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

Percentage Accurate: 100.0% → 100.0%

Time: 3.4s

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

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

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]

Derivation

1. Initial program 100.0%

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

Alternative 2: 75.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{y}{500} \leq -0.004:\\ \;\;\;\;y \cdot 0.002\\ \mathbf{elif}\;\frac{y}{500} \leq 2 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.002\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (/ y 500.0) -0.004)
   (* y 0.002)
   (if (<= (/ y 500.0) 2e-13) x (* y 0.002))))

C

double code(double x, double y) {
	double tmp;
	if ((y / 500.0) <= -0.004) {
		tmp = y * 0.002;
	} else if ((y / 500.0) <= 2e-13) {
		tmp = x;
	} else {
		tmp = y * 0.002;
	}
	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) <= (-0.004d0)) then
        tmp = y * 0.002d0
    else if ((y / 500.0d0) <= 2d-13) then
        tmp = x
    else
        tmp = y * 0.002d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y / 500.0) <= -0.004) {
		tmp = y * 0.002;
	} else if ((y / 500.0) <= 2e-13) {
		tmp = x;
	} else {
		tmp = y * 0.002;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y / 500.0) <= -0.004:
		tmp = y * 0.002
	elif (y / 500.0) <= 2e-13:
		tmp = x
	else:
		tmp = y * 0.002
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(y / 500.0) <= -0.004)
		tmp = Float64(y * 0.002);
	elseif (Float64(y / 500.0) <= 2e-13)
		tmp = x;
	else
		tmp = Float64(y * 0.002);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y / 500.0) <= -0.004)
		tmp = y * 0.002;
	elseif ((y / 500.0) <= 2e-13)
		tmp = x;
	else
		tmp = y * 0.002;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(y / 500.0), $MachinePrecision], -0.004], N[(y * 0.002), $MachinePrecision], If[LessEqual[N[(y / 500.0), $MachinePrecision], 2e-13], x, N[(y * 0.002), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 y #s(literal 500 binary64)) < -0.0040000000000000001 or 2.0000000000000001e-13 < (/.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. *-lowering-*.f64 75.0

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

   5. Simplified 75.0%

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

   if -0.0040000000000000001 < (/.f64 y #s(literal 500 binary64)) < 2.0000000000000001e-13

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 83.3%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{500} \leq -0.004:\\ \;\;\;\;y \cdot 0.002\\ \mathbf{elif}\;\frac{y}{500} \leq 2 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.002\\ \end{array} \]
5. 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. +-commutative N/A

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

   2. div-inv N/A

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

   3. accelerator-lowering-fma.f64 N/A

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

   4. metadata-eval 99.9

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

4. Applied egg-rr 99.9%

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

Alternative 4: 51.3% accurate, 15.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 x)

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return x

Julia

function code(x, y)
	return x
end

MATLAB

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

Wolfram

code[x_, y_] := x

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x} \]
4. Step-by-step derivation

5. Simplified 54.9%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024198 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, C"
  :precision binary64
  (+ x (/ y 500.0)))