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

Percentage Accurate: 27.6% → 32.1%

Time: 11.8s

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: 27.6% 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: 32.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(0.0625 \cdot t\right) \cdot z\\ t_2 := \cos \left(\frac{\left(b \cdot \left(a \cdot 2 + 1\right)\right) \cdot t}{16}\right)\\ t_3 := \left(0.0625 \cdot t\right) \cdot \left(z \cdot \left(2 \cdot y\right)\right)\\ \mathbf{if}\;t\_2 \cdot \left(\cos \left(\frac{t \cdot \left(z \cdot \left(1 + 2 \cdot y\right)\right)}{16}\right) \cdot x\right) \leq 4 \cdot 10^{+303}:\\ \;\;\;\;\left(\left(\cos t\_1 \cdot \cos t\_3 - \sin t\_1 \cdot \sin t\_3\right) \cdot x\right) \cdot t\_2\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(1 \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* 0.0625 t) z))
        (t_2 (cos (/ (* (* b (+ (* a 2.0) 1.0)) t) 16.0)))
        (t_3 (* (* 0.0625 t) (* z (* 2.0 y)))))
   (if (<= (* t_2 (* (cos (/ (* t (* z (+ 1.0 (* 2.0 y)))) 16.0)) x)) 4e+303)
     (* (* (- (* (cos t_1) (cos t_3)) (* (sin t_1) (sin t_3))) x) t_2)
     (* 1.0 (* 1.0 x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (0.0625 * t) * z;
	double t_2 = cos((((b * ((a * 2.0) + 1.0)) * t) / 16.0));
	double t_3 = (0.0625 * t) * (z * (2.0 * y));
	double tmp;
	if ((t_2 * (cos(((t * (z * (1.0 + (2.0 * y)))) / 16.0)) * x)) <= 4e+303) {
		tmp = (((cos(t_1) * cos(t_3)) - (sin(t_1) * sin(t_3))) * x) * t_2;
	} else {
		tmp = 1.0 * (1.0 * x);
	}
	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 = (0.0625d0 * t) * z
    t_2 = cos((((b * ((a * 2.0d0) + 1.0d0)) * t) / 16.0d0))
    t_3 = (0.0625d0 * t) * (z * (2.0d0 * y))
    if ((t_2 * (cos(((t * (z * (1.0d0 + (2.0d0 * y)))) / 16.0d0)) * x)) <= 4d+303) then
        tmp = (((cos(t_1) * cos(t_3)) - (sin(t_1) * sin(t_3))) * x) * t_2
    else
        tmp = 1.0d0 * (1.0d0 * x)
    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 = (0.0625 * t) * z;
	double t_2 = Math.cos((((b * ((a * 2.0) + 1.0)) * t) / 16.0));
	double t_3 = (0.0625 * t) * (z * (2.0 * y));
	double tmp;
	if ((t_2 * (Math.cos(((t * (z * (1.0 + (2.0 * y)))) / 16.0)) * x)) <= 4e+303) {
		tmp = (((Math.cos(t_1) * Math.cos(t_3)) - (Math.sin(t_1) * Math.sin(t_3))) * x) * t_2;
	} else {
		tmp = 1.0 * (1.0 * x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (0.0625 * t) * z
	t_2 = math.cos((((b * ((a * 2.0) + 1.0)) * t) / 16.0))
	t_3 = (0.0625 * t) * (z * (2.0 * y))
	tmp = 0
	if (t_2 * (math.cos(((t * (z * (1.0 + (2.0 * y)))) / 16.0)) * x)) <= 4e+303:
		tmp = (((math.cos(t_1) * math.cos(t_3)) - (math.sin(t_1) * math.sin(t_3))) * x) * t_2
	else:
		tmp = 1.0 * (1.0 * x)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(0.0625 * t) * z)
	t_2 = cos(Float64(Float64(Float64(b * Float64(Float64(a * 2.0) + 1.0)) * t) / 16.0))
	t_3 = Float64(Float64(0.0625 * t) * Float64(z * Float64(2.0 * y)))
	tmp = 0.0
	if (Float64(t_2 * Float64(cos(Float64(Float64(t * Float64(z * Float64(1.0 + Float64(2.0 * y)))) / 16.0)) * x)) <= 4e+303)
		tmp = Float64(Float64(Float64(Float64(cos(t_1) * cos(t_3)) - Float64(sin(t_1) * sin(t_3))) * x) * t_2);
	else
		tmp = Float64(1.0 * Float64(1.0 * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (0.0625 * t) * z;
	t_2 = cos((((b * ((a * 2.0) + 1.0)) * t) / 16.0));
	t_3 = (0.0625 * t) * (z * (2.0 * y));
	tmp = 0.0;
	if ((t_2 * (cos(((t * (z * (1.0 + (2.0 * y)))) / 16.0)) * x)) <= 4e+303)
		tmp = (((cos(t_1) * cos(t_3)) - (sin(t_1) * sin(t_3))) * x) * t_2;
	else
		tmp = 1.0 * (1.0 * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(0.0625 * t), $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$2 = N[Cos[N[(N[(N[(b * N[(N[(a * 2.0), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] / 16.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$3 = N[(N[(0.0625 * t), $MachinePrecision] * N[(z * N[(2.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$2 * N[(N[Cos[N[(N[(t * N[(z * N[(1.0 + N[(2.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / 16.0), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], 4e+303], N[(N[(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] * x), $MachinePrecision] * t$95$2), $MachinePrecision], N[(1.0 * N[(1.0 * x), $MachinePrecision]), $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)))) < 4e303

   1. Initial program 48.2%

      \[\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right) \]
   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 49.2%

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

   if 4e303 < (*.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 t 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 2.9%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 12.5%

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

4. Final simplification 32.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\cos \left(\frac{\left(b \cdot \left(a \cdot 2 + 1\right)\right) \cdot t}{16}\right) \cdot \left(\cos \left(\frac{t \cdot \left(z \cdot \left(1 + 2 \cdot y\right)\right)}{16}\right) \cdot x\right) \leq 4 \cdot 10^{+303}:\\ \;\;\;\;\left(\left(\cos \left(\left(0.0625 \cdot t\right) \cdot z\right) \cdot \cos \left(\left(0.0625 \cdot t\right) \cdot \left(z \cdot \left(2 \cdot y\right)\right)\right) - \sin \left(\left(0.0625 \cdot t\right) \cdot z\right) \cdot \sin \left(\left(0.0625 \cdot t\right) \cdot \left(z \cdot \left(2 \cdot y\right)\right)\right)\right) \cdot x\right) \cdot \cos \left(\frac{\left(b \cdot \left(a \cdot 2 + 1\right)\right) \cdot t}{16}\right)\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(1 \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 30.9% accurate, 24.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 26.4%

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

3. Taylor expanded in t 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 26.9%

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

6. Taylor expanded in b around 0

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

8. Applied rewrites 30.9%

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

9. Final simplification 30.9%

   \[\leadsto 1 \cdot \left(1 \cdot x\right) \]
10. Add Preprocessing

Developer Target 1: 30.6% 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 2024268 
(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))))