Data.Colour.SRGB:transferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 3.3s

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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. sub-neg 100.0%

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

   2. *-commutative 100.0%

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

   3. +-commutative 100.0%

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

   4. distribute-lft-in 100.0%

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

   5. *-rgt-identity 100.0%

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

   6. associate-+l+ 100.0%

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

   7. *-commutative 100.0%

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

   8. +-commutative 100.0%

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

   9. *-commutative 100.0%

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

   10. neg-mul-1 100.0%

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

   11. distribute-rgt-out 100.0%

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

   12. fma-define 100.0%

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

3. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, y + -1, y\right)} \]
4. Add Preprocessing

5. Final simplification 100.0%

   \[\leadsto \mathsf{fma}\left(x, y + -1, y\right) \]
6. Add Preprocessing

Alternative 2: 60.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.1 \cdot 10^{+258}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{+190}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{+31}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-93}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-7}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -7.1e+258)
   (* x y)
   (if (<= y -1.6e+190)
     y
     (if (<= y -6.8e+31)
       (* x y)
       (if (<= y -4.8e-93) y (if (<= y 8.2e-7) (- x) y))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -7.1e+258) {
		tmp = x * y;
	} else if (y <= -1.6e+190) {
		tmp = y;
	} else if (y <= -6.8e+31) {
		tmp = x * y;
	} else if (y <= -4.8e-93) {
		tmp = y;
	} else if (y <= 8.2e-7) {
		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 <= (-7.1d+258)) then
        tmp = x * y
    else if (y <= (-1.6d+190)) then
        tmp = y
    else if (y <= (-6.8d+31)) then
        tmp = x * y
    else if (y <= (-4.8d-93)) then
        tmp = y
    else if (y <= 8.2d-7) 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 <= -7.1e+258) {
		tmp = x * y;
	} else if (y <= -1.6e+190) {
		tmp = y;
	} else if (y <= -6.8e+31) {
		tmp = x * y;
	} else if (y <= -4.8e-93) {
		tmp = y;
	} else if (y <= 8.2e-7) {
		tmp = -x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -7.1e+258:
		tmp = x * y
	elif y <= -1.6e+190:
		tmp = y
	elif y <= -6.8e+31:
		tmp = x * y
	elif y <= -4.8e-93:
		tmp = y
	elif y <= 8.2e-7:
		tmp = -x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -7.1e+258)
		tmp = Float64(x * y);
	elseif (y <= -1.6e+190)
		tmp = y;
	elseif (y <= -6.8e+31)
		tmp = Float64(x * y);
	elseif (y <= -4.8e-93)
		tmp = y;
	elseif (y <= 8.2e-7)
		tmp = Float64(-x);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -7.1e+258)
		tmp = x * y;
	elseif (y <= -1.6e+190)
		tmp = y;
	elseif (y <= -6.8e+31)
		tmp = x * y;
	elseif (y <= -4.8e-93)
		tmp = y;
	elseif (y <= 8.2e-7)
		tmp = -x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -7.1e+258], N[(x * y), $MachinePrecision], If[LessEqual[y, -1.6e+190], y, If[LessEqual[y, -6.8e+31], N[(x * y), $MachinePrecision], If[LessEqual[y, -4.8e-93], y, If[LessEqual[y, 8.2e-7], (-x), y]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.1e258 or -1.6e190 < y < -6.7999999999999996e31

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 66.9%

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

   4. Taylor expanded in y around inf 66.9%

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

   if -7.1e258 < y < -1.6e190 or -6.7999999999999996e31 < y < -4.8000000000000002e-93 or 8.1999999999999998e-7 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 63.7%

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

   if -4.8000000000000002e-93 < y < 8.1999999999999998e-7

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 82.2%

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

      1. neg-mul-1 82.2%

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

   5. Simplified 82.2%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.1 \cdot 10^{+258}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{+190}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{+31}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-93}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-7}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-38} \lor \neg \left(x \leq 1.08 \cdot 10^{-14}\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -5e-38) (not (<= x 1.08e-14))) (* x (+ y -1.0)) y))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -5e-38) || !(x <= 1.08e-14)) {
		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 <= (-5d-38)) .or. (.not. (x <= 1.08d-14))) 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 <= -5e-38) || !(x <= 1.08e-14)) {
		tmp = x * (y + -1.0);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -5e-38) or not (x <= 1.08e-14):
		tmp = x * (y + -1.0)
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -5e-38) || !(x <= 1.08e-14))
		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 <= -5e-38) || ~((x <= 1.08e-14)))
		tmp = x * (y + -1.0);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -5e-38], N[Not[LessEqual[x, 1.08e-14]], $MachinePrecision]], N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision], y]

Derivation

1. Split input into 2 regimes

2. if x < -5.00000000000000033e-38 or 1.08000000000000004e-14 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 97.3%

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

   if -5.00000000000000033e-38 < x < 1.08000000000000004e-14

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 78.8%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-38} \lor \neg \left(x \leq 1.08 \cdot 10^{-14}\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.18 \cdot 10^{-92} \lor \neg \left(y \leq 1450000\right):\\ \;\;\;\;y \cdot \left(x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.18e-92) (not (<= y 1450000.0)))
   (* y (+ x 1.0))
   (* x (+ y -1.0))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.18e-92) || !(y <= 1450000.0)) {
		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 <= (-1.18d-92)) .or. (.not. (y <= 1450000.0d0))) 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 <= -1.18e-92) || !(y <= 1450000.0)) {
		tmp = y * (x + 1.0);
	} else {
		tmp = x * (y + -1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.18e-92) or not (y <= 1450000.0):
		tmp = y * (x + 1.0)
	else:
		tmp = x * (y + -1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.18e-92) || !(y <= 1450000.0))
		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 <= -1.18e-92) || ~((y <= 1450000.0)))
		tmp = y * (x + 1.0);
	else
		tmp = x * (y + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.18e-92], N[Not[LessEqual[y, 1450000.0]], $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 < -1.18e-92 or 1.45e6 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 96.9%

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

   if -1.18e-92 < y < 1.45e6

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 82.6%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.18 \cdot 10^{-92} \lor \neg \left(y \leq 1450000\right):\\ \;\;\;\;y \cdot \left(x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.18 \cdot 10^{-92}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-9}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.18e-92) y (if (<= y 1.9e-9) (- x) y)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.18e-92) {
		tmp = y;
	} else if (y <= 1.9e-9) {
		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 <= (-1.18d-92)) then
        tmp = y
    else if (y <= 1.9d-9) 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 <= -1.18e-92) {
		tmp = y;
	} else if (y <= 1.9e-9) {
		tmp = -x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.18e-92:
		tmp = y
	elif y <= 1.9e-9:
		tmp = -x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.18e-92)
		tmp = y;
	elseif (y <= 1.9e-9)
		tmp = Float64(-x);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.18e-92)
		tmp = y;
	elseif (y <= 1.9e-9)
		tmp = -x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.18e-92], y, If[LessEqual[y, 1.9e-9], (-x), y]]

Derivation

1. Split input into 2 regimes

2. if y < -1.18e-92 or 1.90000000000000006e-9 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 54.3%

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

   if -1.18e-92 < y < 1.90000000000000006e-9

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 82.2%

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

      1. neg-mul-1 82.2%

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

   5. Simplified 82.2%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.18 \cdot 10^{-92}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-9}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 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. Add Preprocessing

3. Final simplification 100.0%

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

Alternative 7: 39.2% 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 40.1%

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

4. Final simplification 40.1%

   \[\leadsto y \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024043 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1.0) y) x))