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. Final simplification 100.0%

   \[\leadsto x + \frac{y}{500} \]
4. Add Preprocessing

Alternative 2: 75.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{y}{500} \leq -2 \cdot 10^{-44} \lor \neg \left(\frac{y}{500} \leq 10000\right):\\ \;\;\;\;\frac{y}{500}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= (/ y 500.0) -2e-44) (not (<= (/ y 500.0) 10000.0)))
   (/ y 500.0)
   x))

C

double code(double x, double y) {
	double tmp;
	if (((y / 500.0) <= -2e-44) || !((y / 500.0) <= 10000.0)) {
		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) <= (-2d-44)) .or. (.not. ((y / 500.0d0) <= 10000.0d0))) 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) <= -2e-44) || !((y / 500.0) <= 10000.0)) {
		tmp = y / 500.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if ((y / 500.0) <= -2e-44) or not ((y / 500.0) <= 10000.0):
		tmp = y / 500.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((Float64(y / 500.0) <= -2e-44) || !(Float64(y / 500.0) <= 10000.0))
		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) <= -2e-44) || ~(((y / 500.0) <= 10000.0)))
		tmp = y / 500.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[N[(y / 500.0), $MachinePrecision], -2e-44], N[Not[LessEqual[N[(y / 500.0), $MachinePrecision], 10000.0]], $MachinePrecision]], N[(y / 500.0), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (/.f64 y 500) < -1.99999999999999991e-44 or 1e4 < (/.f64 y 500)

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. distribute-frac-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. neg-mul-1 100.0%

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

      5. associate-/l* 99.6%

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

      6. associate-/r/ 99.8%

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

      7. cancel-sign-sub-inv 99.8%

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

      8. metadata-eval 99.8%

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

      9. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 80.1%

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

      1. *-commutative 80.1%

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

      2. metadata-eval 80.1%

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

      3. div-inv 80.3%

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

   7. Applied egg-rr 80.3%

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

   if -1.99999999999999991e-44 < (/.f64 y 500) < 1e4

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. distribute-frac-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. neg-mul-1 100.0%

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

      5. associate-/l* 99.5%

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

      6. associate-/r/ 99.9%

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

      7. cancel-sign-sub-inv 99.9%

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

      8. metadata-eval 99.9%

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

      9. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 77.1%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{500} \leq -2 \cdot 10^{-44} \lor \neg \left(\frac{y}{500} \leq 10000\right):\\ \;\;\;\;\frac{y}{500}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-41} \lor \neg \left(y \leq 4500000\right):\\ \;\;\;\;y \cdot 0.002\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1e-41) (not (<= y 4500000.0))) (* y 0.002) x))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1e-41) || !(y <= 4500000.0)) {
		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 <= (-1d-41)) .or. (.not. (y <= 4500000.0d0))) 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 <= -1e-41) || !(y <= 4500000.0)) {
		tmp = y * 0.002;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1e-41) or not (y <= 4500000.0):
		tmp = y * 0.002
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1e-41) || !(y <= 4500000.0))
		tmp = Float64(y * 0.002);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1e-41) || ~((y <= 4500000.0)))
		tmp = y * 0.002;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1e-41], N[Not[LessEqual[y, 4500000.0]], $MachinePrecision]], N[(y * 0.002), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.00000000000000001e-41 or 4.5e6 < y

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. distribute-frac-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. neg-mul-1 100.0%

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

      5. associate-/l* 99.6%

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

      6. associate-/r/ 99.8%

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

      7. cancel-sign-sub-inv 99.8%

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

      8. metadata-eval 99.8%

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

      9. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 80.1%

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

   if -1.00000000000000001e-41 < y < 4.5e6

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. distribute-frac-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. neg-mul-1 100.0%

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

      5. associate-/l* 99.5%

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

      6. associate-/r/ 99.9%

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

      7. cancel-sign-sub-inv 99.9%

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

      8. metadata-eval 99.9%

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

      9. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 77.1%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-41} \lor \neg \left(y \leq 4500000\right):\\ \;\;\;\;y \cdot 0.002\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
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. remove-double-neg 100.0%

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

   2. distribute-frac-neg 100.0%

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

   3. unsub-neg 100.0%

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

   4. neg-mul-1 100.0%

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

   5. associate-/l* 99.5%

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

   6. associate-/r/ 99.9%

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

   7. cancel-sign-sub-inv 99.9%

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

   8. metadata-eval 99.9%

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

   9. metadata-eval 99.9%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

   \[\leadsto x + y \cdot 0.002 \]
6. Add Preprocessing

Alternative 5: 50.4% 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. remove-double-neg 100.0%

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

   2. distribute-frac-neg 100.0%

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

   3. unsub-neg 100.0%

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

   4. neg-mul-1 100.0%

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

   5. associate-/l* 99.5%

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

   6. associate-/r/ 99.9%

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

   7. cancel-sign-sub-inv 99.9%

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

   8. metadata-eval 99.9%

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

   9. metadata-eval 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in x around inf 49.3%

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

6. Final simplification 49.3%

   \[\leadsto x \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024040 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, C"
  :precision binary64
  (+ x (/ y 500.0)))