Data.Colour.SRGB:transferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 777.0ms

Alternatives: 4

Speedup: 1.0×

Specification

\[\mathsf{TRUE}\left(\right)\]

Math

\[\begin{array}{l} \\ \left(x + 1\right) \cdot y - x \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- (* (+ x 1.0) y) x))

C

double code(double x, double y) {
	return ((x + 1.0) * y) - x;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((x + 1.0d0) * y) - x
end function

Java

public static double code(double x, double y) {
	return ((x + 1.0) * y) - x;
}

Python

def code(x, y):
	return ((x + 1.0) * y) - x

Julia

function code(x, y)
	return Float64(Float64(Float64(x + 1.0) * y) - x)
end

MATLAB

function tmp = code(x, y)
	tmp = ((x + 1.0) * y) - x;
end

Wolfram

code[x_, y_] := N[(N[(N[(x + 1.0), $MachinePrecision] * y), $MachinePrecision] - x), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x + 1\right) \cdot y - x \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- (* (+ x 1.0) y) x))

C

double code(double x, double y) {
	return ((x + 1.0) * y) - x;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((x + 1.0d0) * y) - x
end function

Java

public static double code(double x, double y) {
	return ((x + 1.0) * y) - x;
}

Python

def code(x, y):
	return ((x + 1.0) * y) - x

Julia

function code(x, y)
	return Float64(Float64(Float64(x + 1.0) * y) - x)
end

MATLAB

function tmp = code(x, y)
	tmp = ((x + 1.0) * y) - x;
end

Wolfram

code[x_, y_] := N[(N[(N[(x + 1.0), $MachinePrecision] * y), $MachinePrecision] - x), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x + 1\right) \cdot y - x \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- (* (+ x 1.0) y) x))

C

double code(double x, double y) {
	return ((x + 1.0) * y) - x;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((x + 1.0d0) * y) - x
end function

Java

public static double code(double x, double y) {
	return ((x + 1.0) * y) - x;
}

Python

def code(x, y):
	return ((x + 1.0) * y) - x

Julia

function code(x, y)
	return Float64(Float64(Float64(x + 1.0) * y) - x)
end

MATLAB

function tmp = code(x, y)
	tmp = ((x + 1.0) * y) - x;
end

Wolfram

code[x_, y_] := N[(N[(N[(x + 1.0), $MachinePrecision] * y), $MachinePrecision] - x), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\left(x + 1\right) \cdot y - x \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 73.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x + 1\right) \cdot y\\ \mathbf{if}\;y \leq -8.5 \cdot 10^{-147}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{-23}:\\ \;\;\;\;\left(\left(x + 1\right) - x\right) - x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (+ x 1.0) y)))
   (if (<= y -8.5e-147) t_0 (if (<= y 1.18e-23) (- (- (+ x 1.0) x) x) t_0))))

C

double code(double x, double y) {
	double t_0 = (x + 1.0) * y;
	double tmp;
	if (y <= -8.5e-147) {
		tmp = t_0;
	} else if (y <= 1.18e-23) {
		tmp = ((x + 1.0) - x) - x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x + 1.0d0) * y
    if (y <= (-8.5d-147)) then
        tmp = t_0
    else if (y <= 1.18d-23) then
        tmp = ((x + 1.0d0) - x) - x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (x + 1.0) * y;
	double tmp;
	if (y <= -8.5e-147) {
		tmp = t_0;
	} else if (y <= 1.18e-23) {
		tmp = ((x + 1.0) - x) - x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (x + 1.0) * y
	tmp = 0
	if y <= -8.5e-147:
		tmp = t_0
	elif y <= 1.18e-23:
		tmp = ((x + 1.0) - x) - x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(x + 1.0) * y)
	tmp = 0.0
	if (y <= -8.5e-147)
		tmp = t_0;
	elseif (y <= 1.18e-23)
		tmp = Float64(Float64(Float64(x + 1.0) - x) - x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (x + 1.0) * y;
	tmp = 0.0;
	if (y <= -8.5e-147)
		tmp = t_0;
	elseif (y <= 1.18e-23)
		tmp = ((x + 1.0) - x) - x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(x + 1.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -8.5e-147], t$95$0, If[LessEqual[y, 1.18e-23], N[(N[(N[(x + 1.0), $MachinePrecision] - x), $MachinePrecision] - x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -8.5000000000000002e-147 or 1.18e-23 < y

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 92.1%

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

   if -8.5000000000000002e-147 < y < 1.18e-23

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 3.0%

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

   6. Taylor expanded in x around 0

      \[\leadsto 1 - x \]

   8. Applied rewrites 56.5%

      \[\leadsto \left(\left(x + 1\right) - \color{blue}{x}\right) - x \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 63.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \left(x + 1\right) \cdot y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* (+ x 1.0) y))

C

double code(double x, double y) {
	return (x + 1.0) * y;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x + 1.0d0) * y
end function

Java

public static double code(double x, double y) {
	return (x + 1.0) * y;
}

Python

def code(x, y):
	return (x + 1.0) * y

Julia

function code(x, y)
	return Float64(Float64(x + 1.0) * y)
end

MATLAB

function tmp = code(x, y)
	tmp = (x + 1.0) * y;
end

Wolfram

code[x_, y_] := N[(N[(x + 1.0), $MachinePrecision] * y), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\left(x + 1\right) \cdot y - x \]
2. Add Preprocessing

3. Taylor expanded in x around 0

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

5. Applied rewrites 67.0%

   \[\leadsto \color{blue}{\left(x + 1\right) \cdot y} \]
6. Add Preprocessing

Alternative 4: 2.9% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ x + 1 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (+ x 1.0))

C

double code(double x, double y) {
	return x + 1.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x + 1.0d0
end function

Java

public static double code(double x, double y) {
	return x + 1.0;
}

Python

def code(x, y):
	return x + 1.0

Julia

function code(x, y)
	return Float64(x + 1.0)
end

MATLAB

function tmp = code(x, y)
	tmp = x + 1.0;
end

Wolfram

code[x_, y_] := N[(x + 1.0), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\left(x + 1\right) \cdot y - x \]
2. Add Preprocessing

3. Taylor expanded in x around 0

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

5. Applied rewrites 67.0%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 3.1%

   \[\leadsto x + \color{blue}{1} \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024321 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  :pre (TRUE)
  (- (* (+ x 1.0) y) x))