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

Percentage Accurate: 27.3% → 31.5%

Time: 15.5s

Alternatives: 2

Speedup: 24.5×

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: 31.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y \cdot \left(2 \cdot z\right)\right) \cdot \left(t \cdot 0.0625\right)\\ t_2 := \cos \left(\frac{t \cdot \left(\left(1 + 2 \cdot a\right) \cdot b\right)}{16}\right)\\ t_3 := z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{if}\;\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot t\_2 \leq 2 \cdot 10^{+304}:\\ \;\;\;\;t\_2 \cdot \left(x \cdot \left(\cos t\_1 \cdot \cos t\_3 - \sin t\_1 \cdot \sin t\_3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 1\right) \cdot 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* y (* 2.0 z)) (* t 0.0625)))
        (t_2 (cos (/ (* t (* (+ 1.0 (* 2.0 a)) b)) 16.0)))
        (t_3 (* z (* t 0.0625))))
   (if (<= (* (* x (cos (/ (* (* (+ (* y 2.0) 1.0) z) t) 16.0))) t_2) 2e+304)
     (* t_2 (* x (- (* (cos t_1) (cos t_3)) (* (sin t_1) (sin t_3)))))
     (* (* x 1.0) 1.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * (2.0 * z)) * (t * 0.0625);
	double t_2 = cos(((t * ((1.0 + (2.0 * a)) * b)) / 16.0));
	double t_3 = z * (t * 0.0625);
	double tmp;
	if (((x * cos((((((y * 2.0) + 1.0) * z) * t) / 16.0))) * t_2) <= 2e+304) {
		tmp = t_2 * (x * ((cos(t_1) * cos(t_3)) - (sin(t_1) * sin(t_3))));
	} else {
		tmp = (x * 1.0) * 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (y * (2.0d0 * z)) * (t * 0.0625d0)
    t_2 = cos(((t * ((1.0d0 + (2.0d0 * a)) * b)) / 16.0d0))
    t_3 = z * (t * 0.0625d0)
    if (((x * cos((((((y * 2.0d0) + 1.0d0) * z) * t) / 16.0d0))) * t_2) <= 2d+304) then
        tmp = t_2 * (x * ((cos(t_1) * cos(t_3)) - (sin(t_1) * sin(t_3))))
    else
        tmp = (x * 1.0d0) * 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * (2.0 * z)) * (t * 0.0625);
	double t_2 = Math.cos(((t * ((1.0 + (2.0 * a)) * b)) / 16.0));
	double t_3 = z * (t * 0.0625);
	double tmp;
	if (((x * Math.cos((((((y * 2.0) + 1.0) * z) * t) / 16.0))) * t_2) <= 2e+304) {
		tmp = t_2 * (x * ((Math.cos(t_1) * Math.cos(t_3)) - (Math.sin(t_1) * Math.sin(t_3))));
	} else {
		tmp = (x * 1.0) * 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y * (2.0 * z)) * (t * 0.0625)
	t_2 = math.cos(((t * ((1.0 + (2.0 * a)) * b)) / 16.0))
	t_3 = z * (t * 0.0625)
	tmp = 0
	if ((x * math.cos((((((y * 2.0) + 1.0) * z) * t) / 16.0))) * t_2) <= 2e+304:
		tmp = t_2 * (x * ((math.cos(t_1) * math.cos(t_3)) - (math.sin(t_1) * math.sin(t_3))))
	else:
		tmp = (x * 1.0) * 1.0
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * Float64(2.0 * z)) * Float64(t * 0.0625))
	t_2 = cos(Float64(Float64(t * Float64(Float64(1.0 + Float64(2.0 * a)) * b)) / 16.0))
	t_3 = Float64(z * Float64(t * 0.0625))
	tmp = 0.0
	if (Float64(Float64(x * cos(Float64(Float64(Float64(Float64(Float64(y * 2.0) + 1.0) * z) * t) / 16.0))) * t_2) <= 2e+304)
		tmp = Float64(t_2 * Float64(x * Float64(Float64(cos(t_1) * cos(t_3)) - Float64(sin(t_1) * sin(t_3)))));
	else
		tmp = Float64(Float64(x * 1.0) * 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y * (2.0 * z)) * (t * 0.0625);
	t_2 = cos(((t * ((1.0 + (2.0 * a)) * b)) / 16.0));
	t_3 = z * (t * 0.0625);
	tmp = 0.0;
	if (((x * cos((((((y * 2.0) + 1.0) * z) * t) / 16.0))) * t_2) <= 2e+304)
		tmp = t_2 * (x * ((cos(t_1) * cos(t_3)) - (sin(t_1) * sin(t_3))));
	else
		tmp = (x * 1.0) * 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * N[(2.0 * z), $MachinePrecision]), $MachinePrecision] * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[Cos[N[(N[(t * N[(N[(1.0 + N[(2.0 * a), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] / 16.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(x * N[Cos[N[(N[(N[(N[(N[(y * 2.0), $MachinePrecision] + 1.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] / 16.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision], 2e+304], N[(t$95$2 * N[(x * N[(N[(N[Cos[t$95$1], $MachinePrecision] * N[Cos[t$95$3], $MachinePrecision]), $MachinePrecision] - N[(N[Sin[t$95$1], $MachinePrecision] * N[Sin[t$95$3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 1.0), $MachinePrecision] * 1.0), $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)))) < 1.9999999999999999e304

   1. Initial program 57.1%

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

      1. lift-cos.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-+.f64 N/A

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

      9. +-commutative N/A

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

      10. distribute-lft-in N/A

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

      11. *-rgt-identity N/A

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

      12. *-commutative N/A

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

      13. +-commutative N/A

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

      14. distribute-rgt-in N/A

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

      15. cos-sum N/A

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

      16. lower--.f64 N/A

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

   4. Applied rewrites 57.7%

      \[\leadsto \left(x \cdot \color{blue}{\left(\cos \left(\left(y \cdot \left(2 \cdot z\right)\right) \cdot \left(t \cdot 0.0625\right)\right) \cdot \cos \left(z \cdot \left(t \cdot 0.0625\right)\right) - \sin \left(\left(y \cdot \left(2 \cdot z\right)\right) \cdot \left(t \cdot 0.0625\right)\right) \cdot \sin \left(z \cdot \left(t \cdot 0.0625\right)\right)\right)}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right) \]

   if 1.9999999999999999e304 < (*.f64 (*.f64 x (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y #s(literal 2 binary64)) #s(literal 1 binary64)) z) t) #s(literal 16 binary64)))) (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 a #s(literal 2 binary64)) #s(literal 1 binary64)) b) t) #s(literal 16 binary64))))

   1. Initial program 0.0%

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

   3. Taylor expanded in b around 0

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

   5. Applied rewrites 3.7%

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

   6. Taylor expanded in z around 0

      \[\leadsto \left(x \cdot \color{blue}{1}\right) \cdot 1 \]
   7. Step-by-step derivation

   8. Applied rewrites 10.0%

      \[\leadsto \left(x \cdot \color{blue}{1}\right) \cdot 1 \]
3. Recombined 2 regimes into one program.

4. Final simplification 38.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{t \cdot \left(\left(1 + 2 \cdot a\right) \cdot b\right)}{16}\right) \leq 2 \cdot 10^{+304}:\\ \;\;\;\;\cos \left(\frac{t \cdot \left(\left(1 + 2 \cdot a\right) \cdot b\right)}{16}\right) \cdot \left(x \cdot \left(\cos \left(\left(y \cdot \left(2 \cdot z\right)\right) \cdot \left(t \cdot 0.0625\right)\right) \cdot \cos \left(z \cdot \left(t \cdot 0.0625\right)\right) - \sin \left(\left(y \cdot \left(2 \cdot z\right)\right) \cdot \left(t \cdot 0.0625\right)\right) \cdot \sin \left(z \cdot \left(t \cdot 0.0625\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 1\right) \cdot 1\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 30.4% accurate, 24.5× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot 1\right) \cdot 1 \end{array} \]

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 33.7%

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

3. Taylor expanded in b around 0

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

5. Applied rewrites 34.8%

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

6. Taylor expanded in z around 0

   \[\leadsto \left(x \cdot \color{blue}{1}\right) \cdot 1 \]
7. Step-by-step derivation

8. Applied rewrites 36.5%

   \[\leadsto \left(x \cdot \color{blue}{1}\right) \cdot 1 \]
9. 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 2024219 
(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))))