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

Percentage Accurate: 100.0% → 100.0%

Time: 2.5s

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: 73.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{y}{500} \leq -2 \cdot 10^{-83} \lor \neg \left(\frac{y}{500} \leq 2 \cdot 10^{-65}\right):\\ \;\;\;\;\frac{y}{500}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= (/ y 500.0) -2e-83) (not (<= (/ y 500.0) 2e-65))) (/ y 500.0) x))

C

double code(double x, double y) {
	double tmp;
	if (((y / 500.0) <= -2e-83) || !((y / 500.0) <= 2e-65)) {
		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-83)) .or. (.not. ((y / 500.0d0) <= 2d-65))) 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-83) || !((y / 500.0) <= 2e-65)) {
		tmp = y / 500.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if ((y / 500.0) <= -2e-83) or not ((y / 500.0) <= 2e-65):
		tmp = y / 500.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((Float64(y / 500.0) <= -2e-83) || !(Float64(y / 500.0) <= 2e-65))
		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-83) || ~(((y / 500.0) <= 2e-65)))
		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-83], N[Not[LessEqual[N[(y / 500.0), $MachinePrecision], 2e-65]], $MachinePrecision]], N[(y / 500.0), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (/.f64 y #s(literal 500 binary64)) < -2.0000000000000001e-83 or 1.99999999999999985e-65 < (/.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* 99.9%

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

      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 y around inf 98.8%

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

   6. Taylor expanded in x around 0 74.8%

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

      1. metadata-eval 74.8%

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

      2. div-inv 74.9%

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

   8. Applied egg-rr 74.9%

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

   if -2.0000000000000001e-83 < (/.f64 y #s(literal 500 binary64)) < 1.99999999999999985e-65

   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 83.7%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{500} \leq -2 \cdot 10^{-83} \lor \neg \left(\frac{y}{500} \leq 2 \cdot 10^{-65}\right):\\ \;\;\;\;\frac{y}{500}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-80} \lor \neg \left(y \leq 8.2 \cdot 10^{-61}\right):\\ \;\;\;\;y \cdot 0.002\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.4e-80) (not (<= y 8.2e-61))) (* y 0.002) x))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.4e-80) || !(y <= 8.2e-61)) {
		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 <= (-1.4d-80)) .or. (.not. (y <= 8.2d-61))) 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 <= -1.4e-80) || !(y <= 8.2e-61)) {
		tmp = y * 0.002;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.4e-80) or not (y <= 8.2e-61):
		tmp = y * 0.002
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.4e-80) || !(y <= 8.2e-61))
		tmp = Float64(y * 0.002);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.4e-80) || ~((y <= 8.2e-61)))
		tmp = y * 0.002;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.4e-80], N[Not[LessEqual[y, 8.2e-61]], $MachinePrecision]], N[(y * 0.002), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.39999999999999995e-80 or 8.19999999999999998e-61 < 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* 99.9%

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

      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 y around inf 98.8%

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

   6. Taylor expanded in x around 0 74.8%

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

   if -1.39999999999999995e-80 < y < 8.19999999999999998e-61

   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 83.7%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-80} \lor \neg \left(y \leq 8.2 \cdot 10^{-61}\right):\\ \;\;\;\;y \cdot 0.002\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
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: 51.1% 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 48.2%

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

Reproduce

herbie shell --seed 2024098 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, C"
  :precision binary64
  (+ x (/ y 500.0)))