Data.Colour.SRGB:transferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 4.8s

Alternatives: 7

Speedup: 0.1×

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%

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

   4. distribute-rgt1-in 100.0%

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

   5. associate-+l+ 100.0%

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

   6. +-commutative 100.0%

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

   7. neg-mul-1 100.0%

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

   8. *-commutative 100.0%

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

   9. distribute-lft-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. Final simplification 100.0%

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

Alternative 2: 63.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-14}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-54}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+134}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+203}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.3e-14)
   y
   (if (<= y 1.7e-54)
     (- x)
     (if (<= y 6.6e+134) y (if (<= y 2.5e+203) (* x y) y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.3e-14) {
		tmp = y;
	} else if (y <= 1.7e-54) {
		tmp = -x;
	} else if (y <= 6.6e+134) {
		tmp = y;
	} else if (y <= 2.5e+203) {
		tmp = x * y;
	} 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 <= (-2.3d-14)) then
        tmp = y
    else if (y <= 1.7d-54) then
        tmp = -x
    else if (y <= 6.6d+134) then
        tmp = y
    else if (y <= 2.5d+203) then
        tmp = x * y
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -2.3e-14) {
		tmp = y;
	} else if (y <= 1.7e-54) {
		tmp = -x;
	} else if (y <= 6.6e+134) {
		tmp = y;
	} else if (y <= 2.5e+203) {
		tmp = x * y;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.3e-14:
		tmp = y
	elif y <= 1.7e-54:
		tmp = -x
	elif y <= 6.6e+134:
		tmp = y
	elif y <= 2.5e+203:
		tmp = x * y
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.3e-14)
		tmp = y;
	elseif (y <= 1.7e-54)
		tmp = Float64(-x);
	elseif (y <= 6.6e+134)
		tmp = y;
	elseif (y <= 2.5e+203)
		tmp = Float64(x * y);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -2.3e-14)
		tmp = y;
	elseif (y <= 1.7e-54)
		tmp = -x;
	elseif (y <= 6.6e+134)
		tmp = y;
	elseif (y <= 2.5e+203)
		tmp = x * y;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.3e-14], y, If[LessEqual[y, 1.7e-54], (-x), If[LessEqual[y, 6.6e+134], y, If[LessEqual[y, 2.5e+203], N[(x * y), $MachinePrecision], y]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.29999999999999998e-14 or 1.69999999999999994e-54 < y < 6.6e134 or 2.49999999999999997e203 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

   4. Taylor expanded in x around 0 65.5%

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

   if -2.29999999999999998e-14 < y < 1.69999999999999994e-54

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 86.2%

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

      1. neg-mul-1 86.2%

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

   5. Simplified 86.2%

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

   if 6.6e134 < y < 2.49999999999999997e203

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 73.4%

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

      1. *-commutative 73.4%

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

   5. Simplified 73.4%

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

   6. Taylor expanded in y around inf 73.4%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-14}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-54}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+134}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+203}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -14500000000 \lor \neg \left(y \leq 0.025\right):\\ \;\;\;\;y \cdot \left(x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -14500000000.0) (not (<= y 0.025))) (* y (+ x 1.0)) (- y x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -14500000000.0) || !(y <= 0.025)) {
		tmp = y * (x + 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 ((y <= (-14500000000.0d0)) .or. (.not. (y <= 0.025d0))) then
        tmp = y * (x + 1.0d0)
    else
        tmp = y - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -14500000000.0) || !(y <= 0.025)) {
		tmp = y * (x + 1.0);
	} else {
		tmp = y - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -14500000000.0) or not (y <= 0.025):
		tmp = y * (x + 1.0)
	else:
		tmp = y - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -14500000000.0) || !(y <= 0.025))
		tmp = Float64(y * Float64(x + 1.0));
	else
		tmp = Float64(y - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -14500000000.0) || ~((y <= 0.025)))
		tmp = y * (x + 1.0);
	else
		tmp = y - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -14500000000.0], N[Not[LessEqual[y, 0.025]], $MachinePrecision]], N[(y * N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(y - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.45e10 or 0.025000000000000001 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

   4. Taylor expanded in y around inf 99.8%

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

      1. +-commutative 99.8%

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

   6. Simplified 99.8%

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

   if -1.45e10 < y < 0.025000000000000001

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 99.5%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -14500000000 \lor \neg \left(y \leq 0.025\right):\\ \;\;\;\;y \cdot \left(x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 8.5 \cdot 10^{+135} \lor \neg \left(y \leq 5.2 \cdot 10^{+202}\right):\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y 8.5e+135) (not (<= y 5.2e+202))) (- y x) (* x y)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= 8.5e+135) || !(y <= 5.2e+202)) {
		tmp = y - 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 ((y <= 8.5d+135) .or. (.not. (y <= 5.2d+202))) then
        tmp = y - x
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= 8.5e+135) || !(y <= 5.2e+202)) {
		tmp = y - x;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= 8.5e+135) or not (y <= 5.2e+202):
		tmp = y - x
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= 8.5e+135) || !(y <= 5.2e+202))
		tmp = Float64(y - x);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= 8.5e+135) || ~((y <= 5.2e+202)))
		tmp = y - x;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, 8.5e+135], N[Not[LessEqual[y, 5.2e+202]], $MachinePrecision]], N[(y - x), $MachinePrecision], N[(x * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 8.49999999999999992e135 or 5.2000000000000004e202 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 84.6%

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

   if 8.49999999999999992e135 < y < 5.2000000000000004e202

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 73.4%

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

      1. *-commutative 73.4%

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

   5. Simplified 73.4%

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

   6. Taylor expanded in y around inf 73.4%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 8.5 \cdot 10^{+135} \lor \neg \left(y \leq 5.2 \cdot 10^{+202}\right):\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 62.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-14}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-53}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -9.5e-14) y (if (<= y 6.8e-53) (- x) y)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -9.5e-14) {
		tmp = y;
	} else if (y <= 6.8e-53) {
		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 <= (-9.5d-14)) then
        tmp = y
    else if (y <= 6.8d-53) 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 <= -9.5e-14) {
		tmp = y;
	} else if (y <= 6.8e-53) {
		tmp = -x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -9.5e-14:
		tmp = y
	elif y <= 6.8e-53:
		tmp = -x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -9.5e-14)
		tmp = y;
	elseif (y <= 6.8e-53)
		tmp = Float64(-x);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -9.5e-14)
		tmp = y;
	elseif (y <= 6.8e-53)
		tmp = -x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -9.5e-14], y, If[LessEqual[y, 6.8e-53], (-x), y]]

Derivation

1. Split input into 2 regimes

2. if y < -9.4999999999999999e-14 or 6.8e-53 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

   4. Taylor expanded in x around 0 61.1%

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

   if -9.4999999999999999e-14 < y < 6.8e-53

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 86.2%

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

      1. neg-mul-1 86.2%

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

   5. Simplified 86.2%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-14}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-53}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = y + (x * (y + (-1.0d0)))
end function

Java

public static double code(double x, double y) {
	return y + (x * (y + -1.0));
}

Python

def code(x, y):
	return y + (x * (y + -1.0))

Julia

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

MATLAB

function tmp = code(x, y)
	tmp = y + (x * (y + -1.0));
end

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in x around 0 100.0%

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

4. Final simplification 100.0%

   \[\leadsto y + x \cdot \left(y + -1\right) \]
5. 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 0 100.0%

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

4. Taylor expanded in x around 0 40.0%

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

5. Final simplification 40.0%

   \[\leadsto y \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024046 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1.0) y) x))