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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. fma-neg 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 62.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+213}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{+67}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-16}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-94}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 30000000000:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -5e+213)
   (- x)
   (if (<= x -2.6e+67)
     (* x y)
     (if (<= x -6.5e-16)
       (- x)
       (if (<= x 3.7e-94) y (if (<= x 30000000000.0) (- x) (* x y)))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -5e+213) {
		tmp = -x;
	} else if (x <= -2.6e+67) {
		tmp = x * y;
	} else if (x <= -6.5e-16) {
		tmp = -x;
	} else if (x <= 3.7e-94) {
		tmp = y;
	} else if (x <= 30000000000.0) {
		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 <= (-5d+213)) then
        tmp = -x
    else if (x <= (-2.6d+67)) then
        tmp = x * y
    else if (x <= (-6.5d-16)) then
        tmp = -x
    else if (x <= 3.7d-94) then
        tmp = y
    else if (x <= 30000000000.0d0) 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 <= -5e+213) {
		tmp = -x;
	} else if (x <= -2.6e+67) {
		tmp = x * y;
	} else if (x <= -6.5e-16) {
		tmp = -x;
	} else if (x <= 3.7e-94) {
		tmp = y;
	} else if (x <= 30000000000.0) {
		tmp = -x;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -5e+213:
		tmp = -x
	elif x <= -2.6e+67:
		tmp = x * y
	elif x <= -6.5e-16:
		tmp = -x
	elif x <= 3.7e-94:
		tmp = y
	elif x <= 30000000000.0:
		tmp = -x
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -5e+213)
		tmp = Float64(-x);
	elseif (x <= -2.6e+67)
		tmp = Float64(x * y);
	elseif (x <= -6.5e-16)
		tmp = Float64(-x);
	elseif (x <= 3.7e-94)
		tmp = y;
	elseif (x <= 30000000000.0)
		tmp = Float64(-x);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -5e+213)
		tmp = -x;
	elseif (x <= -2.6e+67)
		tmp = x * y;
	elseif (x <= -6.5e-16)
		tmp = -x;
	elseif (x <= 3.7e-94)
		tmp = y;
	elseif (x <= 30000000000.0)
		tmp = -x;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -5e+213], (-x), If[LessEqual[x, -2.6e+67], N[(x * y), $MachinePrecision], If[LessEqual[x, -6.5e-16], (-x), If[LessEqual[x, 3.7e-94], y, If[LessEqual[x, 30000000000.0], (-x), N[(x * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.9999999999999998e213 or -2.6e67 < x < -6.50000000000000011e-16 or 3.6999999999999998e-94 < x < 3e10

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 78.7%

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

      1. neg-mul-1 78.7%

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

   5. Simplified 78.7%

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

   if -4.9999999999999998e213 < x < -2.6e67 or 3e10 < x

   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 61.3%

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

   if -6.50000000000000011e-16 < x < 3.6999999999999998e-94

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 81.3%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+213}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{+67}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-16}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-94}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 30000000000:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{-16} \lor \neg \left(x \leq 3.7 \cdot 10^{-94}\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.6e-16) (not (<= x 3.7e-94))) (* x (+ y -1.0)) y))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.6e-16) || !(x <= 3.7e-94)) {
		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 <= (-1.6d-16)) .or. (.not. (x <= 3.7d-94))) 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 <= -1.6e-16) || !(x <= 3.7e-94)) {
		tmp = x * (y + -1.0);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.6e-16) or not (x <= 3.7e-94):
		tmp = x * (y + -1.0)
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.6e-16) || !(x <= 3.7e-94))
		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 <= -1.6e-16) || ~((x <= 3.7e-94)))
		tmp = x * (y + -1.0);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.6e-16], N[Not[LessEqual[x, 3.7e-94]], $MachinePrecision]], N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision], y]

Derivation

1. Split input into 2 regimes

2. if x < -1.60000000000000011e-16 or 3.6999999999999998e-94 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 96.9%

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

   if -1.60000000000000011e-16 < x < 3.6999999999999998e-94

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 81.3%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{-16} \lor \neg \left(x \leq 3.7 \cdot 10^{-94}\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9500 \lor \neg \left(x \leq 1.15 \cdot 10^{-94}\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + 1\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -9500.0) (not (<= x 1.15e-94)))
   (* x (+ y -1.0))
   (* (+ x 1.0) y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -9500.0) || !(x <= 1.15e-94)) {
		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 <= (-9500.0d0)) .or. (.not. (x <= 1.15d-94))) 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 <= -9500.0) || !(x <= 1.15e-94)) {
		tmp = x * (y + -1.0);
	} else {
		tmp = (x + 1.0) * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -9500.0) or not (x <= 1.15e-94):
		tmp = x * (y + -1.0)
	else:
		tmp = (x + 1.0) * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -9500.0) || !(x <= 1.15e-94))
		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 <= -9500.0) || ~((x <= 1.15e-94)))
		tmp = x * (y + -1.0);
	else
		tmp = (x + 1.0) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -9500.0], N[Not[LessEqual[x, 1.15e-94]], $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 < -9500 or 1.15e-94 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 98.0%

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

   if -9500 < x < 1.15e-94

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 80.9%

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

      1. +-commutative 80.9%

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

   5. Simplified 80.9%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9500 \lor \neg \left(x \leq 1.15 \cdot 10^{-94}\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + 1\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 61.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{-16} \lor \neg \left(x \leq 3.8 \cdot 10^{-95}\right):\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -8.2e-16) (not (<= x 3.8e-95))) (- x) y))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -8.2e-16) || !(x <= 3.8e-95)) {
		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 <= (-8.2d-16)) .or. (.not. (x <= 3.8d-95))) 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 <= -8.2e-16) || !(x <= 3.8e-95)) {
		tmp = -x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -8.2e-16) or not (x <= 3.8e-95):
		tmp = -x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -8.2e-16) || !(x <= 3.8e-95))
		tmp = Float64(-x);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -8.2e-16) || ~((x <= 3.8e-95)))
		tmp = -x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -8.2e-16], N[Not[LessEqual[x, 3.8e-95]], $MachinePrecision]], (-x), y]

Derivation

1. Split input into 2 regimes

2. if x < -8.20000000000000012e-16 or 3.7999999999999997e-95 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 51.6%

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

      1. neg-mul-1 51.6%

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

   5. Simplified 51.6%

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

   if -8.20000000000000012e-16 < x < 3.7999999999999997e-95

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 81.3%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{-16} \lor \neg \left(x \leq 3.8 \cdot 10^{-95}\right):\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 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 7: 38.5% 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 39.0%

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

4. Final simplification 39.0%

   \[\leadsto y \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024059 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1.0) y) x))