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

Percentage Accurate: 99.9% → 100.0%

Time: 4.7s

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

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

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 99.9%

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

3. Taylor expanded in y around inf 87.0%

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

   1. clear-num 86.9%

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

   2. un-div-inv 87.0%

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

5. Applied egg-rr 87.0%

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

6. Taylor expanded in y around 0 100.0%

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

   1. +-commutative 100.0%

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

   2. fma-define 100.0%

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

   3. *-commutative 100.0%

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

8. Simplified 100.0%

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

Alternative 2: 71.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3300000 \lor \neg \left(y \leq 3 \cdot 10^{-143}\right):\\ \;\;\;\;y \cdot -200\\ \mathbf{else}:\\ \;\;\;\;200 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -3300000.0) (not (<= y 3e-143))) (* y -200.0) (* 200.0 x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -3300000.0) || !(y <= 3e-143)) {
		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 ((y <= (-3300000.0d0)) .or. (.not. (y <= 3d-143))) 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 ((y <= -3300000.0) || !(y <= 3e-143)) {
		tmp = y * -200.0;
	} else {
		tmp = 200.0 * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -3300000.0) or not (y <= 3e-143):
		tmp = y * -200.0
	else:
		tmp = 200.0 * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -3300000.0) || !(y <= 3e-143))
		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 ((y <= -3300000.0) || ~((y <= 3e-143)))
		tmp = y * -200.0;
	else
		tmp = 200.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -3300000.0], N[Not[LessEqual[y, 3e-143]], $MachinePrecision]], N[(y * -200.0), $MachinePrecision], N[(200.0 * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.3e6 or 2.99999999999999985e-143 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 74.5%

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

   if -3.3e6 < y < 2.99999999999999985e-143

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 87.7%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3300000 \lor \neg \left(y \leq 3 \cdot 10^{-143}\right):\\ \;\;\;\;y \cdot -200\\ \mathbf{else}:\\ \;\;\;\;200 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 100.0% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   \[\leadsto y \cdot -200 + 200 \cdot x \]
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 99.9%

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

Alternative 5: 50.5% 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 99.9%

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

3. Taylor expanded in x around 0 51.0%

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

4. Final simplification 51.0%

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

Reproduce

herbie shell --seed 2024116 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, C"
  :precision binary64
  (* 200.0 (- x y)))