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, 0.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in x around 0 99.9%

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

   1. +-commutative 99.9%

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

   2. fma-def 100.0%

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

4. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(-200, y, 200 \cdot x\right)} \]
5. Step-by-step derivation

   1. fma-udef 99.9%

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

   2. flip-+ 49.4%

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

   3. *-commutative 49.4%

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

   4. *-commutative 49.4%

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

   5. *-commutative 49.4%

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

   6. *-commutative 49.4%

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

   7. swap-sqr 49.3%

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

   8. metadata-eval 49.3%

      \[\leadsto \frac{\left(y \cdot -200\right) \cdot \left(y \cdot -200\right) - \left(x \cdot x\right) \cdot \color{blue}{40000}}{-200 \cdot y - 200 \cdot x} \]

   9. *-commutative 49.3%

      \[\leadsto \frac{\left(y \cdot -200\right) \cdot \left(y \cdot -200\right) - \left(x \cdot x\right) \cdot 40000}{\color{blue}{y \cdot -200} - 200 \cdot x} \]

   10. *-commutative 49.3%

       \[\leadsto \frac{\left(y \cdot -200\right) \cdot \left(y \cdot -200\right) - \left(x \cdot x\right) \cdot 40000}{y \cdot -200 - \color{blue}{x \cdot 200}} \]

6. Applied egg-rr 49.3%

   \[\leadsto \color{blue}{\frac{\left(y \cdot -200\right) \cdot \left(y \cdot -200\right) - \left(x \cdot x\right) \cdot 40000}{y \cdot -200 - x \cdot 200}} \]
7. Step-by-step derivation

   1. swap-sqr 48.9%

      \[\leadsto \frac{\color{blue}{\left(y \cdot y\right) \cdot \left(-200 \cdot -200\right)} - \left(x \cdot x\right) \cdot 40000}{y \cdot -200 - x \cdot 200} \]

   2. metadata-eval 48.9%

      \[\leadsto \frac{\left(y \cdot y\right) \cdot \color{blue}{40000} - \left(x \cdot x\right) \cdot 40000}{y \cdot -200 - x \cdot 200} \]

   3. associate-*l* 48.9%

      \[\leadsto \frac{\left(y \cdot y\right) \cdot 40000 - \color{blue}{x \cdot \left(x \cdot 40000\right)}}{y \cdot -200 - x \cdot 200} \]

   4. *-commutative 48.9%

      \[\leadsto \frac{\left(y \cdot y\right) \cdot 40000 - x \cdot \left(x \cdot 40000\right)}{\color{blue}{-200 \cdot y} - x \cdot 200} \]

   5. *-commutative 48.9%

      \[\leadsto \frac{\left(y \cdot y\right) \cdot 40000 - x \cdot \left(x \cdot 40000\right)}{-200 \cdot y - \color{blue}{200 \cdot x}} \]

8. Simplified 48.9%

   \[\leadsto \color{blue}{\frac{\left(y \cdot y\right) \cdot 40000 - x \cdot \left(x \cdot 40000\right)}{-200 \cdot y - 200 \cdot x}} \]

9. Taylor expanded in y around inf 25.3%

   \[\leadsto \frac{\color{blue}{40000 \cdot {y}^{2}}}{-200 \cdot y - 200 \cdot x} \]
10. Step-by-step derivation

    1. unpow2 25.3%

       \[\leadsto \frac{40000 \cdot \color{blue}{\left(y \cdot y\right)}}{-200 \cdot y - 200 \cdot x} \]

    2. *-commutative 25.3%

       \[\leadsto \frac{\color{blue}{\left(y \cdot y\right) \cdot 40000}}{-200 \cdot y - 200 \cdot x} \]

    3. associate-*r* 25.5%

       \[\leadsto \frac{\color{blue}{y \cdot \left(y \cdot 40000\right)}}{-200 \cdot y - 200 \cdot x} \]

11. Simplified 25.5%

    \[\leadsto \frac{\color{blue}{y \cdot \left(y \cdot 40000\right)}}{-200 \cdot y - 200 \cdot x} \]

12. Taylor expanded in y around inf 99.9%

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

    1. fma-def 100.0%

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

    2. *-commutative 100.0%

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

14. Simplified 100.0%

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

15. Final simplification 100.0%

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

Alternative 2: 74.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+51}:\\ \;\;\;\;200 \cdot x\\ \mathbf{elif}\;x \leq -68000000000 \lor \neg \left(x \leq -1.75 \cdot 10^{-30}\right) \land x \leq 7 \cdot 10^{-29}:\\ \;\;\;\;y \cdot -200\\ \mathbf{else}:\\ \;\;\;\;200 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -5.5e+51)
   (* 200.0 x)
   (if (or (<= x -68000000000.0) (and (not (<= x -1.75e-30)) (<= x 7e-29)))
     (* y -200.0)
     (* 200.0 x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -5.5e+51) {
		tmp = 200.0 * x;
	} else if ((x <= -68000000000.0) || (!(x <= -1.75e-30) && (x <= 7e-29))) {
		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 <= (-5.5d+51)) then
        tmp = 200.0d0 * x
    else if ((x <= (-68000000000.0d0)) .or. (.not. (x <= (-1.75d-30))) .and. (x <= 7d-29)) 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 <= -5.5e+51) {
		tmp = 200.0 * x;
	} else if ((x <= -68000000000.0) || (!(x <= -1.75e-30) && (x <= 7e-29))) {
		tmp = y * -200.0;
	} else {
		tmp = 200.0 * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -5.5e+51:
		tmp = 200.0 * x
	elif (x <= -68000000000.0) or (not (x <= -1.75e-30) and (x <= 7e-29)):
		tmp = y * -200.0
	else:
		tmp = 200.0 * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -5.5e+51)
		tmp = Float64(200.0 * x);
	elseif ((x <= -68000000000.0) || (!(x <= -1.75e-30) && (x <= 7e-29)))
		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 <= -5.5e+51)
		tmp = 200.0 * x;
	elseif ((x <= -68000000000.0) || (~((x <= -1.75e-30)) && (x <= 7e-29)))
		tmp = y * -200.0;
	else
		tmp = 200.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -5.5e+51], N[(200.0 * x), $MachinePrecision], If[Or[LessEqual[x, -68000000000.0], And[N[Not[LessEqual[x, -1.75e-30]], $MachinePrecision], LessEqual[x, 7e-29]]], N[(y * -200.0), $MachinePrecision], N[(200.0 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.5e51 or -6.8e10 < x < -1.7500000000000001e-30 or 6.9999999999999995e-29 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 82.3%

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

   if -5.5e51 < x < -6.8e10 or -1.7500000000000001e-30 < x < 6.9999999999999995e-29

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 83.9%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+51}:\\ \;\;\;\;200 \cdot x\\ \mathbf{elif}\;x \leq -68000000000 \lor \neg \left(x \leq -1.75 \cdot 10^{-30}\right) \land x \leq 7 \cdot 10^{-29}:\\ \;\;\;\;y \cdot -200\\ \mathbf{else}:\\ \;\;\;\;200 \cdot x\\ \end{array} \]

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. Final simplification 100.0%

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

Alternative 4: 50.9% accurate, 1.7× 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. Taylor expanded in x around 0 48.4%

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

3. Final simplification 48.4%

   \[\leadsto y \cdot -200 \]

Reproduce

herbie shell --seed 2023230 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, C"
  :precision binary64
  (* 200.0 (- x y)))