Data.Colour.SRGB:transferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 3.0s

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

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

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. Final simplification 100.0%

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

Alternative 2: 62.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{+245}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq -1:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-24}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+68} \lor \neg \left(x \leq 5 \cdot 10^{+151}\right):\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -7.6e+245)
   (- x)
   (if (<= x -1.0)
     (* x y)
     (if (<= x 2.1e-24)
       y
       (if (or (<= x 8.5e+68) (not (<= x 5e+151))) (- x) (* x y))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -7.6e+245) {
		tmp = -x;
	} else if (x <= -1.0) {
		tmp = x * y;
	} else if (x <= 2.1e-24) {
		tmp = y;
	} else if ((x <= 8.5e+68) || !(x <= 5e+151)) {
		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 <= (-7.6d+245)) then
        tmp = -x
    else if (x <= (-1.0d0)) then
        tmp = x * y
    else if (x <= 2.1d-24) then
        tmp = y
    else if ((x <= 8.5d+68) .or. (.not. (x <= 5d+151))) 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 <= -7.6e+245) {
		tmp = -x;
	} else if (x <= -1.0) {
		tmp = x * y;
	} else if (x <= 2.1e-24) {
		tmp = y;
	} else if ((x <= 8.5e+68) || !(x <= 5e+151)) {
		tmp = -x;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -7.6e+245:
		tmp = -x
	elif x <= -1.0:
		tmp = x * y
	elif x <= 2.1e-24:
		tmp = y
	elif (x <= 8.5e+68) or not (x <= 5e+151):
		tmp = -x
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -7.6e+245)
		tmp = Float64(-x);
	elseif (x <= -1.0)
		tmp = Float64(x * y);
	elseif (x <= 2.1e-24)
		tmp = y;
	elseif ((x <= 8.5e+68) || !(x <= 5e+151))
		tmp = Float64(-x);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -7.6e+245)
		tmp = -x;
	elseif (x <= -1.0)
		tmp = x * y;
	elseif (x <= 2.1e-24)
		tmp = y;
	elseif ((x <= 8.5e+68) || ~((x <= 5e+151)))
		tmp = -x;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -7.6e+245], (-x), If[LessEqual[x, -1.0], N[(x * y), $MachinePrecision], If[LessEqual[x, 2.1e-24], y, If[Or[LessEqual[x, 8.5e+68], N[Not[LessEqual[x, 5e+151]], $MachinePrecision]], (-x), N[(x * y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.5999999999999999e245 or 2.0999999999999999e-24 < x < 8.49999999999999966e68 or 5.0000000000000002e151 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 64.8%

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

      1. neg-mul-1 64.8%

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

   5. Simplified 64.8%

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

   if -7.5999999999999999e245 < x < -1 or 8.49999999999999966e68 < x < 5.0000000000000002e151

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 100.0%

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

   4. Taylor expanded in y around inf 60.8%

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

   if -1 < x < 2.0999999999999999e-24

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 80.3%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{+245}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq -1:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-24}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+68} \lor \neg \left(x \leq 5 \cdot 10^{+151}\right):\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{-65} \lor \neg \left(x \leq 2.2 \cdot 10^{-24}\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.3e-65) (not (<= x 2.2e-24))) (* x (+ y -1.0)) y))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.3e-65) || !(x <= 2.2e-24)) {
		tmp = x * (y + -1.0);
	} 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 ((x <= (-1.3d-65)) .or. (.not. (x <= 2.2d-24))) then
        tmp = x * (y + (-1.0d0))
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -1.3e-65) || !(x <= 2.2e-24)) {
		tmp = x * (y + -1.0);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.3e-65) or not (x <= 2.2e-24):
		tmp = x * (y + -1.0)
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.3e-65) || !(x <= 2.2e-24))
		tmp = Float64(x * Float64(y + -1.0));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.3e-65) || ~((x <= 2.2e-24)))
		tmp = x * (y + -1.0);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.3e-65], N[Not[LessEqual[x, 2.2e-24]], $MachinePrecision]], N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision], y]

Derivation

1. Split input into 2 regimes

2. if x < -1.30000000000000005e-65 or 2.20000000000000002e-24 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 95.0%

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

   if -1.30000000000000005e-65 < x < 2.20000000000000002e-24

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 83.8%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{-65} \lor \neg \left(x \leq 2.2 \cdot 10^{-24}\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.00029 \lor \neg \left(x \leq 2.05 \cdot 10^{-24}\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + 1\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -0.00029) (not (<= x 2.05e-24)))
   (* x (+ y -1.0))
   (* (+ x 1.0) y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -0.00029) || !(x <= 2.05e-24)) {
		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 <= (-0.00029d0)) .or. (.not. (x <= 2.05d-24))) 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 <= -0.00029) || !(x <= 2.05e-24)) {
		tmp = x * (y + -1.0);
	} else {
		tmp = (x + 1.0) * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -0.00029) or not (x <= 2.05e-24):
		tmp = x * (y + -1.0)
	else:
		tmp = (x + 1.0) * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -0.00029) || !(x <= 2.05e-24))
		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 <= -0.00029) || ~((x <= 2.05e-24)))
		tmp = x * (y + -1.0);
	else
		tmp = (x + 1.0) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -0.00029], N[Not[LessEqual[x, 2.05e-24]], $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 < -2.9e-4 or 2.05000000000000007e-24 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 98.2%

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

   if -2.9e-4 < x < 2.05000000000000007e-24

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 81.0%

      \[\leadsto \color{blue}{y \cdot \left(1 + x\right)} \]
   4. Step-by-step derivation

      1. +-commutative 81.0%

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

   5. Simplified 81.0%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.00029 \lor \neg \left(x \leq 2.05 \cdot 10^{-24}\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + 1\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 62.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{-65} \lor \neg \left(x \leq 2.6 \cdot 10^{-24}\right):\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.75e-65) (not (<= x 2.6e-24))) (- x) y))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.75e-65) || !(x <= 2.6e-24)) {
		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 ((x <= (-1.75d-65)) .or. (.not. (x <= 2.6d-24))) then
        tmp = -x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -1.75e-65) || !(x <= 2.6e-24)) {
		tmp = -x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.75e-65) or not (x <= 2.6e-24):
		tmp = -x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.75e-65) || !(x <= 2.6e-24))
		tmp = Float64(-x);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.75e-65) || ~((x <= 2.6e-24)))
		tmp = -x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.75e-65], N[Not[LessEqual[x, 2.6e-24]], $MachinePrecision]], (-x), y]

Derivation

1. Split input into 2 regimes

2. if x < -1.75000000000000002e-65 or 2.6e-24 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 54.2%

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

      1. neg-mul-1 54.2%

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

   5. Simplified 54.2%

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

   if -1.75000000000000002e-65 < x < 2.6e-24

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 83.8%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{-65} \lor \neg \left(x \leq 2.6 \cdot 10^{-24}\right):\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 38.2% 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. Add Preprocessing

3. Taylor expanded in x around 0 38.8%

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

4. Final simplification 38.8%

   \[\leadsto y \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024077 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1.0) y) x))