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

Percentage Accurate: 27.6% → 29.9%

Time: 20.9s

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: 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: 29.9% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

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((((16.0d0 / t) / z) ** (-1.0d0)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 32.0%

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

3. Simplified 33.1%

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

5. Taylor expanded in a around 0 33.4%

   \[\leadsto x \cdot \left(\cos \left(\frac{\mathsf{fma}\left(y, 2, 1\right)}{\frac{\frac{16}{t}}{z}}\right) \cdot \color{blue}{\cos \left(0.0625 \cdot \left(b \cdot t\right)\right)}\right) \]
6. Step-by-step derivation

   1. *-commutative 33.4%

      \[\leadsto x \cdot \left(\cos \left(\frac{\mathsf{fma}\left(y, 2, 1\right)}{\frac{\frac{16}{t}}{z}}\right) \cdot \cos \left(0.0625 \cdot \color{blue}{\left(t \cdot b\right)}\right)\right) \]

7. Simplified 33.4%

   \[\leadsto x \cdot \left(\cos \left(\frac{\mathsf{fma}\left(y, 2, 1\right)}{\frac{\frac{16}{t}}{z}}\right) \cdot \color{blue}{\cos \left(0.0625 \cdot \left(t \cdot b\right)\right)}\right) \]
8. Step-by-step derivation

   1. associate-/l* 33.1%

      \[\leadsto x \cdot \left(\cos \color{blue}{\left(\frac{\mathsf{fma}\left(y, 2, 1\right) \cdot z}{\frac{16}{t}}\right)} \cdot \cos \left(0.0625 \cdot \left(t \cdot b\right)\right)\right) \]

   2. clear-num 32.9%

      \[\leadsto x \cdot \left(\cos \color{blue}{\left(\frac{1}{\frac{\frac{16}{t}}{\mathsf{fma}\left(y, 2, 1\right) \cdot z}}\right)} \cdot \cos \left(0.0625 \cdot \left(t \cdot b\right)\right)\right) \]

   3. inv-pow 32.9%

      \[\leadsto x \cdot \left(\cos \color{blue}{\left({\left(\frac{\frac{16}{t}}{\mathsf{fma}\left(y, 2, 1\right) \cdot z}\right)}^{-1}\right)} \cdot \cos \left(0.0625 \cdot \left(t \cdot b\right)\right)\right) \]

9. Applied egg-rr 32.9%

   \[\leadsto x \cdot \left(\cos \color{blue}{\left({\left(\frac{\frac{16}{t}}{\mathsf{fma}\left(y, 2, 1\right) \cdot z}\right)}^{-1}\right)} \cdot \cos \left(0.0625 \cdot \left(t \cdot b\right)\right)\right) \]

10. Taylor expanded in y around 0 33.7%

    \[\leadsto x \cdot \left(\cos \left({\color{blue}{\left(\frac{16}{t \cdot z}\right)}}^{-1}\right) \cdot \cos \left(0.0625 \cdot \left(t \cdot b\right)\right)\right) \]
11. Step-by-step derivation

    1. associate-/r* 34.2%

       \[\leadsto x \cdot \left(\cos \left({\color{blue}{\left(\frac{\frac{16}{t}}{z}\right)}}^{-1}\right) \cdot \cos \left(0.0625 \cdot \left(t \cdot b\right)\right)\right) \]

12. Simplified 34.2%

    \[\leadsto x \cdot \left(\cos \left({\color{blue}{\left(\frac{\frac{16}{t}}{z}\right)}}^{-1}\right) \cdot \cos \left(0.0625 \cdot \left(t \cdot b\right)\right)\right) \]

13. Taylor expanded in t around 0 34.8%

    \[\leadsto x \cdot \left(\cos \left({\left(\frac{\frac{16}{t}}{z}\right)}^{-1}\right) \cdot \color{blue}{1}\right) \]

14. Final simplification 34.8%

    \[\leadsto x \cdot \cos \left({\left(\frac{\frac{16}{t}}{z}\right)}^{-1}\right) \]
15. Add Preprocessing

Alternative 2: 29.8% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ x \cdot \cos \left(t \cdot \left(0.0625 \cdot b\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (* x (cos (* t (* 0.0625 b)))))

C

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

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((t * (0.0625d0 * b)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x * N[Cos[N[(t * N[(0.0625 * b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 32.0%

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

3. Simplified 33.1%

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

5. Taylor expanded in a around 0 33.4%

   \[\leadsto x \cdot \left(\cos \left(\frac{\mathsf{fma}\left(y, 2, 1\right)}{\frac{\frac{16}{t}}{z}}\right) \cdot \color{blue}{\cos \left(0.0625 \cdot \left(b \cdot t\right)\right)}\right) \]
6. Step-by-step derivation

   1. *-commutative 33.4%

      \[\leadsto x \cdot \left(\cos \left(\frac{\mathsf{fma}\left(y, 2, 1\right)}{\frac{\frac{16}{t}}{z}}\right) \cdot \cos \left(0.0625 \cdot \color{blue}{\left(t \cdot b\right)}\right)\right) \]

7. Simplified 33.4%

   \[\leadsto x \cdot \left(\cos \left(\frac{\mathsf{fma}\left(y, 2, 1\right)}{\frac{\frac{16}{t}}{z}}\right) \cdot \color{blue}{\cos \left(0.0625 \cdot \left(t \cdot b\right)\right)}\right) \]

8. Taylor expanded in z around 0 33.2%

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

   1. *-commutative 33.2%

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

   2. associate-*r* 33.2%

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

10. Simplified 33.2%

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

11. Final simplification 33.2%

    \[\leadsto x \cdot \cos \left(t \cdot \left(0.0625 \cdot b\right)\right) \]
12. Add Preprocessing

Alternative 3: 29.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ x \cdot \cos \left(z \cdot \left(t \cdot 0.0625\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (* x (cos (* z (* t 0.0625)))))

C

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

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((z * (t * 0.0625d0)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x * N[Cos[N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 32.0%

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

3. Simplified 33.1%

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

5. Taylor expanded in a around 0 33.4%

   \[\leadsto x \cdot \left(\cos \left(\frac{\mathsf{fma}\left(y, 2, 1\right)}{\frac{\frac{16}{t}}{z}}\right) \cdot \color{blue}{\cos \left(0.0625 \cdot \left(b \cdot t\right)\right)}\right) \]
6. Step-by-step derivation

   1. *-commutative 33.4%

      \[\leadsto x \cdot \left(\cos \left(\frac{\mathsf{fma}\left(y, 2, 1\right)}{\frac{\frac{16}{t}}{z}}\right) \cdot \cos \left(0.0625 \cdot \color{blue}{\left(t \cdot b\right)}\right)\right) \]

7. Simplified 33.4%

   \[\leadsto x \cdot \left(\cos \left(\frac{\mathsf{fma}\left(y, 2, 1\right)}{\frac{\frac{16}{t}}{z}}\right) \cdot \color{blue}{\cos \left(0.0625 \cdot \left(t \cdot b\right)\right)}\right) \]

8. Taylor expanded in y around 0 33.6%

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

   1. associate-*r* 33.6%

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

10. Simplified 33.6%

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

11. Taylor expanded in b around 0 33.9%

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

    1. *-commutative 33.9%

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

    2. associate-*r* 34.0%

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

13. Simplified 34.0%

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

14. Final simplification 34.0%

    \[\leadsto x \cdot \cos \left(z \cdot \left(t \cdot 0.0625\right)\right) \]
15. Add Preprocessing

Alternative 4: 30.8% 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 32.0%

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

3. Simplified 33.1%

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

5. Taylor expanded in a around 0 33.4%

   \[\leadsto x \cdot \left(\cos \left(\frac{\mathsf{fma}\left(y, 2, 1\right)}{\frac{\frac{16}{t}}{z}}\right) \cdot \color{blue}{\cos \left(0.0625 \cdot \left(b \cdot t\right)\right)}\right) \]
6. Step-by-step derivation

   1. *-commutative 33.4%

      \[\leadsto x \cdot \left(\cos \left(\frac{\mathsf{fma}\left(y, 2, 1\right)}{\frac{\frac{16}{t}}{z}}\right) \cdot \cos \left(0.0625 \cdot \color{blue}{\left(t \cdot b\right)}\right)\right) \]

7. Simplified 33.4%

   \[\leadsto x \cdot \left(\cos \left(\frac{\mathsf{fma}\left(y, 2, 1\right)}{\frac{\frac{16}{t}}{z}}\right) \cdot \color{blue}{\cos \left(0.0625 \cdot \left(t \cdot b\right)\right)}\right) \]

8. Taylor expanded in t around 0 32.8%

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

9. Final simplification 32.8%

   \[\leadsto x \]
10. Add Preprocessing

Developer target: 30.3% 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 2024019 
(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))))