Data.Colour.SRGB:transferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 2.5s

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, 1.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 (- (+ y (* y x)) x))

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (y + (y * x)) - x
end function

Java

public static double code(double x, double y) {
	return (y + (y * x)) - x;
}

Python

def code(x, y):
	return (y + (y * x)) - x

Julia

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

MATLAB

function tmp = code(x, y)
	tmp = (y + (y * x)) - x;
end

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in x around 0 100.0%

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

3. Final simplification 100.0%

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

Alternative 2: 63.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+218}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{+172}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq -3.7 \cdot 10^{-17}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-22}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+108}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+245}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -5e+218)
   (- x)
   (if (<= x -6.6e+172)
     (* y x)
     (if (<= x -3.7e-17)
       (- x)
       (if (<= x 4.8e-22)
         y
         (if (<= x 1.1e+108) (- x) (if (<= x 4.2e+245) (* y x) (- x))))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -5e+218) {
		tmp = -x;
	} else if (x <= -6.6e+172) {
		tmp = y * x;
	} else if (x <= -3.7e-17) {
		tmp = -x;
	} else if (x <= 4.8e-22) {
		tmp = y;
	} else if (x <= 1.1e+108) {
		tmp = -x;
	} else if (x <= 4.2e+245) {
		tmp = y * x;
	} 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 <= (-5d+218)) then
        tmp = -x
    else if (x <= (-6.6d+172)) then
        tmp = y * x
    else if (x <= (-3.7d-17)) then
        tmp = -x
    else if (x <= 4.8d-22) then
        tmp = y
    else if (x <= 1.1d+108) then
        tmp = -x
    else if (x <= 4.2d+245) then
        tmp = y * x
    else
        tmp = -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -5e+218) {
		tmp = -x;
	} else if (x <= -6.6e+172) {
		tmp = y * x;
	} else if (x <= -3.7e-17) {
		tmp = -x;
	} else if (x <= 4.8e-22) {
		tmp = y;
	} else if (x <= 1.1e+108) {
		tmp = -x;
	} else if (x <= 4.2e+245) {
		tmp = y * x;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -5e+218:
		tmp = -x
	elif x <= -6.6e+172:
		tmp = y * x
	elif x <= -3.7e-17:
		tmp = -x
	elif x <= 4.8e-22:
		tmp = y
	elif x <= 1.1e+108:
		tmp = -x
	elif x <= 4.2e+245:
		tmp = y * x
	else:
		tmp = -x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -5e+218)
		tmp = Float64(-x);
	elseif (x <= -6.6e+172)
		tmp = Float64(y * x);
	elseif (x <= -3.7e-17)
		tmp = Float64(-x);
	elseif (x <= 4.8e-22)
		tmp = y;
	elseif (x <= 1.1e+108)
		tmp = Float64(-x);
	elseif (x <= 4.2e+245)
		tmp = Float64(y * x);
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -5e+218)
		tmp = -x;
	elseif (x <= -6.6e+172)
		tmp = y * x;
	elseif (x <= -3.7e-17)
		tmp = -x;
	elseif (x <= 4.8e-22)
		tmp = y;
	elseif (x <= 1.1e+108)
		tmp = -x;
	elseif (x <= 4.2e+245)
		tmp = y * x;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -5e+218], (-x), If[LessEqual[x, -6.6e+172], N[(y * x), $MachinePrecision], If[LessEqual[x, -3.7e-17], (-x), If[LessEqual[x, 4.8e-22], y, If[LessEqual[x, 1.1e+108], (-x), If[LessEqual[x, 4.2e+245], N[(y * x), $MachinePrecision], (-x)]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.99999999999999983e218 or -6.59999999999999965e172 < x < -3.6999999999999997e-17 or 4.80000000000000005e-22 < x < 1.1000000000000001e108 or 4.19999999999999992e245 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 60.2%

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

      1. neg-mul-1 60.2%

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

   4. Simplified 60.2%

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

   if -4.99999999999999983e218 < x < -6.59999999999999965e172 or 1.1000000000000001e108 < x < 4.19999999999999992e245

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 66.1%

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

   3. Taylor expanded in x around 0 66.1%

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

   4. Taylor expanded in x around inf 66.1%

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

   if -3.6999999999999997e-17 < x < 4.80000000000000005e-22

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 84.8%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+218}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{+172}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq -3.7 \cdot 10^{-17}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-22}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+108}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+245}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 3: 86.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-14} \lor \neg \left(y \leq 0.000114\right):\\ \;\;\;\;y \cdot \left(x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -4.5e-14) (not (<= y 0.000114))) (* y (+ x 1.0)) (- x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -4.5e-14) || !(y <= 0.000114)) {
		tmp = y * (x + 1.0);
	} 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 <= (-4.5d-14)) .or. (.not. (y <= 0.000114d0))) then
        tmp = y * (x + 1.0d0)
    else
        tmp = -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -4.5e-14) || !(y <= 0.000114)) {
		tmp = y * (x + 1.0);
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -4.5e-14) or not (y <= 0.000114):
		tmp = y * (x + 1.0)
	else:
		tmp = -x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -4.5e-14) || !(y <= 0.000114))
		tmp = Float64(y * Float64(x + 1.0));
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -4.5e-14) || ~((y <= 0.000114)))
		tmp = y * (x + 1.0);
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -4.5e-14], N[Not[LessEqual[y, 0.000114]], $MachinePrecision]], N[(y * N[(x + 1.0), $MachinePrecision]), $MachinePrecision], (-x)]

Derivation

1. Split input into 2 regimes

2. if y < -4.4999999999999998e-14 or 1.1400000000000001e-4 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 99.4%

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

   if -4.4999999999999998e-14 < y < 1.1400000000000001e-4

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 74.6%

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

      1. neg-mul-1 74.6%

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

   4. Simplified 74.6%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-14} \lor \neg \left(y \leq 0.000114\right):\\ \;\;\;\;y \cdot \left(x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 4: 87.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -11.5 \lor \neg \left(x \leq 1.55 \cdot 10^{-28}\right):\\ \;\;\;\;x \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -11.5) (not (<= x 1.55e-28))) (* x (- y 1.0)) (* y (+ x 1.0))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -11.5) || !(x <= 1.55e-28)) {
		tmp = x * (y - 1.0);
	} else {
		tmp = y * (x + 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 ((x <= (-11.5d0)) .or. (.not. (x <= 1.55d-28))) then
        tmp = x * (y - 1.0d0)
    else
        tmp = y * (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -11.5) || !(x <= 1.55e-28)) {
		tmp = x * (y - 1.0);
	} else {
		tmp = y * (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -11.5) or not (x <= 1.55e-28):
		tmp = x * (y - 1.0)
	else:
		tmp = y * (x + 1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -11.5) || !(x <= 1.55e-28))
		tmp = Float64(x * Float64(y - 1.0));
	else
		tmp = Float64(y * Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -11.5) || ~((x <= 1.55e-28)))
		tmp = x * (y - 1.0);
	else
		tmp = y * (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -11.5], N[Not[LessEqual[x, 1.55e-28]], $MachinePrecision]], N[(x * N[(y - 1.0), $MachinePrecision]), $MachinePrecision], N[(y * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -11.5 or 1.54999999999999996e-28 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 96.9%

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

   if -11.5 < x < 1.54999999999999996e-28

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 84.8%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -11.5 \lor \neg \left(x \leq 1.55 \cdot 10^{-28}\right):\\ \;\;\;\;x \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + 1\right)\\ \end{array} \]

Alternative 5: 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. Final simplification 100.0%

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

Alternative 6: 62.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{-15}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-26}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.5e-15) (- x) (if (<= x 2.05e-26) y (- x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.5e-15) {
		tmp = -x;
	} else if (x <= 2.05e-26) {
		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 <= (-2.5d-15)) then
        tmp = -x
    else if (x <= 2.05d-26) 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 <= -2.5e-15) {
		tmp = -x;
	} else if (x <= 2.05e-26) {
		tmp = y;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.5e-15:
		tmp = -x
	elif x <= 2.05e-26:
		tmp = y
	else:
		tmp = -x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.5e-15)
		tmp = Float64(-x);
	elseif (x <= 2.05e-26)
		tmp = y;
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.5e-15)
		tmp = -x;
	elseif (x <= 2.05e-26)
		tmp = y;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.5e-15], (-x), If[LessEqual[x, 2.05e-26], y, (-x)]]

Derivation

1. Split input into 2 regimes

2. if x < -2.5e-15 or 2.0499999999999999e-26 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 53.6%

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

      1. neg-mul-1 53.6%

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

   4. Simplified 53.6%

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

   if -2.5e-15 < x < 2.0499999999999999e-26

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 84.8%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{-15}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-26}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 7: 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. Taylor expanded in x around 0 43.2%

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

3. Final simplification 43.2%

   \[\leadsto y \]

Reproduce

herbie shell --seed 2023240 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1.0) y) x))