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

Percentage Accurate: 99.9% → 100.0%

Time: 3.1s

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, 0.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in x around 0 100.0%

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

   1. *-commutative 100.0%

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

   2. fma-def 100.0%

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

4. Applied egg-rr 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 100.0% accurate, 0.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in x around 0 100.0%

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

   1. +-commutative 100.0%

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

   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. Final simplification 100.0%

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

Alternative 3: 73.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -34 \lor \neg \left(x \leq 4.6 \cdot 10^{+26}\right) \land \left(x \leq 1.7 \cdot 10^{+78} \lor \neg \left(x \leq 1.76 \cdot 10^{+108}\right)\right):\\ \;\;\;\;x \cdot 200\\ \mathbf{else}:\\ \;\;\;\;-200 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -34.0)
         (and (not (<= x 4.6e+26)) (or (<= x 1.7e+78) (not (<= x 1.76e+108)))))
   (* x 200.0)
   (* -200.0 y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -34.0) || (!(x <= 4.6e+26) && ((x <= 1.7e+78) || !(x <= 1.76e+108)))) {
		tmp = x * 200.0;
	} else {
		tmp = -200.0 * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-34.0d0)) .or. (.not. (x <= 4.6d+26)) .and. (x <= 1.7d+78) .or. (.not. (x <= 1.76d+108))) then
        tmp = x * 200.0d0
    else
        tmp = (-200.0d0) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -34.0) || (!(x <= 4.6e+26) && ((x <= 1.7e+78) || !(x <= 1.76e+108)))) {
		tmp = x * 200.0;
	} else {
		tmp = -200.0 * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -34.0) or (not (x <= 4.6e+26) and ((x <= 1.7e+78) or not (x <= 1.76e+108))):
		tmp = x * 200.0
	else:
		tmp = -200.0 * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -34.0) || (!(x <= 4.6e+26) && ((x <= 1.7e+78) || !(x <= 1.76e+108))))
		tmp = Float64(x * 200.0);
	else
		tmp = Float64(-200.0 * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -34.0) || (~((x <= 4.6e+26)) && ((x <= 1.7e+78) || ~((x <= 1.76e+108)))))
		tmp = x * 200.0;
	else
		tmp = -200.0 * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -34.0], And[N[Not[LessEqual[x, 4.6e+26]], $MachinePrecision], Or[LessEqual[x, 1.7e+78], N[Not[LessEqual[x, 1.76e+108]], $MachinePrecision]]]], N[(x * 200.0), $MachinePrecision], N[(-200.0 * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -34 or 4.6000000000000001e26 < x < 1.70000000000000004e78 or 1.76e108 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 83.7%

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

   if -34 < x < 4.6000000000000001e26 or 1.70000000000000004e78 < x < 1.76e108

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 77.3%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -34 \lor \neg \left(x \leq 4.6 \cdot 10^{+26}\right) \land \left(x \leq 1.7 \cdot 10^{+78} \lor \neg \left(x \leq 1.76 \cdot 10^{+108}\right)\right):\\ \;\;\;\;x \cdot 200\\ \mathbf{else}:\\ \;\;\;\;-200 \cdot y\\ \end{array} \]

Alternative 4: 99.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ -200 \cdot y + x \cdot 200 \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((-200.0d0) * y) + (x * 200.0d0)
end function

Java

public static double code(double x, double y) {
	return (-200.0 * y) + (x * 200.0);
}

Python

def code(x, y):
	return (-200.0 * y) + (x * 200.0)

Julia

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

MATLAB

function tmp = code(x, y)
	tmp = (-200.0 * y) + (x * 200.0);
end

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in x around 0 100.0%

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

3. Final simplification 100.0%

   \[\leadsto -200 \cdot y + x \cdot 200 \]

Alternative 5: 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. Final simplification 99.9%

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

Alternative 6: 51.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ -200 \cdot y \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (-200.0d0) * y
end function

Java

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

Python

def code(x, y):
	return -200.0 * y

Julia

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

MATLAB

function tmp = code(x, y)
	tmp = -200.0 * y;
end

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in x around 0 50.0%

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

3. Final simplification 50.0%

   \[\leadsto -200 \cdot y \]

Reproduce

herbie shell --seed 2023195 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, C"
  :precision binary64
  (* 200.0 (- x y)))