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. distribute-rgt1-in 100.0%

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

   3. *-commutative 100.0%

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

   4. associate-+l+ 100.0%

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

   5. *-commutative 100.0%

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

   6. +-commutative 100.0%

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

   7. *-commutative 100.0%

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

   8. neg-mul-1 100.0%

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

   9. distribute-rgt-out 100.0%

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

   10. 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: 61.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+140}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{-65}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-59}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+176}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.2e+140)
   (* x y)
   (if (<= y -6.8e-65)
     y
     (if (<= y 1.35e-59) (- x) (if (<= y 2.05e+176) y (* x y))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.2e+140) {
		tmp = x * y;
	} else if (y <= -6.8e-65) {
		tmp = y;
	} else if (y <= 1.35e-59) {
		tmp = -x;
	} else if (y <= 2.05e+176) {
		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 <= (-1.2d+140)) then
        tmp = x * y
    else if (y <= (-6.8d-65)) then
        tmp = y
    else if (y <= 1.35d-59) then
        tmp = -x
    else if (y <= 2.05d+176) 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 <= -1.2e+140) {
		tmp = x * y;
	} else if (y <= -6.8e-65) {
		tmp = y;
	} else if (y <= 1.35e-59) {
		tmp = -x;
	} else if (y <= 2.05e+176) {
		tmp = y;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.2e+140:
		tmp = x * y
	elif y <= -6.8e-65:
		tmp = y
	elif y <= 1.35e-59:
		tmp = -x
	elif y <= 2.05e+176:
		tmp = y
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.2e+140)
		tmp = Float64(x * y);
	elseif (y <= -6.8e-65)
		tmp = y;
	elseif (y <= 1.35e-59)
		tmp = Float64(-x);
	elseif (y <= 2.05e+176)
		tmp = y;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.2e+140)
		tmp = x * y;
	elseif (y <= -6.8e-65)
		tmp = y;
	elseif (y <= 1.35e-59)
		tmp = -x;
	elseif (y <= 2.05e+176)
		tmp = y;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.2e+140], N[(x * y), $MachinePrecision], If[LessEqual[y, -6.8e-65], y, If[LessEqual[y, 1.35e-59], (-x), If[LessEqual[y, 2.05e+176], y, N[(x * y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.2e140 or 2.05e176 < y

   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 68.8%

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

   if -1.2e140 < y < -6.79999999999999973e-65 or 1.3499999999999999e-59 < y < 2.05e176

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 61.5%

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

   if -6.79999999999999973e-65 < y < 1.3499999999999999e-59

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 81.9%

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

      1. neg-mul-1 81.9%

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

   5. Simplified 81.9%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+140}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{-65}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-59}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+176}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -12500 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -12500.0) (not (<= x 1.0))) (* x (+ y -1.0)) (- y x)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -12500.0) || !(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 <= (-12500.0d0)) .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 <= -12500.0) || !(x <= 1.0)) {
		tmp = x * (y + -1.0);
	} else {
		tmp = y - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -12500.0) 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 <= -12500.0) || !(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 <= -12500.0) || ~((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, -12500.0], 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 < -12500 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 98.9%

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

   if -12500 < x < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 99.8%

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

   4. Taylor expanded in y around 0 99.8%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -12500 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+137} \lor \neg \left(y \leq 1.35 \cdot 10^{+175}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -5.5e+137) (not (<= y 1.35e+175))) (* x y) (- y x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -5.5e+137) || !(y <= 1.35e+175)) {
		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 <= (-5.5d+137)) .or. (.not. (y <= 1.35d+175))) 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 <= -5.5e+137) || !(y <= 1.35e+175)) {
		tmp = x * y;
	} else {
		tmp = y - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -5.5e+137) or not (y <= 1.35e+175):
		tmp = x * y
	else:
		tmp = y - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -5.5e+137) || !(y <= 1.35e+175))
		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 <= -5.5e+137) || ~((y <= 1.35e+175)))
		tmp = x * y;
	else
		tmp = y - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -5.5e+137], N[Not[LessEqual[y, 1.35e+175]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(y - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.5000000000000002e137 or 1.35e175 < y

   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 68.8%

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

   if -5.5000000000000002e137 < y < 1.35e175

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 88.2%

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

   4. Taylor expanded in y around 0 88.2%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+137} \lor \neg \left(y \leq 1.35 \cdot 10^{+175}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 61.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{-66}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-59}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -8.8e-66) y (if (<= y 2.2e-59) (- x) y)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -8.8e-66) {
		tmp = y;
	} else if (y <= 2.2e-59) {
		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 <= (-8.8d-66)) then
        tmp = y
    else if (y <= 2.2d-59) 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 <= -8.8e-66) {
		tmp = y;
	} else if (y <= 2.2e-59) {
		tmp = -x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -8.8e-66:
		tmp = y
	elif y <= 2.2e-59:
		tmp = -x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -8.8e-66)
		tmp = y;
	elseif (y <= 2.2e-59)
		tmp = Float64(-x);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -8.8e-66)
		tmp = y;
	elseif (y <= 2.2e-59)
		tmp = -x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -8.8e-66], y, If[LessEqual[y, 2.2e-59], (-x), y]]

Derivation

1. Split input into 2 regimes

2. if y < -8.8000000000000004e-66 or 2.1999999999999999e-59 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 50.9%

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

   if -8.8000000000000004e-66 < y < 2.1999999999999999e-59

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 81.9%

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

      1. neg-mul-1 81.9%

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

   5. Simplified 81.9%

      \[\leadsto \color{blue}{-x} \]
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: 38.9% 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 37.8%

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

Reproduce

herbie shell --seed 2024157 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1.0) y) x))