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

Percentage Accurate: 27.6% → 29.8%

Time: 33.9s

Alternatives: 2

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: 27.6% 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: 29.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} t = |t|\\ b = |b|\\ \\ \cos \left(e^{\log \left(b \cdot t\right)} \cdot e^{\log 0.0625}\right) \cdot x \end{array} \]

FPCore

NOTE: t should be positive before calling this function
NOTE: b should be positive before calling this function
(FPCore (x y z t a b)
 :precision binary64
 (* (cos (* (exp (log (* b t))) (exp (log 0.0625)))) x))

C

t = abs(t);
b = abs(b);
double code(double x, double y, double z, double t, double a, double b) {
	return cos((exp(log((b * t))) * exp(log(0.0625)))) * x;
}

Fortran

NOTE: t should be positive before calling this function
NOTE: b should be positive before calling this function
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = cos((exp(log((b * t))) * exp(log(0.0625d0)))) * x
end function

Java

t = Math.abs(t);
b = Math.abs(b);
public static double code(double x, double y, double z, double t, double a, double b) {
	return Math.cos((Math.exp(Math.log((b * t))) * Math.exp(Math.log(0.0625)))) * x;
}

Python

t = abs(t)
b = abs(b)
def code(x, y, z, t, a, b):
	return math.cos((math.exp(math.log((b * t))) * math.exp(math.log(0.0625)))) * x

Julia

t = abs(t)
b = abs(b)
function code(x, y, z, t, a, b)
	return Float64(cos(Float64(exp(log(Float64(b * t))) * exp(log(0.0625)))) * x)
end

MATLAB

t = abs(t)
b = abs(b)
function tmp = code(x, y, z, t, a, b)
	tmp = cos((exp(log((b * t))) * exp(log(0.0625)))) * x;
end

Wolfram

NOTE: t should be positive before calling this function
NOTE: b should be positive before calling this function
code[x_, y_, z_, t_, a_, b_] := N[(N[Cos[N[(N[Exp[N[Log[N[(b * t), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] * N[Exp[N[Log[0.0625], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision]

Derivation

1. Initial program 25.0%

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

   1. associate-*l* 25.0%

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

   2. *-commutative 25.0%

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

   3. *-commutative 25.0%

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

   4. *-commutative 25.0%

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

   5. associate-*l/ 25.0%

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

   6. distribute-lft1-in 25.0%

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

   7. associate-*r* 25.0%

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

   8. *-commutative 25.0%

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

   9. fma-def 25.0%

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

   10. *-commutative 25.0%

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

3. Simplified 25.3%

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

4. Taylor expanded in a around 0 26.3%

   \[\leadsto x \cdot \left(\cos \left(\frac{t}{16} \cdot \mathsf{fma}\left(y, 2 \cdot z, z\right)\right) \cdot \color{blue}{\cos \left(0.0625 \cdot \left(b \cdot t\right)\right)}\right) \]
5. Step-by-step derivation

   1. *-commutative 26.3%

      \[\leadsto x \cdot \left(\cos \left(\frac{t}{16} \cdot \mathsf{fma}\left(y, 2 \cdot z, z\right)\right) \cdot \cos \color{blue}{\left(\left(b \cdot t\right) \cdot 0.0625\right)}\right) \]

   2. associate-*r* 26.3%

      \[\leadsto x \cdot \left(\cos \left(\frac{t}{16} \cdot \mathsf{fma}\left(y, 2 \cdot z, z\right)\right) \cdot \cos \color{blue}{\left(b \cdot \left(t \cdot 0.0625\right)\right)}\right) \]

6. Simplified 26.3%

   \[\leadsto x \cdot \left(\cos \left(\frac{t}{16} \cdot \mathsf{fma}\left(y, 2 \cdot z, z\right)\right) \cdot \color{blue}{\cos \left(b \cdot \left(t \cdot 0.0625\right)\right)}\right) \]

7. Taylor expanded in z around 0 27.8%

   \[\leadsto \color{blue}{x \cdot \cos \left(0.0625 \cdot \left(b \cdot t\right)\right)} \]
8. Step-by-step derivation

   1. *-commutative 27.8%

      \[\leadsto \color{blue}{\cos \left(0.0625 \cdot \left(b \cdot t\right)\right) \cdot x} \]

   2. *-commutative 27.8%

      \[\leadsto \cos \color{blue}{\left(\left(b \cdot t\right) \cdot 0.0625\right)} \cdot x \]

   3. associate-*r* 27.8%

      \[\leadsto \cos \color{blue}{\left(b \cdot \left(t \cdot 0.0625\right)\right)} \cdot x \]

9. Simplified 27.8%

   \[\leadsto \color{blue}{\cos \left(b \cdot \left(t \cdot 0.0625\right)\right) \cdot x} \]
10. Step-by-step derivation

    1. add-exp-log_binary64 21.1%

       \[\leadsto \color{blue}{\cos \left(e^{\log \left(b \cdot \left(t \cdot 0.0625\right)\right)}\right) \cdot x} \]

11. Applied rewrite-once 21.1%

    \[\leadsto \cos \color{blue}{\left(e^{\log \left(b \cdot \left(t \cdot 0.0625\right)\right)}\right)} \cdot x \]
12. Step-by-step derivation

    1. associate-*r* 21.1%

       \[\leadsto \cos \left(e^{\log \color{blue}{\left(\left(b \cdot t\right) \cdot 0.0625\right)}}\right) \cdot x \]

    2. log-prod 21.2%

       \[\leadsto \cos \left(e^{\color{blue}{\log \left(b \cdot t\right) + \log 0.0625}}\right) \cdot x \]

    3. exp-sum 21.8%

       \[\leadsto \cos \color{blue}{\left(e^{\log \left(b \cdot t\right)} \cdot e^{\log 0.0625}\right)} \cdot x \]

13. Applied egg-rr 21.8%

    \[\leadsto \cos \color{blue}{\left(e^{\log \left(b \cdot t\right)} \cdot e^{\log 0.0625}\right)} \cdot x \]

14. Final simplification 21.8%

    \[\leadsto \cos \left(e^{\log \left(b \cdot t\right)} \cdot e^{\log 0.0625}\right) \cdot x \]

Alternative 2: 30.9% accurate, 225.0× speedup

Math

\[\begin{array}{l} t = |t|\\ b = |b|\\ \\ x \end{array} \]

FPCore

NOTE: t should be positive before calling this function
NOTE: b should be positive before calling this function
(FPCore (x y z t a b) :precision binary64 x)

C

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

Fortran

NOTE: t should be positive before calling this function
NOTE: b should be positive before calling this function
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: t should be positive before calling this function
NOTE: b should be positive before calling this function
code[x_, y_, z_, t_, a_, b_] := x

Derivation

1. Initial program 25.0%

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

   1. associate-*l* 25.0%

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

   2. *-commutative 25.0%

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

   3. *-commutative 25.0%

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

   4. *-commutative 25.0%

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

   5. associate-*l/ 25.0%

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

   6. distribute-lft1-in 25.0%

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

   7. associate-*r* 25.0%

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

   8. *-commutative 25.0%

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

   9. fma-def 25.0%

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

   10. *-commutative 25.0%

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

3. Simplified 25.3%

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

4. Taylor expanded in a around 0 26.3%

   \[\leadsto x \cdot \left(\cos \left(\frac{t}{16} \cdot \mathsf{fma}\left(y, 2 \cdot z, z\right)\right) \cdot \color{blue}{\cos \left(0.0625 \cdot \left(b \cdot t\right)\right)}\right) \]
5. Step-by-step derivation

   1. *-commutative 26.3%

      \[\leadsto x \cdot \left(\cos \left(\frac{t}{16} \cdot \mathsf{fma}\left(y, 2 \cdot z, z\right)\right) \cdot \cos \color{blue}{\left(\left(b \cdot t\right) \cdot 0.0625\right)}\right) \]

   2. associate-*r* 26.3%

      \[\leadsto x \cdot \left(\cos \left(\frac{t}{16} \cdot \mathsf{fma}\left(y, 2 \cdot z, z\right)\right) \cdot \cos \color{blue}{\left(b \cdot \left(t \cdot 0.0625\right)\right)}\right) \]

6. Simplified 26.3%

   \[\leadsto x \cdot \left(\cos \left(\frac{t}{16} \cdot \mathsf{fma}\left(y, 2 \cdot z, z\right)\right) \cdot \color{blue}{\cos \left(b \cdot \left(t \cdot 0.0625\right)\right)}\right) \]

7. Taylor expanded in t around 0 28.3%

   \[\leadsto \color{blue}{x} \]

8. Final simplification 28.3%

   \[\leadsto x \]

Developer target: 30.4% 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 2023297 
(FPCore (x y z t a b)
  :name "Codec.Picture.Jpg.FastDct:referenceDct from JuicyPixels-3.2.6.1"
  :precision binary64

  :herbie-target
  (* x (cos (* (/ b 16.0) (/ t (+ (- 1.0 (* a 2.0)) (pow (* a 2.0) 2.0))))))

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