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

Percentage Accurate: 100.0% → 100.0%

Time: 5.2s

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, 0.8× 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. Taylor expanded in x around 0

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

   1. lower-*.f64 49.0

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

5. Applied rewrites 49.0%

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

6. Taylor expanded in x around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 N/A

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

   3. +-commutative N/A

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

   4. *-commutative N/A

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

   5. lower-fma.f64 N/A

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

   6. lower-/.f64 87.7

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

8. Applied rewrites 87.7%

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

10. Applied rewrites 99.1%

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

12. Applied rewrites 100.0%

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

Alternative 2: 73.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{-19} \lor \neg \left(x \leq 1.55 \cdot 10^{-72}\right):\\ \;\;\;\;200 \cdot x\\ \mathbf{else}:\\ \;\;\;\;-200 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -6.8e-19) (not (<= x 1.55e-72))) (* 200.0 x) (* -200.0 y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -6.8e-19) || !(x <= 1.55e-72)) {
		tmp = 200.0 * x;
	} 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 <= (-6.8d-19)) .or. (.not. (x <= 1.55d-72))) then
        tmp = 200.0d0 * x
    else
        tmp = (-200.0d0) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -6.8e-19) || !(x <= 1.55e-72)) {
		tmp = 200.0 * x;
	} else {
		tmp = -200.0 * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -6.8e-19) or not (x <= 1.55e-72):
		tmp = 200.0 * x
	else:
		tmp = -200.0 * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -6.8e-19) || !(x <= 1.55e-72))
		tmp = Float64(200.0 * x);
	else
		tmp = Float64(-200.0 * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -6.8e-19) || ~((x <= 1.55e-72)))
		tmp = 200.0 * x;
	else
		tmp = -200.0 * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -6.8e-19], N[Not[LessEqual[x, 1.55e-72]], $MachinePrecision]], N[(200.0 * x), $MachinePrecision], N[(-200.0 * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.8000000000000004e-19 or 1.5499999999999999e-72 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 80.3

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

   5. Applied rewrites 80.3%

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

   if -6.8000000000000004e-19 < x < 1.5499999999999999e-72

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 84.2

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

   5. Applied rewrites 84.2%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{-19} \lor \neg \left(x \leq 1.55 \cdot 10^{-72}\right):\\ \;\;\;\;200 \cdot x\\ \mathbf{else}:\\ \;\;\;\;-200 \cdot y\\ \end{array} \]
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 100.0%

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

Alternative 4: 50.8% accurate, 1.5× 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

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

   1. lower-*.f64 49.0

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

5. Applied rewrites 49.0%

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

Reproduce

herbie shell --seed 2024340 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, C"
  :precision binary64
  (* 200.0 (- x y)))