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

Percentage Accurate: 99.9% → 100.0%

Time: 3.8s

Alternatives: 5

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 100.0%

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

   1. sub-neg 100.0%

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

   2. distribute-rgt-in 100.0%

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

   3. fma-define 100.0%

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

4. Applied egg-rr 100.0%

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

5. Taylor expanded in x around 0 100.0%

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

   1. metadata-eval 100.0%

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

   2. distribute-lft-neg-in 100.0%

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

   3. +-commutative 100.0%

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

   4. *-commutative 100.0%

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

   5. fma-define 100.0%

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

   6. distribute-lft-neg-in 100.0%

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

   7. metadata-eval 100.0%

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

7. Simplified 100.0%

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

Alternative 2: 73.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+78} \lor \neg \left(y \leq 3.2 \cdot 10^{+86}\right):\\ \;\;\;\;-200 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot 200\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -6e+78) (not (<= y 3.2e+86))) (* -200.0 y) (* x 200.0)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -6e+78) || !(y <= 3.2e+86)) {
		tmp = -200.0 * y;
	} 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 ((y <= (-6d+78)) .or. (.not. (y <= 3.2d+86))) then
        tmp = (-200.0d0) * y
    else
        tmp = x * 200.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -6e+78) || !(y <= 3.2e+86)) {
		tmp = -200.0 * y;
	} else {
		tmp = x * 200.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -6e+78) or not (y <= 3.2e+86):
		tmp = -200.0 * y
	else:
		tmp = x * 200.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -6e+78) || !(y <= 3.2e+86))
		tmp = Float64(-200.0 * y);
	else
		tmp = Float64(x * 200.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -6e+78) || ~((y <= 3.2e+86)))
		tmp = -200.0 * y;
	else
		tmp = x * 200.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -6e+78], N[Not[LessEqual[y, 3.2e+86]], $MachinePrecision]], N[(-200.0 * y), $MachinePrecision], N[(x * 200.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.99999999999999964e78 or 3.2e86 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 89.0%

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

   if -5.99999999999999964e78 < y < 3.2e86

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 72.8%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+78} \lor \neg \left(y \leq 3.2 \cdot 10^{+86}\right):\\ \;\;\;\;-200 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot 200\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 100.0% 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 100.0%

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

3. Taylor expanded in x around 0 100.0%

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

4. Final simplification 100.0%

   \[\leadsto -200 \cdot y + x \cdot 200 \]
5. Add Preprocessing

Alternative 4: 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 5: 50.4% 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 100.0%

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

3. Taylor expanded in x around 0 52.4%

   \[\leadsto \color{blue}{-200 \cdot y} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024144 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, C"
  :precision binary64
  (* 200.0 (- x y)))