Data.Colour.SRGB:transferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 3.8s

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. Add Preprocessing

Alternative 2: 62.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+215}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -7.6 \cdot 10^{+135}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{+83}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -400000:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{-14}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.7e+215)
   y
   (if (<= y -7.6e+135)
     (* x y)
     (if (<= y -1.8e+83)
       y
       (if (<= y -400000.0) (* x y) (if (<= y 5.3e-14) (- x) y))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.7e+215) {
		tmp = y;
	} else if (y <= -7.6e+135) {
		tmp = x * y;
	} else if (y <= -1.8e+83) {
		tmp = y;
	} else if (y <= -400000.0) {
		tmp = x * y;
	} else if (y <= 5.3e-14) {
		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 <= (-2.7d+215)) then
        tmp = y
    else if (y <= (-7.6d+135)) then
        tmp = x * y
    else if (y <= (-1.8d+83)) then
        tmp = y
    else if (y <= (-400000.0d0)) then
        tmp = x * y
    else if (y <= 5.3d-14) 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 <= -2.7e+215) {
		tmp = y;
	} else if (y <= -7.6e+135) {
		tmp = x * y;
	} else if (y <= -1.8e+83) {
		tmp = y;
	} else if (y <= -400000.0) {
		tmp = x * y;
	} else if (y <= 5.3e-14) {
		tmp = -x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.7e+215:
		tmp = y
	elif y <= -7.6e+135:
		tmp = x * y
	elif y <= -1.8e+83:
		tmp = y
	elif y <= -400000.0:
		tmp = x * y
	elif y <= 5.3e-14:
		tmp = -x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.7e+215)
		tmp = y;
	elseif (y <= -7.6e+135)
		tmp = Float64(x * y);
	elseif (y <= -1.8e+83)
		tmp = y;
	elseif (y <= -400000.0)
		tmp = Float64(x * y);
	elseif (y <= 5.3e-14)
		tmp = Float64(-x);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -2.7e+215)
		tmp = y;
	elseif (y <= -7.6e+135)
		tmp = x * y;
	elseif (y <= -1.8e+83)
		tmp = y;
	elseif (y <= -400000.0)
		tmp = x * y;
	elseif (y <= 5.3e-14)
		tmp = -x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.7e+215], y, If[LessEqual[y, -7.6e+135], N[(x * y), $MachinePrecision], If[LessEqual[y, -1.8e+83], y, If[LessEqual[y, -400000.0], N[(x * y), $MachinePrecision], If[LessEqual[y, 5.3e-14], (-x), y]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.7e215 or -7.6000000000000003e135 < y < -1.7999999999999999e83 or 5.3000000000000001e-14 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 63.1%

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

   if -2.7e215 < y < -7.6000000000000003e135 or -1.7999999999999999e83 < y < -4e5

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 95.6%

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

   4. Taylor expanded in x around inf 77.8%

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

   if -4e5 < y < 5.3000000000000001e-14

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 79.6%

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

      1. neg-mul-1 79.6%

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

   5. Simplified 79.6%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+215}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -7.6 \cdot 10^{+135}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{+83}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -400000:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{-14}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2300 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -2300.0) (not (<= x 1.0))) (* x (+ y -1.0)) (- y x)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -2300.0) || !(x <= 1.0)) {
		tmp = x * (y + -1.0);
	} 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 <= (-2300.0d0)) .or. (.not. (x <= 1.0d0))) then
        tmp = x * (y + (-1.0d0))
    else
        tmp = y - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -2300.0) || !(x <= 1.0)) {
		tmp = x * (y + -1.0);
	} else {
		tmp = y - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -2300.0) or not (x <= 1.0):
		tmp = x * (y + -1.0)
	else:
		tmp = y - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -2300.0) || !(x <= 1.0))
		tmp = Float64(x * Float64(y + -1.0));
	else
		tmp = Float64(y - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -2300.0) || ~((x <= 1.0)))
		tmp = x * (y + -1.0);
	else
		tmp = y - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -2300.0], N[Not[LessEqual[x, 1.0]], $MachinePrecision]], N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision], N[(y - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2300 or 1 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 99.5%

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

   if -2300 < x < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 99.2%

      \[\leadsto \color{blue}{1} \cdot y - x \]

   4. Taylor expanded in y around 0 99.2%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2300 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+215}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -6.4 \cdot 10^{+133}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.65e+215) y (if (<= y -6.4e+133) (* x y) (- y x))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.65e+215) {
		tmp = y;
	} else if (y <= -6.4e+133) {
		tmp = x * y;
	} 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 <= (-1.65d+215)) then
        tmp = y
    else if (y <= (-6.4d+133)) then
        tmp = x * y
    else
        tmp = y - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.65e+215) {
		tmp = y;
	} else if (y <= -6.4e+133) {
		tmp = x * y;
	} else {
		tmp = y - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.65e+215:
		tmp = y
	elif y <= -6.4e+133:
		tmp = x * y
	else:
		tmp = y - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.65e+215)
		tmp = y;
	elseif (y <= -6.4e+133)
		tmp = Float64(x * y);
	else
		tmp = Float64(y - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.65e+215)
		tmp = y;
	elseif (y <= -6.4e+133)
		tmp = x * y;
	else
		tmp = y - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.65e+215], y, If[LessEqual[y, -6.4e+133], N[(x * y), $MachinePrecision], N[(y - x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.6499999999999999e215

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 70.5%

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

   if -1.6499999999999999e215 < y < -6.39999999999999994e133

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 100.0%

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

   4. Taylor expanded in x around inf 80.6%

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

   if -6.39999999999999994e133 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 81.3%

      \[\leadsto \color{blue}{1} \cdot y - x \]

   4. Taylor expanded in y around 0 81.3%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+215}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -6.4 \cdot 10^{+133}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 62.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-20}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-13}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.6e-20) y (if (<= y 1.55e-13) (- x) y)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.6e-20) {
		tmp = y;
	} else if (y <= 1.55e-13) {
		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 <= (-1.6d-20)) then
        tmp = y
    else if (y <= 1.55d-13) 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 <= -1.6e-20) {
		tmp = y;
	} else if (y <= 1.55e-13) {
		tmp = -x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.6e-20:
		tmp = y
	elif y <= 1.55e-13:
		tmp = -x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.6e-20)
		tmp = y;
	elseif (y <= 1.55e-13)
		tmp = Float64(-x);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.6e-20)
		tmp = y;
	elseif (y <= 1.55e-13)
		tmp = -x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.6e-20], y, If[LessEqual[y, 1.55e-13], (-x), y]]

Derivation

1. Split input into 2 regimes

2. if y < -1.59999999999999985e-20 or 1.55e-13 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 54.6%

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

   if -1.59999999999999985e-20 < y < 1.55e-13

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 81.8%

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

      1. neg-mul-1 81.8%

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

   5. Simplified 81.8%

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

3. Taylor expanded in x around 0 37.5%

   \[\leadsto \color{blue}{y} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024130 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1.0) y) x))