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

Percentage Accurate: 99.9% → 100.0%

Time: 3.9s

Alternatives: 5

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ 200 \cdot \left(x - y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* 200.0 (- x y)))

C

double code(double x, double y) {
	return 200.0 * (x - y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 200.0d0 * (x - y)
end function

Java

public static double code(double x, double y) {
	return 200.0 * (x - y);
}

Python

def code(x, y):
	return 200.0 * (x - y)

Julia

function code(x, y)
	return Float64(200.0 * Float64(x - y))
end

MATLAB

function tmp = code(x, y)
	tmp = 200.0 * (x - y);
end

Wolfram

code[x_, y_] := N[(200.0 * N[(x - y), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 200 \cdot \left(x - y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* 200.0 (- x y)))

C

double code(double x, double y) {
	return 200.0 * (x - y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 200.0d0 * (x - y)
end function

Java

public static double code(double x, double y) {
	return 200.0 * (x - y);
}

Python

def code(x, y):
	return 200.0 * (x - y)

Julia

function code(x, y)
	return Float64(200.0 * Float64(x - y))
end

MATLAB

function tmp = code(x, y)
	tmp = 200.0 * (x - y);
end

Wolfram

code[x_, y_] := N[(200.0 * N[(x - y), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(x, 200, -200 \cdot y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (fma x 200.0 (* -200.0 y)))

C

double code(double x, double y) {
	return fma(x, 200.0, (-200.0 * y));
}

Julia

function code(x, y)
	return fma(x, 200.0, Float64(-200.0 * y))
end

Wolfram

code[x_, y_] := N[(x * 200.0 + N[(-200.0 * y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[200 \cdot \left(x - y\right) \]

2. Taylor expanded in x around 0 99.9%

   \[\leadsto \color{blue}{200 \cdot x + -200 \cdot y} \]
3. Step-by-step derivation

   1. *-commutative 99.9%

      \[\leadsto \color{blue}{x \cdot 200} + -200 \cdot y \]

   2. fma-def 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, 200, -200 \cdot y\right)} \]

4. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, 200, -200 \cdot y\right)} \]

5. Final simplification 100.0%

   \[\leadsto \mathsf{fma}\left(x, 200, -200 \cdot y\right) \]

Alternative 2: 100.0% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(-200, y, x \cdot 200\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (fma -200.0 y (* x 200.0)))

C

double code(double x, double y) {
	return fma(-200.0, y, (x * 200.0));
}

Julia

function code(x, y)
	return fma(-200.0, y, Float64(x * 200.0))
end

Wolfram

code[x_, y_] := N[(-200.0 * y + N[(x * 200.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[200 \cdot \left(x - y\right) \]

2. Taylor expanded in x around 0 99.9%

   \[\leadsto \color{blue}{200 \cdot x + -200 \cdot y} \]
3. Step-by-step derivation

   1. +-commutative 99.9%

      \[\leadsto \color{blue}{-200 \cdot y + 200 \cdot x} \]

   2. fma-def 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-200, y, 200 \cdot x\right)} \]

4. Simplified 99.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(-200, y, 200 \cdot x\right)} \]

5. Final simplification 99.9%

   \[\leadsto \mathsf{fma}\left(-200, y, x \cdot 200\right) \]

Alternative 3: 74.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.65 \cdot 10^{+17}:\\ \;\;\;\;x \cdot 200\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-31}:\\ \;\;\;\;-200 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot 200\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.65e+17) (* x 200.0) (if (<= x 4e-31) (* -200.0 y) (* x 200.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.65e+17) {
		tmp = x * 200.0;
	} else if (x <= 4e-31) {
		tmp = -200.0 * y;
	} else {
		tmp = x * 200.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-2.65d+17)) then
        tmp = x * 200.0d0
    else if (x <= 4d-31) then
        tmp = (-200.0d0) * y
    else
        tmp = x * 200.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2.65e+17) {
		tmp = x * 200.0;
	} else if (x <= 4e-31) {
		tmp = -200.0 * y;
	} else {
		tmp = x * 200.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.65e+17:
		tmp = x * 200.0
	elif x <= 4e-31:
		tmp = -200.0 * y
	else:
		tmp = x * 200.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.65e+17)
		tmp = Float64(x * 200.0);
	elseif (x <= 4e-31)
		tmp = Float64(-200.0 * y);
	else
		tmp = Float64(x * 200.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.65e+17)
		tmp = x * 200.0;
	elseif (x <= 4e-31)
		tmp = -200.0 * y;
	else
		tmp = x * 200.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.65e+17], N[(x * 200.0), $MachinePrecision], If[LessEqual[x, 4e-31], N[(-200.0 * y), $MachinePrecision], N[(x * 200.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.65e17 or 4e-31 < x

   1. Initial program 99.9%

      \[200 \cdot \left(x - y\right) \]

   2. Taylor expanded in x around inf 76.5%

      \[\leadsto \color{blue}{200 \cdot x} \]

   if -2.65e17 < x < 4e-31

   1. Initial program 99.9%

      \[200 \cdot \left(x - y\right) \]

   2. Taylor expanded in x around 0 78.9%

      \[\leadsto \color{blue}{-200 \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.65 \cdot 10^{+17}:\\ \;\;\;\;x \cdot 200\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-31}:\\ \;\;\;\;-200 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot 200\\ \end{array} \]

Alternative 4: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 200 \cdot \left(x - y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* 200.0 (- x y)))

C

double code(double x, double y) {
	return 200.0 * (x - y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 200.0d0 * (x - y)
end function

Java

public static double code(double x, double y) {
	return 200.0 * (x - y);
}

Python

def code(x, y):
	return 200.0 * (x - y)

Julia

function code(x, y)
	return Float64(200.0 * Float64(x - y))
end

MATLAB

function tmp = code(x, y)
	tmp = 200.0 * (x - y);
end

Wolfram

code[x_, y_] := N[(200.0 * N[(x - y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[200 \cdot \left(x - y\right) \]

2. Final simplification 99.9%

   \[\leadsto 200 \cdot \left(x - y\right) \]

Alternative 5: 51.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ -200 \cdot y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* -200.0 y))

C

double code(double x, double y) {
	return -200.0 * y;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (-200.0d0) * y
end function

Java

public static double code(double x, double y) {
	return -200.0 * y;
}

Python

def code(x, y):
	return -200.0 * y

Julia

function code(x, y)
	return Float64(-200.0 * y)
end

MATLAB

function tmp = code(x, y)
	tmp = -200.0 * y;
end

Wolfram

code[x_, y_] := N[(-200.0 * y), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[200 \cdot \left(x - y\right) \]

2. Taylor expanded in x around 0 49.2%

   \[\leadsto \color{blue}{-200 \cdot y} \]

3. Final simplification 49.2%

   \[\leadsto -200 \cdot y \]

Reproduce

herbie shell --seed 2023274 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, C"
  :precision binary64
  (* 200.0 (- x y)))