Data.Colour.SRGB:transferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 2.4s

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

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

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. Final simplification 100.0%

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

Alternative 2: 62.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+25}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-17}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-109}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-131}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-16}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+245}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.8e+25)
   (* x y)
   (if (<= y -3.5e-17)
     y
     (if (<= y -2.4e-109)
       (- x)
       (if (<= y -1.4e-131)
         y
         (if (<= y 1.35e-16) (- x) (if (<= y 3.1e+245) y (* x y))))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.8e+25) {
		tmp = x * y;
	} else if (y <= -3.5e-17) {
		tmp = y;
	} else if (y <= -2.4e-109) {
		tmp = -x;
	} else if (y <= -1.4e-131) {
		tmp = y;
	} else if (y <= 1.35e-16) {
		tmp = -x;
	} else if (y <= 3.1e+245) {
		tmp = y;
	} 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 (y <= (-1.8d+25)) then
        tmp = x * y
    else if (y <= (-3.5d-17)) then
        tmp = y
    else if (y <= (-2.4d-109)) then
        tmp = -x
    else if (y <= (-1.4d-131)) then
        tmp = y
    else if (y <= 1.35d-16) then
        tmp = -x
    else if (y <= 3.1d+245) then
        tmp = y
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.8e+25) {
		tmp = x * y;
	} else if (y <= -3.5e-17) {
		tmp = y;
	} else if (y <= -2.4e-109) {
		tmp = -x;
	} else if (y <= -1.4e-131) {
		tmp = y;
	} else if (y <= 1.35e-16) {
		tmp = -x;
	} else if (y <= 3.1e+245) {
		tmp = y;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.8e+25:
		tmp = x * y
	elif y <= -3.5e-17:
		tmp = y
	elif y <= -2.4e-109:
		tmp = -x
	elif y <= -1.4e-131:
		tmp = y
	elif y <= 1.35e-16:
		tmp = -x
	elif y <= 3.1e+245:
		tmp = y
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.8e+25)
		tmp = Float64(x * y);
	elseif (y <= -3.5e-17)
		tmp = y;
	elseif (y <= -2.4e-109)
		tmp = Float64(-x);
	elseif (y <= -1.4e-131)
		tmp = y;
	elseif (y <= 1.35e-16)
		tmp = Float64(-x);
	elseif (y <= 3.1e+245)
		tmp = y;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.8e+25)
		tmp = x * y;
	elseif (y <= -3.5e-17)
		tmp = y;
	elseif (y <= -2.4e-109)
		tmp = -x;
	elseif (y <= -1.4e-131)
		tmp = y;
	elseif (y <= 1.35e-16)
		tmp = -x;
	elseif (y <= 3.1e+245)
		tmp = y;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.8e+25], N[(x * y), $MachinePrecision], If[LessEqual[y, -3.5e-17], y, If[LessEqual[y, -2.4e-109], (-x), If[LessEqual[y, -1.4e-131], y, If[LessEqual[y, 1.35e-16], (-x), If[LessEqual[y, 3.1e+245], y, N[(x * y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.80000000000000008e25 or 3.0999999999999999e245 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 100.0%

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

   3. Taylor expanded in x around inf 59.2%

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

   if -1.80000000000000008e25 < y < -3.5000000000000002e-17 or -2.39999999999999989e-109 < y < -1.4e-131 or 1.35e-16 < y < 3.0999999999999999e245

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 66.3%

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

   if -3.5000000000000002e-17 < y < -2.39999999999999989e-109 or -1.4e-131 < y < 1.35e-16

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 79.1%

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

      1. neg-mul-1 79.1%

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

   4. Simplified 79.1%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+25}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-17}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-109}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-131}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-16}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+245}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 3: 86.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-33} \lor \neg \left(y \leq -4.8 \cdot 10^{-110} \lor \neg \left(y \leq -1.4 \cdot 10^{-131}\right) \land y \leq 6.8 \cdot 10^{-22}\right):\\ \;\;\;\;\left(x + 1\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -6.5e-33)
         (not
          (or (<= y -4.8e-110) (and (not (<= y -1.4e-131)) (<= y 6.8e-22)))))
   (* (+ x 1.0) y)
   (- x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -6.5e-33) || !((y <= -4.8e-110) || (!(y <= -1.4e-131) && (y <= 6.8e-22)))) {
		tmp = (x + 1.0) * y;
	} 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 <= (-6.5d-33)) .or. (.not. (y <= (-4.8d-110)) .or. (.not. (y <= (-1.4d-131))) .and. (y <= 6.8d-22))) then
        tmp = (x + 1.0d0) * y
    else
        tmp = -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -6.5e-33) || !((y <= -4.8e-110) || (!(y <= -1.4e-131) && (y <= 6.8e-22)))) {
		tmp = (x + 1.0) * y;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -6.5e-33) or not ((y <= -4.8e-110) or (not (y <= -1.4e-131) and (y <= 6.8e-22))):
		tmp = (x + 1.0) * y
	else:
		tmp = -x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -6.5e-33) || !((y <= -4.8e-110) || (!(y <= -1.4e-131) && (y <= 6.8e-22))))
		tmp = Float64(Float64(x + 1.0) * y);
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -6.5e-33) || ~(((y <= -4.8e-110) || (~((y <= -1.4e-131)) && (y <= 6.8e-22)))))
		tmp = (x + 1.0) * y;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -6.5e-33], N[Not[Or[LessEqual[y, -4.8e-110], And[N[Not[LessEqual[y, -1.4e-131]], $MachinePrecision], LessEqual[y, 6.8e-22]]]], $MachinePrecision]], N[(N[(x + 1.0), $MachinePrecision] * y), $MachinePrecision], (-x)]

Derivation

1. Split input into 2 regimes

2. if y < -6.4999999999999993e-33 or -4.80000000000000013e-110 < y < -1.4e-131 or 6.7999999999999997e-22 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 95.6%

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

   if -6.4999999999999993e-33 < y < -4.80000000000000013e-110 or -1.4e-131 < y < 6.7999999999999997e-22

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 80.1%

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

      1. neg-mul-1 80.1%

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

   4. Simplified 80.1%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-33} \lor \neg \left(y \leq -4.8 \cdot 10^{-110} \lor \neg \left(y \leq -1.4 \cdot 10^{-131}\right) \land y \leq 6.8 \cdot 10^{-22}\right):\\ \;\;\;\;\left(x + 1\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 4: 87.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -22500 \lor \neg \left(x \leq 5.4 \cdot 10^{-18}\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + 1\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -22500.0) (not (<= x 5.4e-18)))
   (* x (+ y -1.0))
   (* (+ x 1.0) y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -22500.0) || !(x <= 5.4e-18)) {
		tmp = x * (y + -1.0);
	} else {
		tmp = (x + 1.0) * 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 <= (-22500.0d0)) .or. (.not. (x <= 5.4d-18))) then
        tmp = x * (y + (-1.0d0))
    else
        tmp = (x + 1.0d0) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -22500.0) || !(x <= 5.4e-18)) {
		tmp = x * (y + -1.0);
	} else {
		tmp = (x + 1.0) * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -22500.0) or not (x <= 5.4e-18):
		tmp = x * (y + -1.0)
	else:
		tmp = (x + 1.0) * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -22500.0) || !(x <= 5.4e-18))
		tmp = Float64(x * Float64(y + -1.0));
	else
		tmp = Float64(Float64(x + 1.0) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -22500.0) || ~((x <= 5.4e-18)))
		tmp = x * (y + -1.0);
	else
		tmp = (x + 1.0) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -22500.0], N[Not[LessEqual[x, 5.4e-18]], $MachinePrecision]], N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + 1.0), $MachinePrecision] * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -22500 or 5.39999999999999977e-18 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 99.8%

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

   if -22500 < x < 5.39999999999999977e-18

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 75.3%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -22500 \lor \neg \left(x \leq 5.4 \cdot 10^{-18}\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + 1\right) \cdot y\\ \end{array} \]

Alternative 5: 63.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{-18}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-15}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -5.4e-18) (- x) (if (<= x 3.4e-15) y (- x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -5.4e-18) {
		tmp = -x;
	} else if (x <= 3.4e-15) {
		tmp = y;
	} 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 <= (-5.4d-18)) then
        tmp = -x
    else if (x <= 3.4d-15) then
        tmp = y
    else
        tmp = -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -5.4e-18) {
		tmp = -x;
	} else if (x <= 3.4e-15) {
		tmp = y;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -5.4e-18:
		tmp = -x
	elif x <= 3.4e-15:
		tmp = y
	else:
		tmp = -x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -5.4e-18)
		tmp = Float64(-x);
	elseif (x <= 3.4e-15)
		tmp = y;
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -5.4e-18)
		tmp = -x;
	elseif (x <= 3.4e-15)
		tmp = y;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -5.4e-18], (-x), If[LessEqual[x, 3.4e-15], y, (-x)]]

Derivation

1. Split input into 2 regimes

2. if x < -5.39999999999999977e-18 or 3.4e-15 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 51.3%

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

      1. neg-mul-1 51.3%

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

   4. Simplified 51.3%

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

   if -5.39999999999999977e-18 < x < 3.4e-15

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 75.5%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{-18}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-15}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 6: 38.7% 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 40.7%

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

3. Final simplification 40.7%

   \[\leadsto y \]

Reproduce

herbie shell --seed 2023185 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1.0) y) x))