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

Percentage Accurate: 26.9% → 31.2%

Time: 17.3s

Alternatives: 4

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: 26.9% 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: 31.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := y \cdot 2 + 1\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;\left(x\_m \cdot \cos \left(\frac{\left(t\_1 \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{t \cdot \left(\left(1 + 2 \cdot a\right) \cdot b\right)}{16}\right) \leq 2 \cdot 10^{+272}:\\ \;\;\;\;\cos \left({\left(\sqrt[3]{t\_1 \cdot \left(z \cdot \left(t \cdot 0.0625\right)\right)}\right)}^{3}\right) \cdot \left(x\_m \cdot \cos \left(-0.125 \cdot \left(a \cdot \left(t \cdot b\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\_m\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* y 2.0) 1.0)))
   (*
    x_s
    (if (<=
         (*
          (* x_m (cos (/ (* (* t_1 z) t) 16.0)))
          (cos (/ (* t (* (+ 1.0 (* 2.0 a)) b)) 16.0)))
         2e+272)
      (*
       (cos (pow (cbrt (* t_1 (* z (* t 0.0625)))) 3.0))
       (* x_m (cos (* -0.125 (* a (* t b))))))
      x_m))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t, double a, double b) {
	double t_1 = (y * 2.0) + 1.0;
	double tmp;
	if (((x_m * cos((((t_1 * z) * t) / 16.0))) * cos(((t * ((1.0 + (2.0 * a)) * b)) / 16.0))) <= 2e+272) {
		tmp = cos(pow(cbrt((t_1 * (z * (t * 0.0625)))), 3.0)) * (x_m * cos((-0.125 * (a * (t * b)))));
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t, double a, double b) {
	double t_1 = (y * 2.0) + 1.0;
	double tmp;
	if (((x_m * Math.cos((((t_1 * z) * t) / 16.0))) * Math.cos(((t * ((1.0 + (2.0 * a)) * b)) / 16.0))) <= 2e+272) {
		tmp = Math.cos(Math.pow(Math.cbrt((t_1 * (z * (t * 0.0625)))), 3.0)) * (x_m * Math.cos((-0.125 * (a * (t * b)))));
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t, a, b)
	t_1 = Float64(Float64(y * 2.0) + 1.0)
	tmp = 0.0
	if (Float64(Float64(x_m * cos(Float64(Float64(Float64(t_1 * z) * t) / 16.0))) * cos(Float64(Float64(t * Float64(Float64(1.0 + Float64(2.0 * a)) * b)) / 16.0))) <= 2e+272)
		tmp = Float64(cos((cbrt(Float64(t_1 * Float64(z * Float64(t * 0.0625)))) ^ 3.0)) * Float64(x_m * cos(Float64(-0.125 * Float64(a * Float64(t * b))))));
	else
		tmp = x_m;
	end
	return Float64(x_s * tmp)
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * 2.0), $MachinePrecision] + 1.0), $MachinePrecision]}, N[(x$95$s * If[LessEqual[N[(N[(x$95$m * N[Cos[N[(N[(N[(t$95$1 * 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], 2e+272], N[(N[Cos[N[Power[N[Power[N[(t$95$1 * N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision], 3.0], $MachinePrecision]], $MachinePrecision] * N[(x$95$m * N[Cos[N[(-0.125 * N[(a * N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x$95$m]), $MachinePrecision]]

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)))) < 2.0000000000000001e272

   1. Initial program 43.7%

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

   3. Simplified 42.6%

      \[\leadsto \color{blue}{\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \left(t \cdot 0.0625\right)\right)\right) \cdot \left(x \cdot \cos \left(\left(b \cdot 0.0625\right) \cdot \left(t \cdot \mathsf{fma}\left(a, -2, -1\right)\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 44.5%

      \[\leadsto \cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \left(t \cdot 0.0625\right)\right)\right) \cdot \left(x \cdot \cos \color{blue}{\left(-0.125 \cdot \left(a \cdot \left(b \cdot t\right)\right)\right)}\right) \]
   6. Step-by-step derivation

      1. add-exp-log 38.5%

         \[\leadsto \cos \left(\color{blue}{e^{\log \left(\mathsf{fma}\left(y, 2, 1\right)\right)}} \cdot \left(z \cdot \left(t \cdot 0.0625\right)\right)\right) \cdot \left(x \cdot \cos \left(-0.125 \cdot \left(a \cdot \left(b \cdot t\right)\right)\right)\right) \]

      2. fma-define 38.5%

         \[\leadsto \cos \left(e^{\log \color{blue}{\left(y \cdot 2 + 1\right)}} \cdot \left(z \cdot \left(t \cdot 0.0625\right)\right)\right) \cdot \left(x \cdot \cos \left(-0.125 \cdot \left(a \cdot \left(b \cdot t\right)\right)\right)\right) \]

      3. +-commutative 38.5%

         \[\leadsto \cos \left(e^{\log \color{blue}{\left(1 + y \cdot 2\right)}} \cdot \left(z \cdot \left(t \cdot 0.0625\right)\right)\right) \cdot \left(x \cdot \cos \left(-0.125 \cdot \left(a \cdot \left(b \cdot t\right)\right)\right)\right) \]

      4. log1p-define 38.5%

         \[\leadsto \cos \left(e^{\color{blue}{\mathsf{log1p}\left(y \cdot 2\right)}} \cdot \left(z \cdot \left(t \cdot 0.0625\right)\right)\right) \cdot \left(x \cdot \cos \left(-0.125 \cdot \left(a \cdot \left(b \cdot t\right)\right)\right)\right) \]

   7. Applied egg-rr 38.5%

      \[\leadsto \cos \left(\color{blue}{e^{\mathsf{log1p}\left(y \cdot 2\right)}} \cdot \left(z \cdot \left(t \cdot 0.0625\right)\right)\right) \cdot \left(x \cdot \cos \left(-0.125 \cdot \left(a \cdot \left(b \cdot t\right)\right)\right)\right) \]
   8. Step-by-step derivation

      1. add-cube-cbrt 38.6%

         \[\leadsto \cos \color{blue}{\left(\left(\sqrt[3]{e^{\mathsf{log1p}\left(y \cdot 2\right)} \cdot \left(z \cdot \left(t \cdot 0.0625\right)\right)} \cdot \sqrt[3]{e^{\mathsf{log1p}\left(y \cdot 2\right)} \cdot \left(z \cdot \left(t \cdot 0.0625\right)\right)}\right) \cdot \sqrt[3]{e^{\mathsf{log1p}\left(y \cdot 2\right)} \cdot \left(z \cdot \left(t \cdot 0.0625\right)\right)}\right)} \cdot \left(x \cdot \cos \left(-0.125 \cdot \left(a \cdot \left(b \cdot t\right)\right)\right)\right) \]

      2. pow3 38.6%

         \[\leadsto \cos \color{blue}{\left({\left(\sqrt[3]{e^{\mathsf{log1p}\left(y \cdot 2\right)} \cdot \left(z \cdot \left(t \cdot 0.0625\right)\right)}\right)}^{3}\right)} \cdot \left(x \cdot \cos \left(-0.125 \cdot \left(a \cdot \left(b \cdot t\right)\right)\right)\right) \]

      3. log1p-undefine 38.6%

         \[\leadsto \cos \left({\left(\sqrt[3]{e^{\color{blue}{\log \left(1 + y \cdot 2\right)}} \cdot \left(z \cdot \left(t \cdot 0.0625\right)\right)}\right)}^{3}\right) \cdot \left(x \cdot \cos \left(-0.125 \cdot \left(a \cdot \left(b \cdot t\right)\right)\right)\right) \]

      4. rem-exp-log 44.5%

         \[\leadsto \cos \left({\left(\sqrt[3]{\color{blue}{\left(1 + y \cdot 2\right)} \cdot \left(z \cdot \left(t \cdot 0.0625\right)\right)}\right)}^{3}\right) \cdot \left(x \cdot \cos \left(-0.125 \cdot \left(a \cdot \left(b \cdot t\right)\right)\right)\right) \]

      5. *-commutative 44.5%

         \[\leadsto \cos \left({\left(\sqrt[3]{\left(1 + \color{blue}{2 \cdot y}\right) \cdot \left(z \cdot \left(t \cdot 0.0625\right)\right)}\right)}^{3}\right) \cdot \left(x \cdot \cos \left(-0.125 \cdot \left(a \cdot \left(b \cdot t\right)\right)\right)\right) \]

   9. Applied egg-rr 44.5%

      \[\leadsto \cos \color{blue}{\left({\left(\sqrt[3]{\left(1 + 2 \cdot y\right) \cdot \left(z \cdot \left(t \cdot 0.0625\right)\right)}\right)}^{3}\right)} \cdot \left(x \cdot \cos \left(-0.125 \cdot \left(a \cdot \left(b \cdot t\right)\right)\right)\right) \]

   if 2.0000000000000001e272 < (*.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 1.2%

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

   3. Simplified 1.2%

      \[\leadsto \color{blue}{x \cdot \left(\cos \left(\left(\mathsf{fma}\left(y, 2, 1\right) \cdot z\right) \cdot \frac{t}{16}\right) \cdot \cos \left(\left(\mathsf{fma}\left(a, 2, 1\right) \cdot b\right) \cdot \frac{t}{16}\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 12.1%

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

4. Final simplification 31.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{t \cdot \left(\left(1 + 2 \cdot a\right) \cdot b\right)}{16}\right) \leq 2 \cdot 10^{+272}:\\ \;\;\;\;\cos \left({\left(\sqrt[3]{\left(y \cdot 2 + 1\right) \cdot \left(z \cdot \left(t \cdot 0.0625\right)\right)}\right)}^{3}\right) \cdot \left(x \cdot \cos \left(-0.125 \cdot \left(a \cdot \left(t \cdot b\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 31.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;\left(x\_m \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{t \cdot \left(\left(1 + 2 \cdot a\right) \cdot b\right)}{16}\right) \leq 2 \cdot 10^{+272}:\\ \;\;\;\;x\_m \cdot \left(\cos \left(\left(z \cdot \mathsf{fma}\left(y, 2, 1\right)\right) \cdot \frac{t}{16}\right) \cdot \cos \left(\frac{1}{\frac{16}{2 \cdot \left(a \cdot \left(t \cdot b\right)\right)}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\_m\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t a b)
 :precision binary64
 (*
  x_s
  (if (<=
       (*
        (* x_m (cos (/ (* (* (+ (* y 2.0) 1.0) z) t) 16.0)))
        (cos (/ (* t (* (+ 1.0 (* 2.0 a)) b)) 16.0)))
       2e+272)
    (*
     x_m
     (*
      (cos (* (* z (fma y 2.0 1.0)) (/ t 16.0)))
      (cos (/ 1.0 (/ 16.0 (* 2.0 (* a (* t b))))))))
    x_m)))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t, double a, double b) {
	double tmp;
	if (((x_m * cos((((((y * 2.0) + 1.0) * z) * t) / 16.0))) * cos(((t * ((1.0 + (2.0 * a)) * b)) / 16.0))) <= 2e+272) {
		tmp = x_m * (cos(((z * fma(y, 2.0, 1.0)) * (t / 16.0))) * cos((1.0 / (16.0 / (2.0 * (a * (t * b)))))));
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(x_m * 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))) <= 2e+272)
		tmp = Float64(x_m * Float64(cos(Float64(Float64(z * fma(y, 2.0, 1.0)) * Float64(t / 16.0))) * cos(Float64(1.0 / Float64(16.0 / Float64(2.0 * Float64(a * Float64(t * b))))))));
	else
		tmp = x_m;
	end
	return Float64(x_s * tmp)
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_, a_, b_] := N[(x$95$s * If[LessEqual[N[(N[(x$95$m * 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], 2e+272], N[(x$95$m * N[(N[Cos[N[(N[(z * N[(y * 2.0 + 1.0), $MachinePrecision]), $MachinePrecision] * N[(t / 16.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(1.0 / N[(16.0 / N[(2.0 * N[(a * N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x$95$m]), $MachinePrecision]

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)))) < 2.0000000000000001e272

   1. Initial program 43.7%

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

   3. Simplified 43.7%

      \[\leadsto \color{blue}{x \cdot \left(\cos \left(\left(\mathsf{fma}\left(y, 2, 1\right) \cdot z\right) \cdot \frac{t}{16}\right) \cdot \cos \left(\left(\mathsf{fma}\left(a, 2, 1\right) \cdot b\right) \cdot \frac{t}{16}\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*r/ 43.7%

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

      2. fma-define 43.7%

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

      3. clear-num 43.6%

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

      4. *-commutative 43.6%

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

      5. *-commutative 43.6%

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

      6. *-commutative 43.6%

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

      7. fma-undefine 43.6%

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

   6. Applied egg-rr 43.6%

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

   7. Taylor expanded in a around inf 44.5%

      \[\leadsto x \cdot \left(\cos \left(\left(\mathsf{fma}\left(y, 2, 1\right) \cdot z\right) \cdot \frac{t}{16}\right) \cdot \cos \left(\frac{1}{\frac{16}{\color{blue}{2 \cdot \left(a \cdot \left(b \cdot t\right)\right)}}}\right)\right) \]
   8. Step-by-step derivation

      1. *-commutative 44.5%

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

      2. *-commutative 44.5%

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

   9. Simplified 44.5%

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

   if 2.0000000000000001e272 < (*.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 1.2%

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

   3. Simplified 1.2%

      \[\leadsto \color{blue}{x \cdot \left(\cos \left(\left(\mathsf{fma}\left(y, 2, 1\right) \cdot z\right) \cdot \frac{t}{16}\right) \cdot \cos \left(\left(\mathsf{fma}\left(a, 2, 1\right) \cdot b\right) \cdot \frac{t}{16}\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 12.1%

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

4. Final simplification 31.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{t \cdot \left(\left(1 + 2 \cdot a\right) \cdot b\right)}{16}\right) \leq 2 \cdot 10^{+272}:\\ \;\;\;\;x \cdot \left(\cos \left(\left(z \cdot \mathsf{fma}\left(y, 2, 1\right)\right) \cdot \frac{t}{16}\right) \cdot \cos \left(\frac{1}{\frac{16}{2 \cdot \left(a \cdot \left(t \cdot b\right)\right)}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 31.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := y \cdot 2 + 1\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;\left(x\_m \cdot \cos \left(\frac{\left(t\_1 \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{t \cdot \left(\left(1 + 2 \cdot a\right) \cdot b\right)}{16}\right) \leq 2 \cdot 10^{+272}:\\ \;\;\;\;\left(x\_m \cdot \cos \left(-0.125 \cdot \left(a \cdot \left(t \cdot b\right)\right)\right)\right) \cdot \cos \left(t\_1 \cdot \left(z \cdot \left(t \cdot 0.0625\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\_m\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* y 2.0) 1.0)))
   (*
    x_s
    (if (<=
         (*
          (* x_m (cos (/ (* (* t_1 z) t) 16.0)))
          (cos (/ (* t (* (+ 1.0 (* 2.0 a)) b)) 16.0)))
         2e+272)
      (*
       (* x_m (cos (* -0.125 (* a (* t b)))))
       (cos (* t_1 (* z (* t 0.0625)))))
      x_m))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t, double a, double b) {
	double t_1 = (y * 2.0) + 1.0;
	double tmp;
	if (((x_m * cos((((t_1 * z) * t) / 16.0))) * cos(((t * ((1.0 + (2.0 * a)) * b)) / 16.0))) <= 2e+272) {
		tmp = (x_m * cos((-0.125 * (a * (t * b))))) * cos((t_1 * (z * (t * 0.0625))));
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t, a, b)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y * 2.0d0) + 1.0d0
    if (((x_m * cos((((t_1 * z) * t) / 16.0d0))) * cos(((t * ((1.0d0 + (2.0d0 * a)) * b)) / 16.0d0))) <= 2d+272) then
        tmp = (x_m * cos(((-0.125d0) * (a * (t * b))))) * cos((t_1 * (z * (t * 0.0625d0))))
    else
        tmp = x_m
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t, double a, double b) {
	double t_1 = (y * 2.0) + 1.0;
	double tmp;
	if (((x_m * Math.cos((((t_1 * z) * t) / 16.0))) * Math.cos(((t * ((1.0 + (2.0 * a)) * b)) / 16.0))) <= 2e+272) {
		tmp = (x_m * Math.cos((-0.125 * (a * (t * b))))) * Math.cos((t_1 * (z * (t * 0.0625))));
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t, a, b):
	t_1 = (y * 2.0) + 1.0
	tmp = 0
	if ((x_m * math.cos((((t_1 * z) * t) / 16.0))) * math.cos(((t * ((1.0 + (2.0 * a)) * b)) / 16.0))) <= 2e+272:
		tmp = (x_m * math.cos((-0.125 * (a * (t * b))))) * math.cos((t_1 * (z * (t * 0.0625))))
	else:
		tmp = x_m
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t, a, b)
	t_1 = Float64(Float64(y * 2.0) + 1.0)
	tmp = 0.0
	if (Float64(Float64(x_m * cos(Float64(Float64(Float64(t_1 * z) * t) / 16.0))) * cos(Float64(Float64(t * Float64(Float64(1.0 + Float64(2.0 * a)) * b)) / 16.0))) <= 2e+272)
		tmp = Float64(Float64(x_m * cos(Float64(-0.125 * Float64(a * Float64(t * b))))) * cos(Float64(t_1 * Float64(z * Float64(t * 0.0625)))));
	else
		tmp = x_m;
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t, a, b)
	t_1 = (y * 2.0) + 1.0;
	tmp = 0.0;
	if (((x_m * cos((((t_1 * z) * t) / 16.0))) * cos(((t * ((1.0 + (2.0 * a)) * b)) / 16.0))) <= 2e+272)
		tmp = (x_m * cos((-0.125 * (a * (t * b))))) * cos((t_1 * (z * (t * 0.0625))));
	else
		tmp = x_m;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * 2.0), $MachinePrecision] + 1.0), $MachinePrecision]}, N[(x$95$s * If[LessEqual[N[(N[(x$95$m * N[Cos[N[(N[(N[(t$95$1 * 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], 2e+272], N[(N[(x$95$m * N[Cos[N[(-0.125 * N[(a * N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Cos[N[(t$95$1 * N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], x$95$m]), $MachinePrecision]]

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)))) < 2.0000000000000001e272

   1. Initial program 43.7%

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

   3. Simplified 42.6%

      \[\leadsto \color{blue}{\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \left(t \cdot 0.0625\right)\right)\right) \cdot \left(x \cdot \cos \left(\left(b \cdot 0.0625\right) \cdot \left(t \cdot \mathsf{fma}\left(a, -2, -1\right)\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 44.5%

      \[\leadsto \cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \left(t \cdot 0.0625\right)\right)\right) \cdot \left(x \cdot \cos \color{blue}{\left(-0.125 \cdot \left(a \cdot \left(b \cdot t\right)\right)\right)}\right) \]
   6. Step-by-step derivation

      1. fma-define 44.5%

         \[\leadsto \cos \left(\color{blue}{\left(y \cdot 2 + 1\right)} \cdot \left(z \cdot \left(t \cdot 0.0625\right)\right)\right) \cdot \left(x \cdot \cos \left(-0.125 \cdot \left(a \cdot \left(b \cdot t\right)\right)\right)\right) \]

   7. Applied egg-rr 44.5%

      \[\leadsto \cos \left(\color{blue}{\left(y \cdot 2 + 1\right)} \cdot \left(z \cdot \left(t \cdot 0.0625\right)\right)\right) \cdot \left(x \cdot \cos \left(-0.125 \cdot \left(a \cdot \left(b \cdot t\right)\right)\right)\right) \]

   if 2.0000000000000001e272 < (*.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 1.2%

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

   3. Simplified 1.2%

      \[\leadsto \color{blue}{x \cdot \left(\cos \left(\left(\mathsf{fma}\left(y, 2, 1\right) \cdot z\right) \cdot \frac{t}{16}\right) \cdot \cos \left(\left(\mathsf{fma}\left(a, 2, 1\right) \cdot b\right) \cdot \frac{t}{16}\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 12.1%

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

4. Final simplification 31.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{t \cdot \left(\left(1 + 2 \cdot a\right) \cdot b\right)}{16}\right) \leq 2 \cdot 10^{+272}:\\ \;\;\;\;\left(x \cdot \cos \left(-0.125 \cdot \left(a \cdot \left(t \cdot b\right)\right)\right)\right) \cdot \cos \left(\left(y \cdot 2 + 1\right) \cdot \left(z \cdot \left(t \cdot 0.0625\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 30.2% accurate, 225.0× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot x\_m \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t a b) :precision binary64 (* x_s x_m))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t, double a, double b) {
	return x_s * x_m;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t, a, b)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    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_s * x_m
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t, double a, double b) {
	return x_s * x_m;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t, a, b):
	return x_s * x_m

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t, a, b)
	return Float64(x_s * x_m)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp = code(x_s, x_m, y, z, t, a, b)
	tmp = x_s * x_m;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_, a_, b_] := N[(x$95$s * x$95$m), $MachinePrecision]

Derivation

1. Initial program 26.7%

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

3. Simplified 26.7%

   \[\leadsto \color{blue}{x \cdot \left(\cos \left(\left(\mathsf{fma}\left(y, 2, 1\right) \cdot z\right) \cdot \frac{t}{16}\right) \cdot \cos \left(\left(\mathsf{fma}\left(a, 2, 1\right) \cdot b\right) \cdot \frac{t}{16}\right)\right)} \]
4. Add Preprocessing

5. Taylor expanded in t around 0 29.8%

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

Developer Target 1: 29.7% 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 2024170 
(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))))