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

Percentage Accurate: 100.0% → 100.0%

Time: 4.6s

Alternatives: 4

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ 500 \cdot \left(x - y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* 500.0 (- x y)))

C

double code(double x, double y) {
	return 500.0 * (x - y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 500.0d0 * (x - y)
end function

Java

public static double code(double x, double y) {
	return 500.0 * (x - y);
}

Python

def code(x, y):
	return 500.0 * (x - y)

Julia

function code(x, y)
	return Float64(500.0 * Float64(x - y))
end

MATLAB

function tmp = code(x, y)
	tmp = 500.0 * (x - y);
end

Wolfram

code[x_, y_] := N[(500.0 * N[(x - y), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 500 \cdot \left(x - y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* 500.0 (- x y)))

C

double code(double x, double y) {
	return 500.0 * (x - y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 500.0d0 * (x - y)
end function

Java

public static double code(double x, double y) {
	return 500.0 * (x - y);
}

Python

def code(x, y):
	return 500.0 * (x - y)

Julia

function code(x, y)
	return Float64(500.0 * Float64(x - y))
end

MATLAB

function tmp = code(x, y)
	tmp = 500.0 * (x - y);
end

Wolfram

code[x_, y_] := N[(500.0 * N[(x - y), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(x, 500, y \cdot -500\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (fma x 500.0 (* y -500.0)))

C

double code(double x, double y) {
	return fma(x, 500.0, (y * -500.0));
}

Julia

function code(x, y)
	return fma(x, 500.0, Float64(y * -500.0))
end

Wolfram

code[x_, y_] := N[(x * 500.0 + N[(y * -500.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[500 \cdot \left(x - y\right) \]
2. Add Preprocessing
3. Step-by-step derivation

   1. sub-neg N/A

      \[\leadsto 500 \cdot \left(x + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right) \]

   2. distribute-rgt-in N/A

      \[\leadsto x \cdot 500 + \color{blue}{\left(\mathsf{neg}\left(y\right)\right) \cdot 500} \]

   3. accelerator-lowering-fma.f64 N/A

      \[\leadsto \mathsf{fma.f64}\left(x, \color{blue}{500}, \left(\left(\mathsf{neg}\left(y\right)\right) \cdot 500\right)\right) \]

   4. distribute-lft-neg-out N/A

      \[\leadsto \mathsf{fma.f64}\left(x, 500, \left(\mathsf{neg}\left(y \cdot 500\right)\right)\right) \]

   5. distribute-rgt-neg-in N/A

      \[\leadsto \mathsf{fma.f64}\left(x, 500, \left(y \cdot \left(\mathsf{neg}\left(500\right)\right)\right)\right) \]

   6. metadata-eval N/A

      \[\leadsto \mathsf{fma.f64}\left(x, 500, \left(y \cdot -500\right)\right) \]

   7. metadata-eval N/A

      \[\leadsto \mathsf{fma.f64}\left(x, 500, \left(y \cdot \left(500 \cdot -1\right)\right)\right) \]

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

      \[\leadsto \mathsf{fma.f64}\left(x, 500, \mathsf{*.f64}\left(y, \left(500 \cdot -1\right)\right)\right) \]

   9. metadata-eval 100.0%

      \[\leadsto \mathsf{fma.f64}\left(x, 500, \mathsf{*.f64}\left(y, -500\right)\right) \]

4. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, 500, y \cdot -500\right)} \]
5. Add Preprocessing

Alternative 2: 74.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.35 \cdot 10^{-50}:\\ \;\;\;\;x \cdot 500\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+85}:\\ \;\;\;\;y \cdot -500\\ \mathbf{else}:\\ \;\;\;\;x \cdot 500\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.35e-50)
   (* x 500.0)
   (if (<= x 3.8e+85) (* y -500.0) (* x 500.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.35e-50) {
		tmp = x * 500.0;
	} else if (x <= 3.8e+85) {
		tmp = y * -500.0;
	} else {
		tmp = x * 500.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-2.35d-50)) then
        tmp = x * 500.0d0
    else if (x <= 3.8d+85) then
        tmp = y * (-500.0d0)
    else
        tmp = x * 500.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2.35e-50) {
		tmp = x * 500.0;
	} else if (x <= 3.8e+85) {
		tmp = y * -500.0;
	} else {
		tmp = x * 500.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.35e-50:
		tmp = x * 500.0
	elif x <= 3.8e+85:
		tmp = y * -500.0
	else:
		tmp = x * 500.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.35e-50)
		tmp = Float64(x * 500.0);
	elseif (x <= 3.8e+85)
		tmp = Float64(y * -500.0);
	else
		tmp = Float64(x * 500.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.35e-50)
		tmp = x * 500.0;
	elseif (x <= 3.8e+85)
		tmp = y * -500.0;
	else
		tmp = x * 500.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.35e-50], N[(x * 500.0), $MachinePrecision], If[LessEqual[x, 3.8e+85], N[(y * -500.0), $MachinePrecision], N[(x * 500.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.3500000000000001e-50 or 3.79999999999999992e85 < x

   1. Initial program 100.0%

      \[500 \cdot \left(x - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(500, \color{blue}{x}\right) \]
   4. Step-by-step derivation

   5. Simplified 75.4%

      \[\leadsto 500 \cdot \color{blue}{x} \]

   if -2.3500000000000001e-50 < x < 3.79999999999999992e85

   1. Initial program 100.0%

      \[500 \cdot \left(x - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-500 \cdot y} \]
   4. Step-by-step derivation

      1. +-rgt-identity N/A

         \[\leadsto -500 \cdot y + \color{blue}{0} \]

      2. *-commutative N/A

         \[\leadsto y \cdot -500 + 0 \]

      3. accelerator-lowering-fma.f64 78.4%

         \[\leadsto \mathsf{fma.f64}\left(y, \color{blue}{-500}, 0\right) \]

   5. Simplified 78.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, -500, 0\right)} \]
   6. Step-by-step derivation

      1. +-rgt-identity N/A

         \[\leadsto y \cdot \color{blue}{-500} \]

      2. *-lowering-*.f64 78.4%

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{-500}\right) \]

   7. Applied egg-rr 78.4%

      \[\leadsto \color{blue}{y \cdot -500} \]
3. Recombined 2 regimes into one program.

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.35 \cdot 10^{-50}:\\ \;\;\;\;x \cdot 500\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+85}:\\ \;\;\;\;y \cdot -500\\ \mathbf{else}:\\ \;\;\;\;x \cdot 500\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 500 \cdot \left(x - y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* 500.0 (- x y)))

C

double code(double x, double y) {
	return 500.0 * (x - y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 500.0d0 * (x - y)
end function

Java

public static double code(double x, double y) {
	return 500.0 * (x - y);
}

Python

def code(x, y):
	return 500.0 * (x - y)

Julia

function code(x, y)
	return Float64(500.0 * Float64(x - y))
end

MATLAB

function tmp = code(x, y)
	tmp = 500.0 * (x - y);
end

Wolfram

code[x_, y_] := N[(500.0 * N[(x - y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[500 \cdot \left(x - y\right) \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 4: 51.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ x \cdot 500 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* x 500.0))

C

double code(double x, double y) {
	return x * 500.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x * 500.0d0
end function

Java

public static double code(double x, double y) {
	return x * 500.0;
}

Python

def code(x, y):
	return x * 500.0

Julia

function code(x, y)
	return Float64(x * 500.0)
end

MATLAB

function tmp = code(x, y)
	tmp = x * 500.0;
end

Wolfram

code[x_, y_] := N[(x * 500.0), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[500 \cdot \left(x - y\right) \]
2. Add Preprocessing

3. Taylor expanded in x around inf

   \[\leadsto \mathsf{*.f64}\left(500, \color{blue}{x}\right) \]
4. Step-by-step derivation

5. Simplified 48.6%

   \[\leadsto 500 \cdot \color{blue}{x} \]

6. Final simplification 48.6%

   \[\leadsto x \cdot 500 \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024193 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, B"
  :precision binary64
  (* 500.0 (- x y)))