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

Percentage Accurate: 99.9% → 100.0%

Time: 1.5s

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

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

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 * Float64(-y)))
end

Wolfram

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

Derivation

1. Initial program 100.0%

   \[200 \cdot \left(x - y\right) \]
2. Step-by-step derivation

   1. sub-neg 100.0%

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

   2. distribute-rgt-in 99.9%

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

   3. fma-def 100.0%

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

3. Applied egg-rr 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 75.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+20} \lor \neg \left(x \leq -4.2 \cdot 10^{-67} \lor \neg \left(x \leq -5.4 \cdot 10^{-92}\right) \land x \leq 3.6 \cdot 10^{-40}\right):\\ \;\;\;\;x \cdot 200\\ \mathbf{else}:\\ \;\;\;\;y \cdot -200\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.75e+20)
         (not (or (<= x -4.2e-67) (and (not (<= x -5.4e-92)) (<= x 3.6e-40)))))
   (* x 200.0)
   (* y -200.0)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.75e+20) || !((x <= -4.2e-67) || (!(x <= -5.4e-92) && (x <= 3.6e-40)))) {
		tmp = x * 200.0;
	} else {
		tmp = y * -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 <= (-1.75d+20)) .or. (.not. (x <= (-4.2d-67)) .or. (.not. (x <= (-5.4d-92))) .and. (x <= 3.6d-40))) then
        tmp = x * 200.0d0
    else
        tmp = y * (-200.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -1.75e+20) || !((x <= -4.2e-67) || (!(x <= -5.4e-92) && (x <= 3.6e-40)))) {
		tmp = x * 200.0;
	} else {
		tmp = y * -200.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.75e+20) or not ((x <= -4.2e-67) or (not (x <= -5.4e-92) and (x <= 3.6e-40))):
		tmp = x * 200.0
	else:
		tmp = y * -200.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.75e+20) || !((x <= -4.2e-67) || (!(x <= -5.4e-92) && (x <= 3.6e-40))))
		tmp = Float64(x * 200.0);
	else
		tmp = Float64(y * -200.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.75e+20) || ~(((x <= -4.2e-67) || (~((x <= -5.4e-92)) && (x <= 3.6e-40)))))
		tmp = x * 200.0;
	else
		tmp = y * -200.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.75e+20], N[Not[Or[LessEqual[x, -4.2e-67], And[N[Not[LessEqual[x, -5.4e-92]], $MachinePrecision], LessEqual[x, 3.6e-40]]]], $MachinePrecision]], N[(x * 200.0), $MachinePrecision], N[(y * -200.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.75e20 or -4.2000000000000003e-67 < x < -5.3999999999999999e-92 or 3.6e-40 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 76.6%

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

   if -1.75e20 < x < -4.2000000000000003e-67 or -5.3999999999999999e-92 < x < 3.6e-40

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 81.5%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+20} \lor \neg \left(x \leq -4.2 \cdot 10^{-67} \lor \neg \left(x \leq -5.4 \cdot 10^{-92}\right) \land x \leq 3.6 \cdot 10^{-40}\right):\\ \;\;\;\;x \cdot 200\\ \mathbf{else}:\\ \;\;\;\;y \cdot -200\\ \end{array} \]

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 100.0%

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

2. Final simplification 100.0%

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

Alternative 4: 50.7% accurate, 1.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in x around 0 50.2%

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

3. Final simplification 50.2%

   \[\leadsto y \cdot -200 \]

Reproduce

herbie shell --seed 2023320 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, C"
  :precision binary64
  (* 200.0 (- x y)))