Data.Colour.SRGB:transferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 2.0s

Alternatives: 6

Speedup: 1.0×

Specification

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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\left(x + 1\right) \cdot y - x \]

2. Taylor expanded in x around 0 100.0%

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

3. Final simplification 100.0%

   \[\leadsto \left(y + y \cdot x\right) - x \]

Alternative 2: 98.8% accurate, 0.8× speedup

Math

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

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.0) (not (<= x 1.0))) (- (* y x) x) (- y x)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.0) || !(x <= 1.0)) {
		tmp = (y * x) - x;
	} else {
		tmp = y - 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 <= (-1.0d0)) .or. (.not. (x <= 1.0d0))) then
        tmp = (y * x) - x
    else
        tmp = y - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -1.0) || !(x <= 1.0)) {
		tmp = (y * x) - x;
	} else {
		tmp = y - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.0) or not (x <= 1.0):
		tmp = (y * x) - x
	else:
		tmp = y - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.0) || !(x <= 1.0))
		tmp = Float64(Float64(y * x) - x);
	else
		tmp = Float64(y - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.0) || ~((x <= 1.0)))
		tmp = (y * x) - x;
	else
		tmp = y - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.0], N[Not[LessEqual[x, 1.0]], $MachinePrecision]], N[(N[(y * x), $MachinePrecision] - x), $MachinePrecision], N[(y - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1 or 1 < x

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]

   2. Taylor expanded in x around inf 98.7%

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

   if -1 < x < 1

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]

   2. Taylor expanded in x around 0 99.3%

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

4. Final simplification 99.0%

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

Alternative 3: 61.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+17}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3e+17) (* y x) (if (<= y 1.0) (- x) (* y x))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3e+17) {
		tmp = y * x;
	} else if (y <= 1.0) {
		tmp = -x;
	} else {
		tmp = y * 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 <= (-3d+17)) then
        tmp = y * x
    else if (y <= 1.0d0) then
        tmp = -x
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -3e+17) {
		tmp = y * x;
	} else if (y <= 1.0) {
		tmp = -x;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3e+17:
		tmp = y * x
	elif y <= 1.0:
		tmp = -x
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3e+17)
		tmp = Float64(y * x);
	elseif (y <= 1.0)
		tmp = Float64(-x);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -3e+17)
		tmp = y * x;
	elseif (y <= 1.0)
		tmp = -x;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3e+17], N[(y * x), $MachinePrecision], If[LessEqual[y, 1.0], (-x), N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3e17 or 1 < y

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]

   2. Taylor expanded in x around inf 48.2%

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

   3. Taylor expanded in y around inf 47.3%

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

   if -3e17 < y < 1

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]

   2. Taylor expanded in x around inf 76.0%

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

   3. Taylor expanded in y around 0 75.0%

      \[\leadsto \color{blue}{-1 \cdot x} \]
   4. Step-by-step derivation

      1. neg-mul-1 75.0%

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

   5. Simplified 75.0%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+17}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 4: 75.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 7 \cdot 10^{+48}:\\ \;\;\;\;y - x\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+205}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 7e+48) (- y x) (if (<= y 1.95e+205) (* y x) (- y x))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 7e+48) {
		tmp = y - x;
	} else if (y <= 1.95e+205) {
		tmp = y * x;
	} else {
		tmp = y - 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 <= 7d+48) then
        tmp = y - x
    else if (y <= 1.95d+205) then
        tmp = y * x
    else
        tmp = y - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 7e+48) {
		tmp = y - x;
	} else if (y <= 1.95e+205) {
		tmp = y * x;
	} else {
		tmp = y - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 7e+48:
		tmp = y - x
	elif y <= 1.95e+205:
		tmp = y * x
	else:
		tmp = y - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 7e+48)
		tmp = Float64(y - x);
	elseif (y <= 1.95e+205)
		tmp = Float64(y * x);
	else
		tmp = Float64(y - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 7e+48)
		tmp = y - x;
	elseif (y <= 1.95e+205)
		tmp = y * x;
	else
		tmp = y - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 7e+48], N[(y - x), $MachinePrecision], If[LessEqual[y, 1.95e+205], N[(y * x), $MachinePrecision], N[(y - x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < 6.9999999999999995e48 or 1.9499999999999999e205 < y

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]

   2. Taylor expanded in x around 0 81.6%

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

   if 6.9999999999999995e48 < y < 1.9499999999999999e205

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]

   2. Taylor expanded in x around inf 67.4%

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

   3. Taylor expanded in y around inf 67.4%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 7 \cdot 10^{+48}:\\ \;\;\;\;y - x\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+205}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \]

Alternative 5: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\left(x + 1\right) \cdot y - x \]

2. Final simplification 100.0%

   \[\leadsto y \cdot \left(x + 1\right) - x \]

Alternative 6: 39.3% accurate, 3.5× 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 Float64(-x)
end

MATLAB

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

Wolfram

code[x_, y_] := (-x)

Derivation

1. Initial program 100.0%

   \[\left(x + 1\right) \cdot y - x \]

2. Taylor expanded in x around inf 60.4%

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

3. Taylor expanded in y around 0 34.2%

   \[\leadsto \color{blue}{-1 \cdot x} \]
4. Step-by-step derivation

   1. neg-mul-1 34.2%

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

5. Simplified 34.2%

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

6. Final simplification 34.2%

   \[\leadsto -x \]

Reproduce

herbie shell --seed 2023229 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1.0) y) x))