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

Percentage Accurate: 100.0% → 100.0%

Time: 2.6s

Alternatives: 5

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ x + \frac{y}{500} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (+ x (/ y 500.0)))

C

double code(double x, double y) {
	return x + (y / 500.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x + (y / 500.0d0)
end function

Java

public static double code(double x, double y) {
	return x + (y / 500.0);
}

Python

def code(x, y):
	return x + (y / 500.0)

Julia

function code(x, y)
	return Float64(x + Float64(y / 500.0))
end

MATLAB

function tmp = code(x, y)
	tmp = x + (y / 500.0);
end

Wolfram

code[x_, y_] := N[(x + N[(y / 500.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{y}{500} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (+ x (/ y 500.0)))

C

double code(double x, double y) {
	return x + (y / 500.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x + (y / 500.0d0)
end function

Java

public static double code(double x, double y) {
	return x + (y / 500.0);
}

Python

def code(x, y):
	return x + (y / 500.0)

Julia

function code(x, y)
	return Float64(x + Float64(y / 500.0))
end

MATLAB

function tmp = code(x, y)
	tmp = x + (y / 500.0);
end

Wolfram

code[x_, y_] := N[(x + N[(y / 500.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{y}{500} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (+ x (/ y 500.0)))

C

double code(double x, double y) {
	return x + (y / 500.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x + (y / 500.0d0)
end function

Java

public static double code(double x, double y) {
	return x + (y / 500.0);
}

Python

def code(x, y):
	return x + (y / 500.0)

Julia

function code(x, y)
	return Float64(x + Float64(y / 500.0))
end

MATLAB

function tmp = code(x, y)
	tmp = x + (y / 500.0);
end

Wolfram

code[x_, y_] := N[(x + N[(y / 500.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[x + \frac{y}{500} \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 74.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{y}{500} \leq -1 \cdot 10^{+79} \lor \neg \left(\frac{y}{500} \leq -5 \cdot 10^{-48}\right) \land \left(\frac{y}{500} \leq -5 \cdot 10^{-80} \lor \neg \left(\frac{y}{500} \leq -5 \cdot 10^{-126} \lor \neg \left(\frac{y}{500} \leq -1 \cdot 10^{-145}\right) \land \frac{y}{500} \leq 200000\right)\right):\\ \;\;\;\;\frac{y}{500}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= (/ y 500.0) -1e+79)
         (and (not (<= (/ y 500.0) -5e-48))
              (or (<= (/ y 500.0) -5e-80)
                  (not
                   (or (<= (/ y 500.0) -5e-126)
                       (and (not (<= (/ y 500.0) -1e-145))
                            (<= (/ y 500.0) 200000.0)))))))
   (/ y 500.0)
   x))

C

double code(double x, double y) {
	double tmp;
	if (((y / 500.0) <= -1e+79) || (!((y / 500.0) <= -5e-48) && (((y / 500.0) <= -5e-80) || !(((y / 500.0) <= -5e-126) || (!((y / 500.0) <= -1e-145) && ((y / 500.0) <= 200000.0)))))) {
		tmp = y / 500.0;
	} else {
		tmp = 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 / 500.0d0) <= (-1d+79)) .or. (.not. ((y / 500.0d0) <= (-5d-48))) .and. ((y / 500.0d0) <= (-5d-80)) .or. (.not. ((y / 500.0d0) <= (-5d-126)) .or. (.not. ((y / 500.0d0) <= (-1d-145))) .and. ((y / 500.0d0) <= 200000.0d0))) then
        tmp = y / 500.0d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (((y / 500.0) <= -1e+79) || (!((y / 500.0) <= -5e-48) && (((y / 500.0) <= -5e-80) || !(((y / 500.0) <= -5e-126) || (!((y / 500.0) <= -1e-145) && ((y / 500.0) <= 200000.0)))))) {
		tmp = y / 500.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if ((y / 500.0) <= -1e+79) or (not ((y / 500.0) <= -5e-48) and (((y / 500.0) <= -5e-80) or not (((y / 500.0) <= -5e-126) or (not ((y / 500.0) <= -1e-145) and ((y / 500.0) <= 200000.0))))):
		tmp = y / 500.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((Float64(y / 500.0) <= -1e+79) || (!(Float64(y / 500.0) <= -5e-48) && ((Float64(y / 500.0) <= -5e-80) || !((Float64(y / 500.0) <= -5e-126) || (!(Float64(y / 500.0) <= -1e-145) && (Float64(y / 500.0) <= 200000.0))))))
		tmp = Float64(y / 500.0);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (((y / 500.0) <= -1e+79) || (~(((y / 500.0) <= -5e-48)) && (((y / 500.0) <= -5e-80) || ~((((y / 500.0) <= -5e-126) || (~(((y / 500.0) <= -1e-145)) && ((y / 500.0) <= 200000.0)))))))
		tmp = y / 500.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[N[(y / 500.0), $MachinePrecision], -1e+79], And[N[Not[LessEqual[N[(y / 500.0), $MachinePrecision], -5e-48]], $MachinePrecision], Or[LessEqual[N[(y / 500.0), $MachinePrecision], -5e-80], N[Not[Or[LessEqual[N[(y / 500.0), $MachinePrecision], -5e-126], And[N[Not[LessEqual[N[(y / 500.0), $MachinePrecision], -1e-145]], $MachinePrecision], LessEqual[N[(y / 500.0), $MachinePrecision], 200000.0]]]], $MachinePrecision]]]], N[(y / 500.0), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (/.f64 y #s(literal 500 binary64)) < -9.99999999999999967e78 or -4.9999999999999999e-48 < (/.f64 y #s(literal 500 binary64)) < -5e-80 or -5.00000000000000006e-126 < (/.f64 y #s(literal 500 binary64)) < -9.99999999999999915e-146 or 2e5 < (/.f64 y #s(literal 500 binary64))

   1. Initial program 100.0%

      \[x + \frac{y}{500} \]
   2. Step-by-step derivation

      1. *-rgt-identity 100.0%

         \[\leadsto x + \color{blue}{\frac{y}{500} \cdot 1} \]

      2. metadata-eval 100.0%

         \[\leadsto x + \frac{y}{500} \cdot \color{blue}{\left(--1\right)} \]

      3. associate-*l/ 100.0%

         \[\leadsto x + \color{blue}{\frac{y \cdot \left(--1\right)}{500}} \]

      4. associate-/l* 99.8%

         \[\leadsto x + \color{blue}{y \cdot \frac{--1}{500}} \]

      5. metadata-eval 99.8%

         \[\leadsto x + y \cdot \frac{\color{blue}{1}}{500} \]

      6. metadata-eval 99.8%

         \[\leadsto x + y \cdot \color{blue}{0.002} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + y \cdot 0.002} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 99.7%

      \[\leadsto \color{blue}{y \cdot \left(0.002 + \frac{x}{y}\right)} \]

   6. Taylor expanded in x around 0 82.2%

      \[\leadsto y \cdot \color{blue}{0.002} \]
   7. Step-by-step derivation

      1. metadata-eval 82.2%

         \[\leadsto y \cdot \color{blue}{\frac{1}{500}} \]

      2. div-inv 82.4%

         \[\leadsto \color{blue}{\frac{y}{500}} \]

   8. Applied egg-rr 82.4%

      \[\leadsto \color{blue}{\frac{y}{500}} \]

   if -9.99999999999999967e78 < (/.f64 y #s(literal 500 binary64)) < -4.9999999999999999e-48 or -5e-80 < (/.f64 y #s(literal 500 binary64)) < -5.00000000000000006e-126 or -9.99999999999999915e-146 < (/.f64 y #s(literal 500 binary64)) < 2e5

   1. Initial program 100.0%

      \[x + \frac{y}{500} \]
   2. Step-by-step derivation

      1. *-rgt-identity 100.0%

         \[\leadsto x + \color{blue}{\frac{y}{500} \cdot 1} \]

      2. metadata-eval 100.0%

         \[\leadsto x + \frac{y}{500} \cdot \color{blue}{\left(--1\right)} \]

      3. associate-*l/ 100.0%

         \[\leadsto x + \color{blue}{\frac{y \cdot \left(--1\right)}{500}} \]

      4. associate-/l* 100.0%

         \[\leadsto x + \color{blue}{y \cdot \frac{--1}{500}} \]

      5. metadata-eval 100.0%

         \[\leadsto x + y \cdot \frac{\color{blue}{1}}{500} \]

      6. metadata-eval 100.0%

         \[\leadsto x + y \cdot \color{blue}{0.002} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x + y \cdot 0.002} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 82.6%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{500} \leq -1 \cdot 10^{+79} \lor \neg \left(\frac{y}{500} \leq -5 \cdot 10^{-48}\right) \land \left(\frac{y}{500} \leq -5 \cdot 10^{-80} \lor \neg \left(\frac{y}{500} \leq -5 \cdot 10^{-126} \lor \neg \left(\frac{y}{500} \leq -1 \cdot 10^{-145}\right) \land \frac{y}{500} \leq 200000\right)\right):\\ \;\;\;\;\frac{y}{500}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+80} \lor \neg \left(y \leq -7.2 \cdot 10^{-53}\right) \land \left(y \leq -2.8 \cdot 10^{-77} \lor \neg \left(y \leq -1 \cdot 10^{-125} \lor \neg \left(y \leq -4.1 \cdot 10^{-144}\right) \land y \leq 85000000\right)\right):\\ \;\;\;\;y \cdot 0.002\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -3.3e+80)
         (and (not (<= y -7.2e-53))
              (or (<= y -2.8e-77)
                  (not
                   (or (<= y -1e-125)
                       (and (not (<= y -4.1e-144)) (<= y 85000000.0)))))))
   (* y 0.002)
   x))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -3.3e+80) || (!(y <= -7.2e-53) && ((y <= -2.8e-77) || !((y <= -1e-125) || (!(y <= -4.1e-144) && (y <= 85000000.0)))))) {
		tmp = y * 0.002;
	} else {
		tmp = 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 <= (-3.3d+80)) .or. (.not. (y <= (-7.2d-53))) .and. (y <= (-2.8d-77)) .or. (.not. (y <= (-1d-125)) .or. (.not. (y <= (-4.1d-144))) .and. (y <= 85000000.0d0))) then
        tmp = y * 0.002d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -3.3e+80) || (!(y <= -7.2e-53) && ((y <= -2.8e-77) || !((y <= -1e-125) || (!(y <= -4.1e-144) && (y <= 85000000.0)))))) {
		tmp = y * 0.002;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -3.3e+80) or (not (y <= -7.2e-53) and ((y <= -2.8e-77) or not ((y <= -1e-125) or (not (y <= -4.1e-144) and (y <= 85000000.0))))):
		tmp = y * 0.002
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -3.3e+80) || (!(y <= -7.2e-53) && ((y <= -2.8e-77) || !((y <= -1e-125) || (!(y <= -4.1e-144) && (y <= 85000000.0))))))
		tmp = Float64(y * 0.002);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -3.3e+80) || (~((y <= -7.2e-53)) && ((y <= -2.8e-77) || ~(((y <= -1e-125) || (~((y <= -4.1e-144)) && (y <= 85000000.0)))))))
		tmp = y * 0.002;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -3.3e+80], And[N[Not[LessEqual[y, -7.2e-53]], $MachinePrecision], Or[LessEqual[y, -2.8e-77], N[Not[Or[LessEqual[y, -1e-125], And[N[Not[LessEqual[y, -4.1e-144]], $MachinePrecision], LessEqual[y, 85000000.0]]]], $MachinePrecision]]]], N[(y * 0.002), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -3.29999999999999991e80 or -7.1999999999999998e-53 < y < -2.7999999999999999e-77 or -1.00000000000000001e-125 < y < -4.1e-144 or 8.5e7 < y

   1. Initial program 100.0%

      \[x + \frac{y}{500} \]
   2. Step-by-step derivation

      1. *-rgt-identity 100.0%

         \[\leadsto x + \color{blue}{\frac{y}{500} \cdot 1} \]

      2. metadata-eval 100.0%

         \[\leadsto x + \frac{y}{500} \cdot \color{blue}{\left(--1\right)} \]

      3. associate-*l/ 100.0%

         \[\leadsto x + \color{blue}{\frac{y \cdot \left(--1\right)}{500}} \]

      4. associate-/l* 99.8%

         \[\leadsto x + \color{blue}{y \cdot \frac{--1}{500}} \]

      5. metadata-eval 99.8%

         \[\leadsto x + y \cdot \frac{\color{blue}{1}}{500} \]

      6. metadata-eval 99.8%

         \[\leadsto x + y \cdot \color{blue}{0.002} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + y \cdot 0.002} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 99.7%

      \[\leadsto \color{blue}{y \cdot \left(0.002 + \frac{x}{y}\right)} \]

   6. Taylor expanded in x around 0 82.2%

      \[\leadsto y \cdot \color{blue}{0.002} \]

   if -3.29999999999999991e80 < y < -7.1999999999999998e-53 or -2.7999999999999999e-77 < y < -1.00000000000000001e-125 or -4.1e-144 < y < 8.5e7

   1. Initial program 100.0%

      \[x + \frac{y}{500} \]
   2. Step-by-step derivation

      1. *-rgt-identity 100.0%

         \[\leadsto x + \color{blue}{\frac{y}{500} \cdot 1} \]

      2. metadata-eval 100.0%

         \[\leadsto x + \frac{y}{500} \cdot \color{blue}{\left(--1\right)} \]

      3. associate-*l/ 100.0%

         \[\leadsto x + \color{blue}{\frac{y \cdot \left(--1\right)}{500}} \]

      4. associate-/l* 100.0%

         \[\leadsto x + \color{blue}{y \cdot \frac{--1}{500}} \]

      5. metadata-eval 100.0%

         \[\leadsto x + y \cdot \frac{\color{blue}{1}}{500} \]

      6. metadata-eval 100.0%

         \[\leadsto x + y \cdot \color{blue}{0.002} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x + y \cdot 0.002} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 82.6%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+80} \lor \neg \left(y \leq -7.2 \cdot 10^{-53}\right) \land \left(y \leq -2.8 \cdot 10^{-77} \lor \neg \left(y \leq -1 \cdot 10^{-125} \lor \neg \left(y \leq -4.1 \cdot 10^{-144}\right) \land y \leq 85000000\right)\right):\\ \;\;\;\;y \cdot 0.002\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + y \cdot 0.002 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (+ x (* y 0.002)))

C

double code(double x, double y) {
	return x + (y * 0.002);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x + (y * 0.002d0)
end function

Java

public static double code(double x, double y) {
	return x + (y * 0.002);
}

Python

def code(x, y):
	return x + (y * 0.002)

Julia

function code(x, y)
	return Float64(x + Float64(y * 0.002))
end

MATLAB

function tmp = code(x, y)
	tmp = x + (y * 0.002);
end

Wolfram

code[x_, y_] := N[(x + N[(y * 0.002), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[x + \frac{y}{500} \]
2. Step-by-step derivation

   1. *-rgt-identity 100.0%

      \[\leadsto x + \color{blue}{\frac{y}{500} \cdot 1} \]

   2. metadata-eval 100.0%

      \[\leadsto x + \frac{y}{500} \cdot \color{blue}{\left(--1\right)} \]

   3. associate-*l/ 100.0%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(--1\right)}{500}} \]

   4. associate-/l* 99.9%

      \[\leadsto x + \color{blue}{y \cdot \frac{--1}{500}} \]

   5. metadata-eval 99.9%

      \[\leadsto x + y \cdot \frac{\color{blue}{1}}{500} \]

   6. metadata-eval 99.9%

      \[\leadsto x + y \cdot \color{blue}{0.002} \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{x + y \cdot 0.002} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 5: 49.9% accurate, 5.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 x)

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return x

Julia

function code(x, y)
	return x
end

MATLAB

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

Wolfram

code[x_, y_] := x

Derivation

1. Initial program 100.0%

   \[x + \frac{y}{500} \]
2. Step-by-step derivation

   1. *-rgt-identity 100.0%

      \[\leadsto x + \color{blue}{\frac{y}{500} \cdot 1} \]

   2. metadata-eval 100.0%

      \[\leadsto x + \frac{y}{500} \cdot \color{blue}{\left(--1\right)} \]

   3. associate-*l/ 100.0%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(--1\right)}{500}} \]

   4. associate-/l* 99.9%

      \[\leadsto x + \color{blue}{y \cdot \frac{--1}{500}} \]

   5. metadata-eval 99.9%

      \[\leadsto x + y \cdot \frac{\color{blue}{1}}{500} \]

   6. metadata-eval 99.9%

      \[\leadsto x + y \cdot \color{blue}{0.002} \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{x + y \cdot 0.002} \]
4. Add Preprocessing

5. Taylor expanded in x around inf 48.4%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024091 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, C"
  :precision binary64
  (+ x (/ y 500.0)))