      \[\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right) \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right) \cdot x\right) \cdot \cos \color{blue}{\left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)} \]

      2. associate-*l* N/A

         \[\leadsto \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right) \cdot \color{blue}{\left(x \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right), \color{blue}{\left(x \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right)}\right) \]

   3. Simplified 2.1%

      \[\leadsto \color{blue}{\cos \left(\left(z \cdot t\right) \cdot \left(0.0625 + y \cdot 0.125\right)\right) \cdot \left(x \cdot \cos \left(\left(t \cdot b\right) \cdot \left(0.0625 + a \cdot 0.125\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x} \]
   6. Step-by-step derivation

   7. Simplified 10.6%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 34.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{t \cdot \left(\left(1 + 2 \cdot a\right) \cdot b\right)}{16}\right) \leq 5 \cdot 10^{+306}:\\ \;\;\;\;\left(x \cdot \cos \left(\left(t \cdot b\right) \cdot \left(0.0625 + a \cdot 0.125\right)\right)\right) \cdot \cos \left(\left(z \cdot t\right) \cdot \left(y \cdot 0.125 + 0.0625\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 31.1% accurate, 225.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 x)

C

double code(double x, double y, double z, double t, double a, double b) {
	return x;
}

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 = x
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x;
}

Python

def code(x, y, z, t, a, b):
	return x

Julia

function code(x, y, z, t, a, b)
	return x
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := x

Derivation

1. Initial program 29.9%

   \[\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right) \]
2. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \left(\cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right) \cdot x\right) \cdot \cos \color{blue}{\left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)} \]

   2. associate-*l* N/A

      \[\leadsto \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right) \cdot \color{blue}{\left(x \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right)} \]

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right), \color{blue}{\left(x \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right)}\right) \]

3. Simplified 31.1%

   \[\leadsto \color{blue}{\cos \left(\left(z \cdot t\right) \cdot \left(0.0625 + y \cdot 0.125\right)\right) \cdot \left(x \cdot \cos \left(\left(t \cdot b\right) \cdot \left(0.0625 + a \cdot 0.125\right)\right)\right)} \]
4. Add Preprocessing

5. Taylor expanded in t around 0

   \[\leadsto \color{blue}{x} \]
6. Step-by-step derivation

7. Simplified 32.4%

   \[\leadsto \color{blue}{x} \]
8. Add Preprocessing

Developer Target 1: 30.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \cos \left(\frac{b}{16} \cdot \frac{t}{\left(1 - a \cdot 2\right) + {\left(a \cdot 2\right)}^{2}}\right) \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (* x (cos (* (/ b 16.0) (/ t (+ (- 1.0 (* a 2.0)) (pow (* a 2.0) 2.0)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x * cos(((b / 16.0) * (t / ((1.0 - (a * 2.0)) + pow((a * 2.0), 2.0)))));
}

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 = x * cos(((b / 16.0d0) * (t / ((1.0d0 - (a * 2.0d0)) + ((a * 2.0d0) ** 2.0d0)))))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x * Math.cos(((b / 16.0) * (t / ((1.0 - (a * 2.0)) + Math.pow((a * 2.0), 2.0)))));
}

Python

def code(x, y, z, t, a, b):
	return x * math.cos(((b / 16.0) * (t / ((1.0 - (a * 2.0)) + math.pow((a * 2.0), 2.0)))))

Julia

function code(x, y, z, t, a, b)
	return Float64(x * cos(Float64(Float64(b / 16.0) * Float64(t / Float64(Float64(1.0 - Float64(a * 2.0)) + (Float64(a * 2.0) ^ 2.0))))))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x * cos(((b / 16.0) * (t / ((1.0 - (a * 2.0)) + ((a * 2.0) ^ 2.0)))));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x * N[Cos[N[(N[(b / 16.0), $MachinePrecision] * N[(t / N[(N[(1.0 - N[(a * 2.0), $MachinePrecision]), $MachinePrecision] + N[Power[N[(a * 2.0), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024158 
(FPCore (x y z t a b)
  :name "Codec.Picture.Jpg.FastDct:referenceDct from JuicyPixels-3.2.6.1"
  :precision binary64

  :alt
  (! :herbie-platform default (* x (cos (* (/ b 16) (/ t (+ (- 1 (* a 2)) (pow (* a 2) 2)))))))

  (* (* x (cos (/ (* (* (+ (* y 2.0) 1.0) z) t) 16.0))) (cos (/ (* (* (+ (* a 2.0) 1.0) b) t) 16.0))))