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

Percentage Accurate: 100.0% → 100.0%

Time: 5.0s

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: 100.0% 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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. sub-neg 99.9%

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

   2. distribute-rgt-in 99.9%

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

   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. Step-by-step derivation

   1. distribute-lft-neg-out 100.0%

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

   2. distribute-rgt-neg-in 100.0%

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

   3. metadata-eval 100.0%

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

   4. *-commutative 100.0%

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

   5. fma-define 99.9%

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

   6. *-commutative 99.9%

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

   7. +-commutative 99.9%

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

   8. *-commutative 99.9%

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

   9. fma-define 100.0%

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

   10. *-commutative 100.0%

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

6. Applied egg-rr 100.0%

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

   1. fma-undefine 99.9%

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

   2. +-commutative 99.9%

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

   3. fma-define 100.0%

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

8. Applied egg-rr 100.0%

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

Alternative 2: 75.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+15} \lor \neg \left(y \leq 1.55 \cdot 10^{+16}\right):\\ \;\;\;\;y \cdot -200\\ \mathbf{else}:\\ \;\;\;\;x \cdot 200\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.2e+15) (not (<= y 1.55e+16))) (* y -200.0) (* x 200.0)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.2e+15) || !(y <= 1.55e+16)) {
		tmp = y * -200.0;
	} 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 <= (-1.2d+15)) .or. (.not. (y <= 1.55d+16))) then
        tmp = y * (-200.0d0)
    else
        tmp = x * 200.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.2e+15) || !(y <= 1.55e+16)) {
		tmp = y * -200.0;
	} else {
		tmp = x * 200.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.2e+15) or not (y <= 1.55e+16):
		tmp = y * -200.0
	else:
		tmp = x * 200.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.2e+15) || !(y <= 1.55e+16))
		tmp = Float64(y * -200.0);
	else
		tmp = Float64(x * 200.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.2e+15) || ~((y <= 1.55e+16)))
		tmp = y * -200.0;
	else
		tmp = x * 200.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.2e+15], N[Not[LessEqual[y, 1.55e+16]], $MachinePrecision]], N[(y * -200.0), $MachinePrecision], N[(x * 200.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.2e15 or 1.55e16 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 83.5%

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

   if -1.2e15 < y < 1.55e16

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 83.1%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+15} \lor \neg \left(y \leq 1.55 \cdot 10^{+16}\right):\\ \;\;\;\;y \cdot -200\\ \mathbf{else}:\\ \;\;\;\;x \cdot 200\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 100.0% 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 4: 50.1% 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 48.6%

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

4. Final simplification 48.6%

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

Reproduce

herbie shell --seed 2024095 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, C"
  :precision binary64
  (* 200.0 (- x y)))