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

Percentage Accurate: 27.3% → 30.0%

Time: 15.2s

Alternatives: 2

Speedup: 44.8×

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: 27.3% 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: 30.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot 1\right) \cdot \cos \left(\frac{\frac{1}{\mathsf{fma}\left(a, a \cdot 4, -1\right)}}{\frac{16}{b}} \cdot \left(-t\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (* (* x 1.0) (cos (* (/ (/ 1.0 (fma a (* a 4.0) -1.0)) (/ 16.0 b)) (- t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x * 1.0) * cos((((1.0 / fma(a, (a * 4.0), -1.0)) / (16.0 / b)) * -t));
}

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x * 1.0) * cos(Float64(Float64(Float64(1.0 / fma(a, Float64(a * 4.0), -1.0)) / Float64(16.0 / b)) * Float64(-t))))
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x * 1.0), $MachinePrecision] * N[Cos[N[(N[(N[(1.0 / N[(a * N[(a * 4.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] / N[(16.0 / b), $MachinePrecision]), $MachinePrecision] * (-t)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 28.8%

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

3. Taylor expanded in z around 0

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

5. Applied rewrites 30.5%

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

7. Applied rewrites 25.8%

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

8. Taylor expanded in a around 0

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

   1. mul-1-neg N/A

      \[\leadsto \left(x \cdot 1\right) \cdot \cos \left(\frac{\frac{1}{\mathsf{fma}\left(a, a \cdot 4, -1\right)}}{\frac{16}{b}} \cdot \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}\right) \]

   2. lower-neg.f64 33.0

      \[\leadsto \left(x \cdot 1\right) \cdot \cos \left(\frac{\frac{1}{\mathsf{fma}\left(a, a \cdot 4, -1\right)}}{\frac{16}{b}} \cdot \color{blue}{\left(-t\right)}\right) \]

10. Applied rewrites 33.0%

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

Alternative 2: 30.4% accurate, 44.8× speedup

Math

\[\begin{array}{l} \\ x \cdot 1 \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (* x 1.0))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x * 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 * 1.0d0
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x * 1.0;
}

Python

def code(x, y, z, t, a, b):
	return x * 1.0

Julia

function code(x, y, z, t, a, b)
	return Float64(x * 1.0)
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x * 1.0;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x * 1.0), $MachinePrecision]

Derivation

1. Initial program 28.8%

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

   1. lift-/.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. associate-/l* N/A

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

   4. clear-num N/A

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

   5. un-div-inv N/A

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

   6. lower-/.f64 N/A

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

   7. lift-*.f64 N/A

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

   8. *-commutative N/A

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

   9. lift-+.f64 N/A

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

   10. distribute-rgt-in N/A

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

   11. *-lft-identity N/A

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

   12. lower-fma.f64 N/A

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

   13. lift-*.f64 N/A

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

   14. *-commutative N/A

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

   15. lower-*.f64 N/A

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

   16. lower-/.f64 28.8

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

4. Applied rewrites 28.8%

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

5. Taylor expanded in a around 0

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

   1. lower-*.f64 N/A

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

   2. *-commutative N/A

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

   3. lower-*.f64 N/A

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

   4. lower-cos.f64 N/A

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

   5. lower-*.f64 N/A

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

   6. lower-*.f64 N/A

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

   7. +-commutative N/A

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

   8. distribute-lft-in N/A

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

   9. *-rgt-identity N/A

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

   10. lower-fma.f64 N/A

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

   11. *-commutative N/A

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

   12. lower-*.f64 N/A

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

   13. lower-cos.f64 N/A

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

   14. lower-*.f64 N/A

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

   15. *-commutative N/A

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

   16. lower-*.f64 30.3

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

7. Applied rewrites 30.3%

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

8. Taylor expanded in t around 0

   \[\leadsto x \cdot 1 \]
9. Step-by-step derivation

10. Applied rewrites 32.7%

    \[\leadsto x \cdot 1 \]
11. Add Preprocessing

Developer Target 1: 30.0% accurate, 1.1× 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 2024221 
(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))))