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

Percentage Accurate: 99.9% → 100.0%

Time: 4.8s

Alternatives: 6

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 99.9%

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

2. Taylor expanded in x around 0 99.9%

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

   1. *-commutative 99.9%

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

   2. fma-def 100.0%

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

4. Applied egg-rr 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 100.0% accurate, 0.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in x around 0 99.9%

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

   1. +-commutative 99.9%

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

   2. fma-def 99.9%

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

4. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 3: 70.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+19} \lor \neg \left(y \leq -7.1 \cdot 10^{-47}\right) \land \left(y \leq -2.8 \cdot 10^{-141} \lor \neg \left(y \leq 5.2 \cdot 10^{-111}\right) \land \left(y \leq 4.8 \cdot 10^{-36} \lor \neg \left(y \leq 9.4 \cdot 10^{+58}\right)\right)\right):\\ \;\;\;\;-200 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot 200\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -5.8e+19)
         (and (not (<= y -7.1e-47))
              (or (<= y -2.8e-141)
                  (and (not (<= y 5.2e-111))
                       (or (<= y 4.8e-36) (not (<= y 9.4e+58)))))))
   (* -200.0 y)
   (* x 200.0)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -5.8e+19) || (!(y <= -7.1e-47) && ((y <= -2.8e-141) || (!(y <= 5.2e-111) && ((y <= 4.8e-36) || !(y <= 9.4e+58)))))) {
		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 <= (-5.8d+19)) .or. (.not. (y <= (-7.1d-47))) .and. (y <= (-2.8d-141)) .or. (.not. (y <= 5.2d-111)) .and. (y <= 4.8d-36) .or. (.not. (y <= 9.4d+58))) 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 <= -5.8e+19) || (!(y <= -7.1e-47) && ((y <= -2.8e-141) || (!(y <= 5.2e-111) && ((y <= 4.8e-36) || !(y <= 9.4e+58)))))) {
		tmp = -200.0 * y;
	} else {
		tmp = x * 200.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -5.8e+19) or (not (y <= -7.1e-47) and ((y <= -2.8e-141) or (not (y <= 5.2e-111) and ((y <= 4.8e-36) or not (y <= 9.4e+58))))):
		tmp = -200.0 * y
	else:
		tmp = x * 200.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -5.8e+19) || (!(y <= -7.1e-47) && ((y <= -2.8e-141) || (!(y <= 5.2e-111) && ((y <= 4.8e-36) || !(y <= 9.4e+58))))))
		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 <= -5.8e+19) || (~((y <= -7.1e-47)) && ((y <= -2.8e-141) || (~((y <= 5.2e-111)) && ((y <= 4.8e-36) || ~((y <= 9.4e+58)))))))
		tmp = -200.0 * y;
	else
		tmp = x * 200.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -5.8e+19], And[N[Not[LessEqual[y, -7.1e-47]], $MachinePrecision], Or[LessEqual[y, -2.8e-141], And[N[Not[LessEqual[y, 5.2e-111]], $MachinePrecision], Or[LessEqual[y, 4.8e-36], N[Not[LessEqual[y, 9.4e+58]], $MachinePrecision]]]]]], N[(-200.0 * y), $MachinePrecision], N[(x * 200.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.8e19 or -7.1000000000000002e-47 < y < -2.80000000000000012e-141 or 5.19999999999999965e-111 < y < 4.8e-36 or 9.39999999999999944e58 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 76.9%

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

   if -5.8e19 < y < -7.1000000000000002e-47 or -2.80000000000000012e-141 < y < 5.19999999999999965e-111 or 4.8e-36 < y < 9.39999999999999944e58

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 86.6%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+19} \lor \neg \left(y \leq -7.1 \cdot 10^{-47}\right) \land \left(y \leq -2.8 \cdot 10^{-141} \lor \neg \left(y \leq 5.2 \cdot 10^{-111}\right) \land \left(y \leq 4.8 \cdot 10^{-36} \lor \neg \left(y \leq 9.4 \cdot 10^{+58}\right)\right)\right):\\ \;\;\;\;-200 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot 200\\ \end{array} \]

Alternative 4: 99.9% 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 99.9%

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

2. Taylor expanded in x around 0 99.9%

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

3. Final simplification 99.9%

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

Alternative 5: 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. Final simplification 99.9%

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

Alternative 6: 50.2% 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 99.9%

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

2. Taylor expanded in x around 0 49.6%

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

3. Final simplification 49.6%

   \[\leadsto -200 \cdot y \]

Reproduce

herbie shell --seed 2023173 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, C"
  :precision binary64
  (* 200.0 (- x y)))