Data.Colour.CIE:cieLAB from colour-2.3.3, C

Percentage Accurate: 100.0% → 100.0%

Time: 4.7s

Alternatives: 4

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ x + \frac{y}{500} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (+ x (/ y 500.0)))

C

double code(double x, double y) {
	return x + (y / 500.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x + (y / 500.0d0)
end function

Java

public static double code(double x, double y) {
	return x + (y / 500.0);
}

Python

def code(x, y):
	return x + (y / 500.0)

Julia

function code(x, y)
	return Float64(x + Float64(y / 500.0))
end

MATLAB

function tmp = code(x, y)
	tmp = x + (y / 500.0);
end

Wolfram

code[x_, y_] := N[(x + N[(y / 500.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{y}{500} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (+ x (/ y 500.0)))

C

double code(double x, double y) {
	return x + (y / 500.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x + (y / 500.0d0)
end function

Java

public static double code(double x, double y) {
	return x + (y / 500.0);
}

Python

def code(x, y):
	return x + (y / 500.0)

Julia

function code(x, y)
	return Float64(x + Float64(y / 500.0))
end

MATLAB

function tmp = code(x, y)
	tmp = x + (y / 500.0);
end

Wolfram

code[x_, y_] := N[(x + N[(y / 500.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{y}{500} + x \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (+ (/ y 500.0) x))

C

double code(double x, double y) {
	return (y / 500.0) + x;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (y / 500.0d0) + x
end function

Java

public static double code(double x, double y) {
	return (y / 500.0) + x;
}

Python

def code(x, y):
	return (y / 500.0) + x

Julia

function code(x, y)
	return Float64(Float64(y / 500.0) + x)
end

MATLAB

function tmp = code(x, y)
	tmp = (y / 500.0) + x;
end

Wolfram

code[x_, y_] := N[(N[(y / 500.0), $MachinePrecision] + x), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[x + \frac{y}{500} \]
2. Add Preprocessing

3. Final simplification 100.0%

   \[\leadsto \frac{y}{500} + x \]
4. Add Preprocessing

Alternative 2: 73.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{y}{500} \leq -5 \cdot 10^{+75}:\\ \;\;\;\;0.002 \cdot y\\ \mathbf{elif}\;\frac{y}{500} \leq 10^{-16}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;0.002 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (/ y 500.0) -5e+75)
   (* 0.002 y)
   (if (<= (/ y 500.0) 1e-16) (* 1.0 x) (* 0.002 y))))

C

double code(double x, double y) {
	double tmp;
	if ((y / 500.0) <= -5e+75) {
		tmp = 0.002 * y;
	} else if ((y / 500.0) <= 1e-16) {
		tmp = 1.0 * x;
	} else {
		tmp = 0.002 * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y / 500.0d0) <= (-5d+75)) then
        tmp = 0.002d0 * y
    else if ((y / 500.0d0) <= 1d-16) then
        tmp = 1.0d0 * x
    else
        tmp = 0.002d0 * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y / 500.0) <= -5e+75) {
		tmp = 0.002 * y;
	} else if ((y / 500.0) <= 1e-16) {
		tmp = 1.0 * x;
	} else {
		tmp = 0.002 * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y / 500.0) <= -5e+75:
		tmp = 0.002 * y
	elif (y / 500.0) <= 1e-16:
		tmp = 1.0 * x
	else:
		tmp = 0.002 * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(y / 500.0) <= -5e+75)
		tmp = Float64(0.002 * y);
	elseif (Float64(y / 500.0) <= 1e-16)
		tmp = Float64(1.0 * x);
	else
		tmp = Float64(0.002 * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y / 500.0) <= -5e+75)
		tmp = 0.002 * y;
	elseif ((y / 500.0) <= 1e-16)
		tmp = 1.0 * x;
	else
		tmp = 0.002 * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(y / 500.0), $MachinePrecision], -5e+75], N[(0.002 * y), $MachinePrecision], If[LessEqual[N[(y / 500.0), $MachinePrecision], 1e-16], N[(1.0 * x), $MachinePrecision], N[(0.002 * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 y #s(literal 500 binary64)) < -5.0000000000000002e75 or 9.9999999999999998e-17 < (/.f64 y #s(literal 500 binary64))

   1. Initial program 100.0%

      \[x + \frac{y}{500} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{1}{500} \cdot y} \]
   4. Step-by-step derivation

      1. lower-*.f64 82.1

         \[\leadsto \color{blue}{0.002 \cdot y} \]

   5. Applied rewrites 82.1%

      \[\leadsto \color{blue}{0.002 \cdot y} \]

   if -5.0000000000000002e75 < (/.f64 y #s(literal 500 binary64)) < 9.9999999999999998e-17

   1. Initial program 100.0%

      \[x + \frac{y}{500} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{y}{500}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\frac{y}{500} + x} \]

      3. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{y}{500}} + x \]

      4. div-inv N/A

         \[\leadsto \color{blue}{y \cdot \frac{1}{500}} + x \]

      5. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{1}{500}, x\right)} \]

      6. metadata-eval 100.0

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{0.002}, x\right) \]

   4. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, 0.002, x\right)} \]

   6. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \frac{x}{\mathsf{fma}\left(-0.002, y, x\right)}, -\left(4 \cdot 10^{-6} \cdot y\right) \cdot \frac{y}{\mathsf{fma}\left(-0.002, y, x\right)}\right)} \]

   7. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\left(1 + -1 \cdot \frac{\frac{-1}{250000} \cdot {y}^{2} + \frac{1}{250000} \cdot {y}^{2}}{{x}^{2}}\right) - \frac{-1}{500} \cdot \frac{y}{x}\right)} \]

   9. Applied rewrites 99.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{x}, 0.002, 1\right) \cdot x} \]

   10. Taylor expanded in x around inf

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

   12. Applied rewrites 80.5%

       \[\leadsto 1 \cdot x \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 99.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y, 0.002, x\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (fma y 0.002 x))

C

double code(double x, double y) {
	return fma(y, 0.002, x);
}

Julia

function code(x, y)
	return fma(y, 0.002, x)
end

Wolfram

code[x_, y_] := N[(y * 0.002 + x), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[x + \frac{y}{500} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-+.f64 N/A

      \[\leadsto \color{blue}{x + \frac{y}{500}} \]

   2. +-commutative N/A

      \[\leadsto \color{blue}{\frac{y}{500} + x} \]

   3. lift-/.f64 N/A

      \[\leadsto \color{blue}{\frac{y}{500}} + x \]

   4. div-inv N/A

      \[\leadsto \color{blue}{y \cdot \frac{1}{500}} + x \]

   5. lower-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{1}{500}, x\right)} \]

   6. metadata-eval 99.9

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{0.002}, x\right) \]

4. Applied rewrites 99.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y, 0.002, x\right)} \]
5. Add Preprocessing

Alternative 4: 49.1% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ 0.002 \cdot y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* 0.002 y))

C

double code(double x, double y) {
	return 0.002 * y;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 0.002d0 * y
end function

Java

public static double code(double x, double y) {
	return 0.002 * y;
}

Python

def code(x, y):
	return 0.002 * y

Julia

function code(x, y)
	return Float64(0.002 * y)
end

MATLAB

function tmp = code(x, y)
	tmp = 0.002 * y;
end

Wolfram

code[x_, y_] := N[(0.002 * y), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[x + \frac{y}{500} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\frac{1}{500} \cdot y} \]
4. Step-by-step derivation

   1. lower-*.f64 49.1

      \[\leadsto \color{blue}{0.002 \cdot y} \]

5. Applied rewrites 49.1%

   \[\leadsto \color{blue}{0.002 \cdot y} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024298 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, C"
  :precision binary64
  (+ x (/ y 500.0)))