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

Percentage Accurate: 99.9% → 100.0%

Time: 3.7s

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, 0.8× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

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

   2. distribute-rgt-in N/A

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

   3. *-commutative N/A

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

   4. lower-fma.f64 N/A

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

   5. *-commutative N/A

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

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

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

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

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

   8. metadata-eval N/A

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

   9. metadata-eval N/A

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

   10. lower-*.f64 N/A

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

   11. metadata-eval 100.0

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

4. Applied egg-rr 100.0%

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

Alternative 2: 75.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{-18}:\\ \;\;\;\;x \cdot 200\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-44}:\\ \;\;\;\;y \cdot -200\\ \mathbf{else}:\\ \;\;\;\;x \cdot 200\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3e-18) (* x 200.0) (if (<= x 1.5e-44) (* y -200.0) (* x 200.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3e-18) {
		tmp = x * 200.0;
	} else if (x <= 1.5e-44) {
		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 (x <= (-3d-18)) then
        tmp = x * 200.0d0
    else if (x <= 1.5d-44) 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 (x <= -3e-18) {
		tmp = x * 200.0;
	} else if (x <= 1.5e-44) {
		tmp = y * -200.0;
	} else {
		tmp = x * 200.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3e-18:
		tmp = x * 200.0
	elif x <= 1.5e-44:
		tmp = y * -200.0
	else:
		tmp = x * 200.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3e-18)
		tmp = Float64(x * 200.0);
	elseif (x <= 1.5e-44)
		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 (x <= -3e-18)
		tmp = x * 200.0;
	elseif (x <= 1.5e-44)
		tmp = y * -200.0;
	else
		tmp = x * 200.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3e-18], N[(x * 200.0), $MachinePrecision], If[LessEqual[x, 1.5e-44], N[(y * -200.0), $MachinePrecision], N[(x * 200.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.99999999999999983e-18 or 1.5000000000000001e-44 < x

   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. lower-*.f64 80.8

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

   5. Simplified 80.8%

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

   if -2.99999999999999983e-18 < x < 1.5000000000000001e-44

   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. lower-*.f64 76.6

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

   5. Simplified 76.6%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{-18}:\\ \;\;\;\;x \cdot 200\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-44}:\\ \;\;\;\;y \cdot -200\\ \mathbf{else}:\\ \;\;\;\;x \cdot 200\\ \end{array} \]
5. Add Preprocessing

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. Add Preprocessing
3. Add Preprocessing

Alternative 4: 49.9% accurate, 1.5× 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

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

   1. lower-*.f64 44.9

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

5. Simplified 44.9%

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

6. Final simplification 44.9%

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

Reproduce

herbie shell --seed 2024212 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, C"
  :precision binary64
  (* 200.0 (- x y)))