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

Percentage Accurate: 100.0% → 100.0%

Time: 5.0s

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. Final simplification 100.0%

   \[\leadsto x + \frac{y}{500} \]

Alternative 2: 74.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+65}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+67}:\\ \;\;\;\;y \cdot 0.002\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1e+65) x (if (<= x 7.5e+67) (* y 0.002) x)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1e+65) {
		tmp = x;
	} else if (x <= 7.5e+67) {
		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 (x <= (-1d+65)) then
        tmp = x
    else if (x <= 7.5d+67) 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 (x <= -1e+65) {
		tmp = x;
	} else if (x <= 7.5e+67) {
		tmp = y * 0.002;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1e+65:
		tmp = x
	elif x <= 7.5e+67:
		tmp = y * 0.002
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1e+65)
		tmp = x;
	elseif (x <= 7.5e+67)
		tmp = Float64(y * 0.002);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1e+65)
		tmp = x;
	elseif (x <= 7.5e+67)
		tmp = y * 0.002;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1e+65], x, If[LessEqual[x, 7.5e+67], N[(y * 0.002), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -9.9999999999999999e64 or 7.5000000000000005e67 < x

   1. Initial program 100.0%

      \[x + \frac{y}{500} \]

   2. Taylor expanded in x around inf 80.5%

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

   if -9.9999999999999999e64 < x < 7.5000000000000005e67

   1. Initial program 100.0%

      \[x + \frac{y}{500} \]

   2. Taylor expanded in x around 0 78.5%

      \[\leadsto \color{blue}{0.002 \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+65}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+67}:\\ \;\;\;\;y \cdot 0.002\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 3.3% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ -4 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 -4.0)

C

double code(double x, double y) {
	return -4.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = -4.0d0
end function

Java

public static double code(double x, double y) {
	return -4.0;
}

Python

def code(x, y):
	return -4.0

Julia

function code(x, y)
	return -4.0
end

MATLAB

function tmp = code(x, y)
	tmp = -4.0;
end

Wolfram

code[x_, y_] := -4.0

Derivation

1. Initial program 100.0%

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

   1. flip-+ 47.8%

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

   2. difference-of-squares 48.4%

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

   3. +-commutative 48.4%

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

   4. div-inv 48.4%

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

   5. metadata-eval 48.4%

      \[\leadsto \frac{\left(y \cdot \color{blue}{0.002} + x\right) \cdot \left(x - \frac{y}{500}\right)}{x - \frac{y}{500}} \]

   6. fma-udef 48.4%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y, 0.002, x\right)} \cdot \left(x - \frac{y}{500}\right)}{x - \frac{y}{500}} \]

   7. add-sqr-sqrt 26.4%

      \[\leadsto \frac{\mathsf{fma}\left(y, 0.002, x\right) \cdot \left(x - \frac{y}{500}\right)}{\color{blue}{\sqrt{x - \frac{y}{500}} \cdot \sqrt{x - \frac{y}{500}}}} \]

   8. times-frac 56.5%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(y, 0.002, x\right)}{\sqrt{x - \frac{y}{500}}} \cdot \frac{x - \frac{y}{500}}{\sqrt{x - \frac{y}{500}}}} \]

3. Applied egg-rr 56.4%

   \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(y, 0.002, x\right)}{\sqrt{x + y \cdot -0.002}} \cdot \frac{x + y \cdot -0.002}{\sqrt{x + y \cdot -0.002}}} \]
4. Step-by-step derivation

   1. associate-*r/ 34.2%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(y, 0.002, x\right)}{\sqrt{x + y \cdot -0.002}} \cdot \left(x + y \cdot -0.002\right)}{\sqrt{x + y \cdot -0.002}}} \]

5. Simplified 34.2%

   \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(y, 0.002, x\right)}{\sqrt{x + y \cdot -0.002}} \cdot \left(x + y \cdot -0.002\right)}{\sqrt{x + y \cdot -0.002}}} \]

7. Applied egg-rr 48.3%

   \[\leadsto \color{blue}{{\left(\mathsf{fma}\left(0.002, y, x\right)\right)}^{2} \cdot \frac{1}{\mathsf{fma}\left(0.002, y, x\right)}} \]

9. Applied egg-rr 3.4%

   \[\leadsto \color{blue}{-4} \]

10. Final simplification 3.4%

    \[\leadsto -4 \]

Alternative 4: 3.3% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ -0.25 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 -0.25)

C

double code(double x, double y) {
	return -0.25;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = -0.25d0
end function

Java

public static double code(double x, double y) {
	return -0.25;
}

Python

def code(x, y):
	return -0.25

Julia

function code(x, y)
	return -0.25
end

MATLAB

function tmp = code(x, y)
	tmp = -0.25;
end

Wolfram

code[x_, y_] := -0.25

Derivation

1. Initial program 100.0%

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

   1. flip-+ 47.8%

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

   2. difference-of-squares 48.4%

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

   3. +-commutative 48.4%

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

   4. div-inv 48.4%

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

   5. metadata-eval 48.4%

      \[\leadsto \frac{\left(y \cdot \color{blue}{0.002} + x\right) \cdot \left(x - \frac{y}{500}\right)}{x - \frac{y}{500}} \]

   6. fma-udef 48.4%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y, 0.002, x\right)} \cdot \left(x - \frac{y}{500}\right)}{x - \frac{y}{500}} \]

   7. add-sqr-sqrt 26.4%

      \[\leadsto \frac{\mathsf{fma}\left(y, 0.002, x\right) \cdot \left(x - \frac{y}{500}\right)}{\color{blue}{\sqrt{x - \frac{y}{500}} \cdot \sqrt{x - \frac{y}{500}}}} \]

   8. times-frac 56.5%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(y, 0.002, x\right)}{\sqrt{x - \frac{y}{500}}} \cdot \frac{x - \frac{y}{500}}{\sqrt{x - \frac{y}{500}}}} \]

3. Applied egg-rr 56.4%

   \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(y, 0.002, x\right)}{\sqrt{x + y \cdot -0.002}} \cdot \frac{x + y \cdot -0.002}{\sqrt{x + y \cdot -0.002}}} \]
4. Step-by-step derivation

   1. associate-*r/ 34.2%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(y, 0.002, x\right)}{\sqrt{x + y \cdot -0.002}} \cdot \left(x + y \cdot -0.002\right)}{\sqrt{x + y \cdot -0.002}}} \]

5. Simplified 34.2%

   \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(y, 0.002, x\right)}{\sqrt{x + y \cdot -0.002}} \cdot \left(x + y \cdot -0.002\right)}{\sqrt{x + y \cdot -0.002}}} \]

7. Applied egg-rr 48.3%

   \[\leadsto \color{blue}{{\left(\mathsf{fma}\left(0.002, y, x\right)\right)}^{2} \cdot \frac{1}{\mathsf{fma}\left(0.002, y, x\right)}} \]

9. Applied egg-rr 3.4%

   \[\leadsto \color{blue}{-0.25} \]

10. Final simplification 3.4%

    \[\leadsto -0.25 \]

Alternative 5: 51.6% 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. Taylor expanded in x around inf 46.2%

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

3. Final simplification 46.2%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023301 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, C"
  :precision binary64
  (+ x (/ y 500.0)))