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

Percentage Accurate: 99.9% → 100.0%

Time: 3.1s

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, 0.8× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. lift-*.f64 N/A

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

   2. lift--.f64 N/A

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

   3. sub-neg N/A

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

   4. distribute-rgt-in N/A

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

   5. +-commutative N/A

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

   6. distribute-lft-neg-out N/A

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

   7. distribute-rgt-neg-in N/A

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

   8. metadata-eval N/A

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

   9. metadata-eval N/A

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

   10. lower-fma.f64 N/A

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

   11. metadata-eval N/A

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

   12. lower-*.f64 100.0

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

4. Applied rewrites 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 75.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -400:\\ \;\;\;\;200 \cdot x\\ \mathbf{elif}\;x \leq 10^{-96}:\\ \;\;\;\;-200 \cdot y\\ \mathbf{else}:\\ \;\;\;\;200 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -400.0) (* 200.0 x) (if (<= x 1e-96) (* -200.0 y) (* 200.0 x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -400.0) {
		tmp = 200.0 * x;
	} else if (x <= 1e-96) {
		tmp = -200.0 * y;
	} 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 (x <= (-400.0d0)) then
        tmp = 200.0d0 * x
    else if (x <= 1d-96) then
        tmp = (-200.0d0) * y
    else
        tmp = 200.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -400.0) {
		tmp = 200.0 * x;
	} else if (x <= 1e-96) {
		tmp = -200.0 * y;
	} else {
		tmp = 200.0 * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -400.0:
		tmp = 200.0 * x
	elif x <= 1e-96:
		tmp = -200.0 * y
	else:
		tmp = 200.0 * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -400.0)
		tmp = Float64(200.0 * x);
	elseif (x <= 1e-96)
		tmp = Float64(-200.0 * y);
	else
		tmp = Float64(200.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -400.0)
		tmp = 200.0 * x;
	elseif (x <= 1e-96)
		tmp = -200.0 * y;
	else
		tmp = 200.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -400.0], N[(200.0 * x), $MachinePrecision], If[LessEqual[x, 1e-96], N[(-200.0 * y), $MachinePrecision], N[(200.0 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -400 or 9.9999999999999991e-97 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 80.9

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

   5. Applied rewrites 80.9%

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

   if -400 < x < 9.9999999999999991e-97

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 83.2

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

   5. Applied rewrites 83.2%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -400:\\ \;\;\;\;200 \cdot x\\ \mathbf{elif}\;x \leq 10^{-96}:\\ \;\;\;\;-200 \cdot y\\ \mathbf{else}:\\ \;\;\;\;200 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 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. Step-by-step derivation

   1. lift-*.f64 N/A

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

   2. lift--.f64 N/A

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

   3. sub-neg N/A

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

   4. distribute-rgt-in N/A

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

   5. *-commutative N/A

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

   6. lower-fma.f64 N/A

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

   7. neg-mul-1 N/A

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

   8. associate-*r* N/A

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

   9. lower-*.f64 N/A

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

   10. metadata-eval 100.0

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

4. Applied rewrites 100.0%

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

Alternative 4: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 5: 51.2% accurate, 1.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in y around 0

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

   1. *-commutative N/A

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

   2. lower-*.f64 56.0

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

5. Applied rewrites 56.0%

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

6. Final simplification 56.0%

   \[\leadsto 200 \cdot x \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024255 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, C"
  :precision binary64
  (* 200.0 (- x y)))