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

Percentage Accurate: 99.9% → 100.0%

Time: 4.0s

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

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

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 99.9%

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

   1. sub-neg 99.9%

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

   2. distribute-rgt-in 99.9%

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

   3. fma-define 100.0%

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

4. Applied egg-rr 100.0%

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

5. Final simplification 100.0%

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

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. Add Preprocessing

3. Taylor expanded in x around 0 99.9%

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

   1. fma-define 99.9%

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

5. Simplified 99.9%

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

6. Final simplification 99.9%

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

Alternative 3: 74.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{+24} \lor \neg \left(y \leq 4.3 \cdot 10^{-78}\right):\\ \;\;\;\;y \cdot -200\\ \mathbf{else}:\\ \;\;\;\;x \cdot 200\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -6.6e+24) (not (<= y 4.3e-78))) (* y -200.0) (* x 200.0)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -6.6e+24) || !(y <= 4.3e-78)) {
		tmp = y * -200.0;
	} 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 ((y <= (-6.6d+24)) .or. (.not. (y <= 4.3d-78))) then
        tmp = y * (-200.0d0)
    else
        tmp = x * 200.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -6.6e+24) || !(y <= 4.3e-78)) {
		tmp = y * -200.0;
	} else {
		tmp = x * 200.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -6.6e+24) or not (y <= 4.3e-78):
		tmp = y * -200.0
	else:
		tmp = x * 200.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -6.6e+24) || !(y <= 4.3e-78))
		tmp = Float64(y * -200.0);
	else
		tmp = Float64(x * 200.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -6.6e+24) || ~((y <= 4.3e-78)))
		tmp = y * -200.0;
	else
		tmp = x * 200.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -6.6e+24], N[Not[LessEqual[y, 4.3e-78]], $MachinePrecision]], N[(y * -200.0), $MachinePrecision], N[(x * 200.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.5999999999999998e24 or 4.29999999999999994e-78 < y

   1. Initial program 100.0%

      \[200 \cdot \left(x - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 72.8%

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

   if -6.5999999999999998e24 < y < 4.29999999999999994e-78

   1. Initial program 99.9%

      \[200 \cdot \left(x - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 85.6%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{+24} \lor \neg \left(y \leq 4.3 \cdot 10^{-78}\right):\\ \;\;\;\;y \cdot -200\\ \mathbf{else}:\\ \;\;\;\;x \cdot 200\\ \end{array} \]
5. Add Preprocessing

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. Add Preprocessing

3. Final simplification 99.9%

   \[\leadsto 200 \cdot \left(x - y\right) \]
4. Add Preprocessing

Alternative 5: 51.0% 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 99.9%

   \[200 \cdot \left(x - y\right) \]
2. Add Preprocessing

3. Taylor expanded in x around 0 45.9%

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

4. Final simplification 45.9%

   \[\leadsto y \cdot -200 \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024034 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, C"
  :precision binary64
  (* 200.0 (- x y)))