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

Percentage Accurate: 99.9% → 100.0%

Time: 5.4s

Alternatives: 6

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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

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

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

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

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

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

   6. metadata-eval N/A

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

   7. metadata-eval N/A

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

   8. lower-fma.f64 N/A

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

   9. metadata-eval N/A

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

   10. *-commutative N/A

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

   11. lower-*.f64 100.0

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

4. Applied egg-rr 100.0%

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

Alternative 2: 74.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{-10}:\\ \;\;\;\;200 \cdot x\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-19}:\\ \;\;\;\;y \cdot -200\\ \mathbf{else}:\\ \;\;\;\;200 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.85e-10)
   (* 200.0 x)
   (if (<= x 3.5e-19) (* y -200.0) (* 200.0 x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.85e-10) {
		tmp = 200.0 * x;
	} else if (x <= 3.5e-19) {
		tmp = y * -200.0;
	} else {
		tmp = 200.0 * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-1.85d-10)) then
        tmp = 200.0d0 * x
    else if (x <= 3.5d-19) then
        tmp = y * (-200.0d0)
    else
        tmp = 200.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.85e-10) {
		tmp = 200.0 * x;
	} else if (x <= 3.5e-19) {
		tmp = y * -200.0;
	} else {
		tmp = 200.0 * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.85e-10:
		tmp = 200.0 * x
	elif x <= 3.5e-19:
		tmp = y * -200.0
	else:
		tmp = 200.0 * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.85e-10)
		tmp = Float64(200.0 * x);
	elseif (x <= 3.5e-19)
		tmp = Float64(y * -200.0);
	else
		tmp = Float64(200.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.85e-10)
		tmp = 200.0 * x;
	elseif (x <= 3.5e-19)
		tmp = y * -200.0;
	else
		tmp = 200.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.85e-10], N[(200.0 * x), $MachinePrecision], If[LessEqual[x, 3.5e-19], N[(y * -200.0), $MachinePrecision], N[(200.0 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.85000000000000007e-10 or 3.50000000000000015e-19 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 82.5

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

   5. Simplified 82.5%

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

   if -1.85000000000000007e-10 < x < 3.50000000000000015e-19

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 75.1

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

   5. Simplified 75.1%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{-10}:\\ \;\;\;\;200 \cdot x\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-19}:\\ \;\;\;\;y \cdot -200\\ \mathbf{else}:\\ \;\;\;\;200 \cdot x\\ \end{array} \]
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 100.0%

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

Alternative 4: 50.7% 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 100.0%

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

3. Taylor expanded in x around 0

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

   1. lower-*.f64 45.0

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

5. Simplified 45.0%

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

6. Final simplification 45.0%

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

Alternative 5: 8.8% accurate, 3.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return -y

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := (-y)

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in x around 0

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

   1. lower-*.f64 45.0

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

5. Simplified 45.0%

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

6. Taylor expanded in y around -inf

   \[\leadsto \color{blue}{-1 \cdot y} \]
7. Step-by-step derivation

   1. mul-1-neg N/A

      \[\leadsto \color{blue}{\mathsf{neg}\left(y\right)} \]

   2. lower-neg.f64 8.3

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

8. Simplified 8.3%

   \[\leadsto \color{blue}{-y} \]
9. Add Preprocessing

Alternative 6: 2.2% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 y)

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return y

Julia

function code(x, y)
	return y
end

MATLAB

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

Wolfram

code[x_, y_] := y

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in x around 0

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

   1. lower-*.f64 45.0

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

5. Simplified 45.0%

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

6. Taylor expanded in y around -inf

   \[\leadsto \color{blue}{-1 \cdot y} \]
7. Step-by-step derivation

   1. mul-1-neg N/A

      \[\leadsto \color{blue}{\mathsf{neg}\left(y\right)} \]

   2. lower-neg.f64 8.3

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

8. Simplified 8.3%

   \[\leadsto \color{blue}{-y} \]
9. Step-by-step derivation

   1. neg-sub0 N/A

      \[\leadsto \color{blue}{0 - y} \]

   2. flip3-- N/A

      \[\leadsto \color{blue}{\frac{{0}^{3} - {y}^{3}}{0 \cdot 0 + \left(y \cdot y + 0 \cdot y\right)}} \]

   3. metadata-eval N/A

      \[\leadsto \frac{\color{blue}{0} - {y}^{3}}{0 \cdot 0 + \left(y \cdot y + 0 \cdot y\right)} \]

   4. neg-sub0 N/A

      \[\leadsto \frac{\color{blue}{\mathsf{neg}\left({y}^{3}\right)}}{0 \cdot 0 + \left(y \cdot y + 0 \cdot y\right)} \]

   5. cube-neg N/A

      \[\leadsto \frac{\color{blue}{{\left(\mathsf{neg}\left(y\right)\right)}^{3}}}{0 \cdot 0 + \left(y \cdot y + 0 \cdot y\right)} \]

   6. lift-neg.f64 N/A

      \[\leadsto \frac{{\color{blue}{\left(\mathsf{neg}\left(y\right)\right)}}^{3}}{0 \cdot 0 + \left(y \cdot y + 0 \cdot y\right)} \]

   7. sqr-pow N/A

      \[\leadsto \frac{\color{blue}{{\left(\mathsf{neg}\left(y\right)\right)}^{\left(\frac{3}{2}\right)} \cdot {\left(\mathsf{neg}\left(y\right)\right)}^{\left(\frac{3}{2}\right)}}}{0 \cdot 0 + \left(y \cdot y + 0 \cdot y\right)} \]

   8. pow-prod-down N/A

      \[\leadsto \frac{\color{blue}{{\left(\left(\mathsf{neg}\left(y\right)\right) \cdot \left(\mathsf{neg}\left(y\right)\right)\right)}^{\left(\frac{3}{2}\right)}}}{0 \cdot 0 + \left(y \cdot y + 0 \cdot y\right)} \]

   9. lift-neg.f64 N/A

      \[\leadsto \frac{{\left(\color{blue}{\left(\mathsf{neg}\left(y\right)\right)} \cdot \left(\mathsf{neg}\left(y\right)\right)\right)}^{\left(\frac{3}{2}\right)}}{0 \cdot 0 + \left(y \cdot y + 0 \cdot y\right)} \]

   10. lift-neg.f64 N/A

       \[\leadsto \frac{{\left(\left(\mathsf{neg}\left(y\right)\right) \cdot \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)}^{\left(\frac{3}{2}\right)}}{0 \cdot 0 + \left(y \cdot y + 0 \cdot y\right)} \]

   11. sqr-neg N/A

       \[\leadsto \frac{{\color{blue}{\left(y \cdot y\right)}}^{\left(\frac{3}{2}\right)}}{0 \cdot 0 + \left(y \cdot y + 0 \cdot y\right)} \]

   12. unpow-prod-down N/A

       \[\leadsto \frac{\color{blue}{{y}^{\left(\frac{3}{2}\right)} \cdot {y}^{\left(\frac{3}{2}\right)}}}{0 \cdot 0 + \left(y \cdot y + 0 \cdot y\right)} \]

   13. sqr-pow N/A

       \[\leadsto \frac{\color{blue}{{y}^{3}}}{0 \cdot 0 + \left(y \cdot y + 0 \cdot y\right)} \]

   14. remove-double-neg N/A

       \[\leadsto \frac{{\color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right)}}^{3}}{0 \cdot 0 + \left(y \cdot y + 0 \cdot y\right)} \]

   15. lift-neg.f64 N/A

       \[\leadsto \frac{{\left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right)}^{3}}{0 \cdot 0 + \left(y \cdot y + 0 \cdot y\right)} \]

   16. neg-mul-1 N/A

       \[\leadsto \frac{{\color{blue}{\left(-1 \cdot \left(\mathsf{neg}\left(y\right)\right)\right)}}^{3}}{0 \cdot 0 + \left(y \cdot y + 0 \cdot y\right)} \]

   17. *-commutative N/A

       \[\leadsto \frac{{\color{blue}{\left(\left(\mathsf{neg}\left(y\right)\right) \cdot -1\right)}}^{3}}{0 \cdot 0 + \left(y \cdot y + 0 \cdot y\right)} \]

   18. unpow-prod-down N/A

       \[\leadsto \frac{\color{blue}{{\left(\mathsf{neg}\left(y\right)\right)}^{3} \cdot {-1}^{3}}}{0 \cdot 0 + \left(y \cdot y + 0 \cdot y\right)} \]

   19. metadata-eval N/A

       \[\leadsto \frac{{\left(\mathsf{neg}\left(y\right)\right)}^{3} \cdot \color{blue}{-1}}{0 \cdot 0 + \left(y \cdot y + 0 \cdot y\right)} \]

   20. associate-*l/ N/A

       \[\leadsto \color{blue}{\frac{{\left(\mathsf{neg}\left(y\right)\right)}^{3}}{0 \cdot 0 + \left(y \cdot y + 0 \cdot y\right)} \cdot -1} \]

10. Applied egg-rr 2.3%

    \[\leadsto \color{blue}{y} \]
11. Add Preprocessing

Reproduce

herbie shell --seed 2024214 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, C"
  :precision binary64
  (* 200.0 (- x y)))