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

Percentage Accurate: 100.0% → 100.0%

Time: 7.0s

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, 0.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := N[(N[(N[(x + y), $MachinePrecision] * -500.0), $MachinePrecision] / N[(N[(x + y), $MachinePrecision] / N[(y - x), $MachinePrecision]), $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. fma-define N/A

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

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

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

   5. fmm-undef N/A

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

   6. --lowering--.f64 N/A

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

   7. *-commutative N/A

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

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

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

   9. *-lowering-*.f64 100.0%

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

4. Applied egg-rr 100.0%

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

   1. *-commutative N/A

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

   2. distribute-lft-out-- N/A

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

   3. metadata-eval N/A

      \[\leadsto \frac{500}{1} \cdot \left(\color{blue}{x} - y\right) \]

   4. *-inverses N/A

      \[\leadsto \frac{500}{\frac{x \cdot x - y \cdot y}{x \cdot x - y \cdot y}} \cdot \left(x - y\right) \]

   5. flip-- N/A

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

   6. times-frac N/A

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

   7. difference-of-squares N/A

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

   8. associate-*r* N/A

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

   9. distribute-lft-out N/A

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

   10. *-commutative N/A

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

   11. times-frac N/A

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

   12. *-inverses N/A

       \[\leadsto \frac{500 \cdot x + y \cdot 500}{1} \cdot \frac{x - \color{blue}{y}}{x + y} \]

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

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

6. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{\frac{500 \cdot \left(x + y\right)}{1} \cdot \frac{x - y}{x + y}} \]
7. Step-by-step derivation

   1. associate-/r/ N/A

      \[\leadsto \frac{500 \cdot \left(x + y\right)}{\color{blue}{\frac{1}{\frac{x - y}{x + y}}}} \]

   2. clear-num N/A

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

   3. frac-2neg N/A

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

   4. neg-mul-1 N/A

      \[\leadsto \frac{\mathsf{neg}\left(500 \cdot \left(x + y\right)\right)}{-1 \cdot \color{blue}{\frac{x + y}{x - y}}} \]

   5. metadata-eval N/A

      \[\leadsto \frac{\mathsf{neg}\left(500 \cdot \left(x + y\right)\right)}{\left(\mathsf{neg}\left(1\right)\right) \cdot \frac{\color{blue}{x + y}}{x - y}} \]

   6. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\left(\mathsf{neg}\left(500 \cdot \left(x + y\right)\right)\right), \color{blue}{\left(\left(\mathsf{neg}\left(1\right)\right) \cdot \frac{x + y}{x - y}\right)}\right) \]

   7. *-commutative N/A

      \[\leadsto \mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(x + y\right) \cdot 500\right)\right), \left(\left(\mathsf{neg}\left(\color{blue}{1}\right)\right) \cdot \frac{x + y}{x - y}\right)\right) \]

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

      \[\leadsto \mathsf{/.f64}\left(\left(\left(x + y\right) \cdot \left(\mathsf{neg}\left(500\right)\right)\right), \left(\color{blue}{\left(\mathsf{neg}\left(1\right)\right)} \cdot \frac{x + y}{x - y}\right)\right) \]

   9. metadata-eval N/A

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

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

       \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(x + y\right), -500\right), \left(\color{blue}{\left(\mathsf{neg}\left(1\right)\right)} \cdot \frac{x + y}{x - y}\right)\right) \]

   11. +-lowering-+.f64 N/A

       \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, y\right), -500\right), \left(\left(\mathsf{neg}\left(\color{blue}{1}\right)\right) \cdot \frac{x + y}{x - y}\right)\right) \]

   12. metadata-eval N/A

       \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, y\right), -500\right), \left(-1 \cdot \frac{\color{blue}{x + y}}{x - y}\right)\right) \]

   13. neg-mul-1 N/A

       \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, y\right), -500\right), \left(\mathsf{neg}\left(\frac{x + y}{x - y}\right)\right)\right) \]

   14. distribute-neg-frac2 N/A

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

   15. /-lowering-/.f64 N/A

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

   16. +-lowering-+.f64 N/A

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

   17. sub-neg N/A

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

   18. +-commutative N/A

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

   19. distribute-neg-in N/A

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

   20. remove-double-neg N/A

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

   21. sub-neg N/A

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

   22. --lowering--.f64 100.0%

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

8. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{\frac{\left(x + y\right) \cdot -500}{\frac{x + y}{y - x}}} \]
9. Add Preprocessing

Alternative 2: 73.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{-93}:\\ \;\;\;\;x \cdot 500\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{+31}:\\ \;\;\;\;y \cdot -500\\ \mathbf{else}:\\ \;\;\;\;x \cdot 500\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3e-93) (* x 500.0) (if (<= x 1.75e+31) (* y -500.0) (* x 500.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3e-93) {
		tmp = x * 500.0;
	} else if (x <= 1.75e+31) {
		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 <= (-3d-93)) then
        tmp = x * 500.0d0
    else if (x <= 1.75d+31) 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 <= -3e-93) {
		tmp = x * 500.0;
	} else if (x <= 1.75e+31) {
		tmp = y * -500.0;
	} else {
		tmp = x * 500.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3e-93:
		tmp = x * 500.0
	elif x <= 1.75e+31:
		tmp = y * -500.0
	else:
		tmp = x * 500.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3e-93)
		tmp = Float64(x * 500.0);
	elseif (x <= 1.75e+31)
		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 <= -3e-93)
		tmp = x * 500.0;
	elseif (x <= 1.75e+31)
		tmp = y * -500.0;
	else
		tmp = x * 500.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3e-93], N[(x * 500.0), $MachinePrecision], If[LessEqual[x, 1.75e+31], N[(y * -500.0), $MachinePrecision], N[(x * 500.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.0000000000000001e-93 or 1.75e31 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 78.6%

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

   5. Simplified 78.6%

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

   if -3.0000000000000001e-93 < x < 1.75e31

   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. *-lowering-*.f64 82.0%

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

   5. Simplified 82.0%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{-93}:\\ \;\;\;\;x \cdot 500\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{+31}:\\ \;\;\;\;y \cdot -500\\ \mathbf{else}:\\ \;\;\;\;x \cdot 500\\ \end{array} \]
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: 50.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ y \cdot -500 \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. *-lowering-*.f64 50.8%

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

5. Simplified 50.8%

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

6. Final simplification 50.8%

   \[\leadsto y \cdot -500 \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024160 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, B"
  :precision binary64
  (* 500.0 (- x y)))