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

Percentage Accurate: 99.9% → 100.0%

Time: 4.4s

Alternatives: 4

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

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_] := N[(-200.0 * y + N[(200.0 * x), $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 100.0%

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

4. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 72.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+103}:\\ \;\;\;\;200 \cdot x\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{+47} \lor \neg \left(x \leq -2.6 \cdot 10^{-18}\right) \land x \leq 4.5 \cdot 10^{+64}:\\ \;\;\;\;-200 \cdot y\\ \mathbf{else}:\\ \;\;\;\;200 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.45e+103)
   (* 200.0 x)
   (if (or (<= x -2.9e+47) (and (not (<= x -2.6e-18)) (<= x 4.5e+64)))
     (* -200.0 y)
     (* 200.0 x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.45e+103) {
		tmp = 200.0 * x;
	} else if ((x <= -2.9e+47) || (!(x <= -2.6e-18) && (x <= 4.5e+64))) {
		tmp = -200.0 * y;
	} else {
		tmp = 200.0 * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-1.45d+103)) then
        tmp = 200.0d0 * x
    else if ((x <= (-2.9d+47)) .or. (.not. (x <= (-2.6d-18))) .and. (x <= 4.5d+64)) then
        tmp = (-200.0d0) * y
    else
        tmp = 200.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.45e+103) {
		tmp = 200.0 * x;
	} else if ((x <= -2.9e+47) || (!(x <= -2.6e-18) && (x <= 4.5e+64))) {
		tmp = -200.0 * y;
	} else {
		tmp = 200.0 * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.45e+103:
		tmp = 200.0 * x
	elif (x <= -2.9e+47) or (not (x <= -2.6e-18) and (x <= 4.5e+64)):
		tmp = -200.0 * y
	else:
		tmp = 200.0 * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.45e+103)
		tmp = Float64(200.0 * x);
	elseif ((x <= -2.9e+47) || (!(x <= -2.6e-18) && (x <= 4.5e+64)))
		tmp = Float64(-200.0 * y);
	else
		tmp = Float64(200.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.45e+103)
		tmp = 200.0 * x;
	elseif ((x <= -2.9e+47) || (~((x <= -2.6e-18)) && (x <= 4.5e+64)))
		tmp = -200.0 * y;
	else
		tmp = 200.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.45e+103], N[(200.0 * x), $MachinePrecision], If[Or[LessEqual[x, -2.9e+47], And[N[Not[LessEqual[x, -2.6e-18]], $MachinePrecision], LessEqual[x, 4.5e+64]]], N[(-200.0 * y), $MachinePrecision], N[(200.0 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.4499999999999999e103 or -2.8999999999999998e47 < x < -2.6e-18 or 4.49999999999999973e64 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 80.3%

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

   if -1.4499999999999999e103 < x < -2.8999999999999998e47 or -2.6e-18 < x < 4.49999999999999973e64

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 78.2%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+103}:\\ \;\;\;\;200 \cdot x\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{+47} \lor \neg \left(x \leq -2.6 \cdot 10^{-18}\right) \land x \leq 4.5 \cdot 10^{+64}:\\ \;\;\;\;-200 \cdot y\\ \mathbf{else}:\\ \;\;\;\;200 \cdot x\\ \end{array} \]

Alternative 3: 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 4: 50.3% 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 52.7%

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

3. Final simplification 52.7%

   \[\leadsto -200 \cdot y \]

Reproduce

herbie shell --seed 2023192 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, C"
  :precision binary64
  (* 200.0 (- x y)))