Data.Colour.SRGB:transferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 3.2s

Alternatives: 7

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, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(x, y, y\right) - x \end{array} \]

FPCore

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

C

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

Julia

function code(x, y)
	return Float64(fma(x, y, y) - x)
end

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\left(x + 1\right) \cdot y - x \]
2. Step-by-step derivation

   1. *-commutative 100.0%

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

   2. distribute-rgt-in 100.0%

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

   3. fma-def 100.0%

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

   4. *-lft-identity 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \mathsf{fma}\left(x, y, y\right) - x \]

Alternative 2: 62.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -18500000:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-60}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-28}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+195}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -18500000.0)
   (* x y)
   (if (<= x -1.05e-60)
     (- x)
     (if (<= x 1.6e-28) y (if (<= x 1.3e+195) (- x) (* x y))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -18500000.0) {
		tmp = x * y;
	} else if (x <= -1.05e-60) {
		tmp = -x;
	} else if (x <= 1.6e-28) {
		tmp = y;
	} else if (x <= 1.3e+195) {
		tmp = -x;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-18500000.0d0)) then
        tmp = x * y
    else if (x <= (-1.05d-60)) then
        tmp = -x
    else if (x <= 1.6d-28) then
        tmp = y
    else if (x <= 1.3d+195) then
        tmp = -x
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -18500000.0) {
		tmp = x * y;
	} else if (x <= -1.05e-60) {
		tmp = -x;
	} else if (x <= 1.6e-28) {
		tmp = y;
	} else if (x <= 1.3e+195) {
		tmp = -x;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -18500000.0:
		tmp = x * y
	elif x <= -1.05e-60:
		tmp = -x
	elif x <= 1.6e-28:
		tmp = y
	elif x <= 1.3e+195:
		tmp = -x
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -18500000.0)
		tmp = Float64(x * y);
	elseif (x <= -1.05e-60)
		tmp = Float64(-x);
	elseif (x <= 1.6e-28)
		tmp = y;
	elseif (x <= 1.3e+195)
		tmp = Float64(-x);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -18500000.0)
		tmp = x * y;
	elseif (x <= -1.05e-60)
		tmp = -x;
	elseif (x <= 1.6e-28)
		tmp = y;
	elseif (x <= 1.3e+195)
		tmp = -x;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -18500000.0], N[(x * y), $MachinePrecision], If[LessEqual[x, -1.05e-60], (-x), If[LessEqual[x, 1.6e-28], y, If[LessEqual[x, 1.3e+195], (-x), N[(x * y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.85e7 or 1.30000000000000001e195 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 64.4%

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

   3. Taylor expanded in x around 0 64.4%

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

   4. Taylor expanded in x around inf 63.9%

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

   if -1.85e7 < x < -1.04999999999999996e-60 or 1.59999999999999991e-28 < x < 1.30000000000000001e195

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 57.4%

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

      1. neg-mul-1 57.4%

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

   4. Simplified 57.4%

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

   if -1.04999999999999996e-60 < x < 1.59999999999999991e-28

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 79.7%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -18500000:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-60}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-28}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+195}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 3: 87.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-14} \lor \neg \left(y \leq 4.8 \cdot 10^{-36}\right):\\ \;\;\;\;y \cdot \left(x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -2.2e-14) (not (<= y 4.8e-36))) (* y (+ x 1.0)) (- x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -2.2e-14) || !(y <= 4.8e-36)) {
		tmp = y * (x + 1.0);
	} 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 <= (-2.2d-14)) .or. (.not. (y <= 4.8d-36))) then
        tmp = y * (x + 1.0d0)
    else
        tmp = -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -2.2e-14) || !(y <= 4.8e-36)) {
		tmp = y * (x + 1.0);
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -2.2e-14) or not (y <= 4.8e-36):
		tmp = y * (x + 1.0)
	else:
		tmp = -x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -2.2e-14) || !(y <= 4.8e-36))
		tmp = Float64(y * Float64(x + 1.0));
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -2.2e-14) || ~((y <= 4.8e-36)))
		tmp = y * (x + 1.0);
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -2.2e-14], N[Not[LessEqual[y, 4.8e-36]], $MachinePrecision]], N[(y * N[(x + 1.0), $MachinePrecision]), $MachinePrecision], (-x)]

Derivation

1. Split input into 2 regimes

2. if y < -2.2000000000000001e-14 or 4.8e-36 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 96.2%

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

   if -2.2000000000000001e-14 < y < 4.8e-36

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 77.1%

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

      1. neg-mul-1 77.1%

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

   4. Simplified 77.1%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-14} \lor \neg \left(y \leq 4.8 \cdot 10^{-36}\right):\\ \;\;\;\;y \cdot \left(x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 4: 86.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -31000000000000 \lor \neg \left(y \leq 3.6 \cdot 10^{-33}\right):\\ \;\;\;\;y \cdot \left(x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -31000000000000.0) (not (<= y 3.6e-33)))
   (* y (+ x 1.0))
   (* x (+ y -1.0))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -31000000000000.0) || !(y <= 3.6e-33)) {
		tmp = y * (x + 1.0);
	} else {
		tmp = x * (y + -1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-31000000000000.0d0)) .or. (.not. (y <= 3.6d-33))) then
        tmp = y * (x + 1.0d0)
    else
        tmp = x * (y + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -31000000000000.0) || !(y <= 3.6e-33)) {
		tmp = y * (x + 1.0);
	} else {
		tmp = x * (y + -1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -31000000000000.0) or not (y <= 3.6e-33):
		tmp = y * (x + 1.0)
	else:
		tmp = x * (y + -1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -31000000000000.0) || !(y <= 3.6e-33))
		tmp = Float64(y * Float64(x + 1.0));
	else
		tmp = Float64(x * Float64(y + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -31000000000000.0) || ~((y <= 3.6e-33)))
		tmp = y * (x + 1.0);
	else
		tmp = x * (y + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -31000000000000.0], N[Not[LessEqual[y, 3.6e-33]], $MachinePrecision]], N[(y * N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.1e13 or 3.60000000000000034e-33 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 97.5%

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

   if -3.1e13 < y < 3.60000000000000034e-33

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 78.1%

      \[\leadsto \color{blue}{\left(y - 1\right) \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -31000000000000 \lor \neg \left(y \leq 3.6 \cdot 10^{-33}\right):\\ \;\;\;\;y \cdot \left(x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \end{array} \]

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: 61.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -31000000000000:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-87}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -31000000000000.0) y (if (<= y 5.5e-87) (- x) y)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -31000000000000.0) {
		tmp = y;
	} else if (y <= 5.5e-87) {
		tmp = -x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-31000000000000.0d0)) then
        tmp = y
    else if (y <= 5.5d-87) then
        tmp = -x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -31000000000000.0) {
		tmp = y;
	} else if (y <= 5.5e-87) {
		tmp = -x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -31000000000000.0:
		tmp = y
	elif y <= 5.5e-87:
		tmp = -x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -31000000000000.0)
		tmp = y;
	elseif (y <= 5.5e-87)
		tmp = Float64(-x);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -31000000000000.0)
		tmp = y;
	elseif (y <= 5.5e-87)
		tmp = -x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -31000000000000.0], y, If[LessEqual[y, 5.5e-87], (-x), y]]

Derivation

1. Split input into 2 regimes

2. if y < -3.1e13 or 5.5000000000000004e-87 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 51.6%

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

   if -3.1e13 < y < 5.5000000000000004e-87

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 74.9%

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

      1. neg-mul-1 74.9%

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

   4. Simplified 74.9%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -31000000000000:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-87}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 7: 38.6% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 y)

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return y

Julia

function code(x, y)
	return y
end

MATLAB

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

Wolfram

code[x_, y_] := y

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in x around 0 38.6%

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

3. Final simplification 38.6%

   \[\leadsto y \]

Reproduce

herbie shell --seed 2023257 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1.0) y) x))