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

Percentage Accurate: 100.0% → 100.0%

Time: 6.2s

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: 100.0% 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. Add Preprocessing
3. Step-by-step derivation

   1. sub-neg N/A

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

   2. distribute-rgt-in N/A

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

   3. fma-define N/A

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

   4. fma-lowering-fma.f64 N/A

      \[\leadsto \mathsf{fma.f64}\left(x, \color{blue}{200}, \left(\left(\mathsf{neg}\left(y\right)\right) \cdot 200\right)\right) \]

   5. *-commutative N/A

      \[\leadsto \mathsf{fma.f64}\left(x, 200, \left(200 \cdot \left(\mathsf{neg}\left(y\right)\right)\right)\right) \]

   6. neg-mul-1 N/A

      \[\leadsto \mathsf{fma.f64}\left(x, 200, \left(200 \cdot \left(-1 \cdot y\right)\right)\right) \]

   7. associate-*r* N/A

      \[\leadsto \mathsf{fma.f64}\left(x, 200, \left(\left(200 \cdot -1\right) \cdot y\right)\right) \]

   8. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{fma.f64}\left(x, 200, \mathsf{*.f64}\left(\left(200 \cdot -1\right), y\right)\right) \]

   9. metadata-eval 100.0%

      \[\leadsto \mathsf{fma.f64}\left(x, 200, \mathsf{*.f64}\left(-200, y\right)\right) \]

4. Applied egg-rr 100.0%

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

Alternative 2: 74.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+41}:\\ \;\;\;\;-200 \cdot y\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+29}:\\ \;\;\;\;x \cdot 200\\ \mathbf{else}:\\ \;\;\;\;-200 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -6e+41) (* -200.0 y) (if (<= y 6e+29) (* x 200.0) (* -200.0 y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -6e+41) {
		tmp = -200.0 * y;
	} else if (y <= 6e+29) {
		tmp = x * 200.0;
	} else {
		tmp = -200.0 * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-6d+41)) then
        tmp = (-200.0d0) * y
    else if (y <= 6d+29) then
        tmp = x * 200.0d0
    else
        tmp = (-200.0d0) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -6e+41) {
		tmp = -200.0 * y;
	} else if (y <= 6e+29) {
		tmp = x * 200.0;
	} else {
		tmp = -200.0 * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -6e+41:
		tmp = -200.0 * y
	elif y <= 6e+29:
		tmp = x * 200.0
	else:
		tmp = -200.0 * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -6e+41)
		tmp = Float64(-200.0 * y);
	elseif (y <= 6e+29)
		tmp = Float64(x * 200.0);
	else
		tmp = Float64(-200.0 * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -6e+41)
		tmp = -200.0 * y;
	elseif (y <= 6e+29)
		tmp = x * 200.0;
	else
		tmp = -200.0 * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -6e+41], N[(-200.0 * y), $MachinePrecision], If[LessEqual[y, 6e+29], N[(x * 200.0), $MachinePrecision], N[(-200.0 * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.9999999999999997e41 or 5.9999999999999998e29 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 78.4%

         \[\leadsto \mathsf{*.f64}\left(-200, \color{blue}{y}\right) \]

   5. Simplified 78.4%

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

   if -5.9999999999999997e41 < y < 5.9999999999999998e29

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 77.1%

         \[\leadsto \mathsf{*.f64}\left(200, \color{blue}{x}\right) \]

   5. Simplified 77.1%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+41}:\\ \;\;\;\;-200 \cdot y\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+29}:\\ \;\;\;\;x \cdot 200\\ \mathbf{else}:\\ \;\;\;\;-200 \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 100.0% 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. Add Preprocessing

Alternative 4: 50.7% 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. Add Preprocessing

3. Taylor expanded in x around 0

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

   1. *-lowering-*.f64 48.6%

      \[\leadsto \mathsf{*.f64}\left(-200, \color{blue}{y}\right) \]

5. Simplified 48.6%

   \[\leadsto \color{blue}{-200 \cdot y} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024138 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, C"
  :precision binary64
  (* 200.0 (- x y)))