Data.Colour.SRGB:transferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 4.2s

Alternatives: 8

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. Add Preprocessing
3. Step-by-step derivation

   1. *-commutative 100.0%

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

   2. distribute-lft-in 100.0%

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

   3. *-commutative 100.0%

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

   4. *-un-lft-identity 100.0%

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

4. Applied egg-rr 100.0%

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

5. Final simplification 100.0%

   \[\leadsto \left(y + y \cdot x\right) - x \]
6. Add Preprocessing

Alternative 2: 60.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+240}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{+135}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{+107}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-76}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-123}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+31}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+203}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3.8e+240)
   (* y x)
   (if (<= y -4.1e+135)
     y
     (if (<= y -1.25e+107)
       (* y x)
       (if (<= y -3.2e-76)
         y
         (if (<= y 3.4e-123)
           (- x)
           (if (<= y 1.3e+31) y (if (<= y 1.7e+203) (* y x) y))))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3.8e+240) {
		tmp = y * x;
	} else if (y <= -4.1e+135) {
		tmp = y;
	} else if (y <= -1.25e+107) {
		tmp = y * x;
	} else if (y <= -3.2e-76) {
		tmp = y;
	} else if (y <= 3.4e-123) {
		tmp = -x;
	} else if (y <= 1.3e+31) {
		tmp = y;
	} else if (y <= 1.7e+203) {
		tmp = y * 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 <= (-3.8d+240)) then
        tmp = y * x
    else if (y <= (-4.1d+135)) then
        tmp = y
    else if (y <= (-1.25d+107)) then
        tmp = y * x
    else if (y <= (-3.2d-76)) then
        tmp = y
    else if (y <= 3.4d-123) then
        tmp = -x
    else if (y <= 1.3d+31) then
        tmp = y
    else if (y <= 1.7d+203) then
        tmp = y * x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -3.8e+240) {
		tmp = y * x;
	} else if (y <= -4.1e+135) {
		tmp = y;
	} else if (y <= -1.25e+107) {
		tmp = y * x;
	} else if (y <= -3.2e-76) {
		tmp = y;
	} else if (y <= 3.4e-123) {
		tmp = -x;
	} else if (y <= 1.3e+31) {
		tmp = y;
	} else if (y <= 1.7e+203) {
		tmp = y * x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3.8e+240:
		tmp = y * x
	elif y <= -4.1e+135:
		tmp = y
	elif y <= -1.25e+107:
		tmp = y * x
	elif y <= -3.2e-76:
		tmp = y
	elif y <= 3.4e-123:
		tmp = -x
	elif y <= 1.3e+31:
		tmp = y
	elif y <= 1.7e+203:
		tmp = y * x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3.8e+240)
		tmp = Float64(y * x);
	elseif (y <= -4.1e+135)
		tmp = y;
	elseif (y <= -1.25e+107)
		tmp = Float64(y * x);
	elseif (y <= -3.2e-76)
		tmp = y;
	elseif (y <= 3.4e-123)
		tmp = Float64(-x);
	elseif (y <= 1.3e+31)
		tmp = y;
	elseif (y <= 1.7e+203)
		tmp = Float64(y * x);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -3.8e+240)
		tmp = y * x;
	elseif (y <= -4.1e+135)
		tmp = y;
	elseif (y <= -1.25e+107)
		tmp = y * x;
	elseif (y <= -3.2e-76)
		tmp = y;
	elseif (y <= 3.4e-123)
		tmp = -x;
	elseif (y <= 1.3e+31)
		tmp = y;
	elseif (y <= 1.7e+203)
		tmp = y * x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3.8e+240], N[(y * x), $MachinePrecision], If[LessEqual[y, -4.1e+135], y, If[LessEqual[y, -1.25e+107], N[(y * x), $MachinePrecision], If[LessEqual[y, -3.2e-76], y, If[LessEqual[y, 3.4e-123], (-x), If[LessEqual[y, 1.3e+31], y, If[LessEqual[y, 1.7e+203], N[(y * x), $MachinePrecision], y]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.8000000000000003e240 or -4.1e135 < y < -1.25e107 or 1.3e31 < y < 1.7000000000000001e203

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. distribute-lft-in 100.0%

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

      3. *-commutative 100.0%

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

      4. *-un-lft-identity 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around inf 100.0%

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

   6. Taylor expanded in x around inf 76.2%

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

      1. *-commutative 76.2%

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

   8. Simplified 76.2%

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

   if -3.8000000000000003e240 < y < -4.1e135 or -1.25e107 < y < -3.1999999999999998e-76 or 3.4000000000000001e-123 < y < 1.3e31 or 1.7000000000000001e203 < y

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. distribute-lft-in 100.0%

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

      3. *-commutative 100.0%

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

      4. *-un-lft-identity 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in x around 0 63.3%

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

   if -3.1999999999999998e-76 < y < 3.4000000000000001e-123

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 83.8%

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

      1. neg-mul-1 83.8%

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

   5. Simplified 83.8%

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

Alternative 3: 75.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+242}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{+135}:\\ \;\;\;\;y - x\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{+110}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+30}:\\ \;\;\;\;y - x\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+207}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -5e+242)
   (* y x)
   (if (<= y -2.15e+135)
     (- y x)
     (if (<= y -2.7e+110)
       (* y x)
       (if (<= y 1.95e+30) (- y x) (if (<= y 2.25e+207) (* y x) y))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -5e+242) {
		tmp = y * x;
	} else if (y <= -2.15e+135) {
		tmp = y - x;
	} else if (y <= -2.7e+110) {
		tmp = y * x;
	} else if (y <= 1.95e+30) {
		tmp = y - x;
	} else if (y <= 2.25e+207) {
		tmp = y * 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 <= (-5d+242)) then
        tmp = y * x
    else if (y <= (-2.15d+135)) then
        tmp = y - x
    else if (y <= (-2.7d+110)) then
        tmp = y * x
    else if (y <= 1.95d+30) then
        tmp = y - x
    else if (y <= 2.25d+207) then
        tmp = y * x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -5e+242) {
		tmp = y * x;
	} else if (y <= -2.15e+135) {
		tmp = y - x;
	} else if (y <= -2.7e+110) {
		tmp = y * x;
	} else if (y <= 1.95e+30) {
		tmp = y - x;
	} else if (y <= 2.25e+207) {
		tmp = y * x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -5e+242:
		tmp = y * x
	elif y <= -2.15e+135:
		tmp = y - x
	elif y <= -2.7e+110:
		tmp = y * x
	elif y <= 1.95e+30:
		tmp = y - x
	elif y <= 2.25e+207:
		tmp = y * x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -5e+242)
		tmp = Float64(y * x);
	elseif (y <= -2.15e+135)
		tmp = Float64(y - x);
	elseif (y <= -2.7e+110)
		tmp = Float64(y * x);
	elseif (y <= 1.95e+30)
		tmp = Float64(y - x);
	elseif (y <= 2.25e+207)
		tmp = Float64(y * x);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -5e+242)
		tmp = y * x;
	elseif (y <= -2.15e+135)
		tmp = y - x;
	elseif (y <= -2.7e+110)
		tmp = y * x;
	elseif (y <= 1.95e+30)
		tmp = y - x;
	elseif (y <= 2.25e+207)
		tmp = y * x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -5e+242], N[(y * x), $MachinePrecision], If[LessEqual[y, -2.15e+135], N[(y - x), $MachinePrecision], If[LessEqual[y, -2.7e+110], N[(y * x), $MachinePrecision], If[LessEqual[y, 1.95e+30], N[(y - x), $MachinePrecision], If[LessEqual[y, 2.25e+207], N[(y * x), $MachinePrecision], y]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.0000000000000004e242 or -2.14999999999999986e135 < y < -2.7000000000000001e110 or 1.95000000000000005e30 < y < 2.25000000000000002e207

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. distribute-lft-in 100.0%

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

      3. *-commutative 100.0%

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

      4. *-un-lft-identity 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around inf 100.0%

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

   6. Taylor expanded in x around inf 76.2%

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

      1. *-commutative 76.2%

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

   8. Simplified 76.2%

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

   if -5.0000000000000004e242 < y < -2.14999999999999986e135 or -2.7000000000000001e110 < y < 1.95000000000000005e30

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 92.5%

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

   if 2.25000000000000002e207 < y

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. distribute-lft-in 100.0%

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

      3. *-commutative 100.0%

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

      4. *-un-lft-identity 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in x around 0 61.3%

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

Alternative 4: 98.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 0.029\right):\\ \;\;\;\;x \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.0) (not (<= x 0.029))) (* x (- y 1.0)) (- y x)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.0) || !(x <= 0.029)) {
		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 <= (-1.0d0)) .or. (.not. (x <= 0.029d0))) 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 <= -1.0) || !(x <= 0.029)) {
		tmp = x * (y - 1.0);
	} else {
		tmp = y - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.0) or not (x <= 0.029):
		tmp = x * (y - 1.0)
	else:
		tmp = y - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.0) || !(x <= 0.029))
		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 <= -1.0) || ~((x <= 0.029)))
		tmp = x * (y - 1.0);
	else
		tmp = y - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.0], N[Not[LessEqual[x, 0.029]], $MachinePrecision]], N[(x * N[(y - 1.0), $MachinePrecision]), $MachinePrecision], N[(y - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1 or 0.0290000000000000015 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 99.3%

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

   if -1 < x < 0.0290000000000000015

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 99.4%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 0.029\right):\\ \;\;\;\;x \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;y \cdot x - x\\ \mathbf{elif}\;x \leq 0.029:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y - 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.0) (- (* y x) x) (if (<= x 0.029) (- y x) (* x (- y 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.0) {
		tmp = (y * x) - x;
	} else if (x <= 0.029) {
		tmp = y - x;
	} else {
		tmp = x * (y - 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 <= (-1.0d0)) then
        tmp = (y * x) - x
    else if (x <= 0.029d0) then
        tmp = y - x
    else
        tmp = x * (y - 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.0) {
		tmp = (y * x) - x;
	} else if (x <= 0.029) {
		tmp = y - x;
	} else {
		tmp = x * (y - 1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.0:
		tmp = (y * x) - x
	elif x <= 0.029:
		tmp = y - x
	else:
		tmp = x * (y - 1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.0)
		tmp = Float64(Float64(y * x) - x);
	elseif (x <= 0.029)
		tmp = Float64(y - x);
	else
		tmp = Float64(x * Float64(y - 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.0)
		tmp = (y * x) - x;
	elseif (x <= 0.029)
		tmp = y - x;
	else
		tmp = x * (y - 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.0], N[(N[(y * x), $MachinePrecision] - x), $MachinePrecision], If[LessEqual[x, 0.029], N[(y - x), $MachinePrecision], N[(x * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 98.9%

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

      1. *-commutative 98.9%

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

   5. Simplified 98.9%

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

   if -1 < x < 0.0290000000000000015

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 99.4%

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

   if 0.0290000000000000015 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 99.7%

      \[\leadsto \color{blue}{x \cdot \left(y - 1\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 63.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{-12} \lor \neg \left(x \leq 1.25 \cdot 10^{-15}\right):\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -4.6e-12) (not (<= x 1.25e-15))) (- x) y))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -4.6e-12) || !(x <= 1.25e-15)) {
		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 <= (-4.6d-12)) .or. (.not. (x <= 1.25d-15))) 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 <= -4.6e-12) || !(x <= 1.25e-15)) {
		tmp = -x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -4.6e-12) or not (x <= 1.25e-15):
		tmp = -x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -4.6e-12) || !(x <= 1.25e-15))
		tmp = Float64(-x);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -4.6e-12) || ~((x <= 1.25e-15)))
		tmp = -x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -4.6e-12], N[Not[LessEqual[x, 1.25e-15]], $MachinePrecision]], (-x), y]

Derivation

1. Split input into 2 regimes

2. if x < -4.59999999999999979e-12 or 1.25e-15 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 51.4%

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

      1. neg-mul-1 51.4%

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

   5. Simplified 51.4%

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

   if -4.59999999999999979e-12 < x < 1.25e-15

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. distribute-lft-in 100.0%

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

      3. *-commutative 100.0%

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

      4. *-un-lft-identity 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in x around 0 77.6%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{-12} \lor \neg \left(x \leq 1.25 \cdot 10^{-15}\right):\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 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 8: 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. Step-by-step derivation

   1. *-commutative 100.0%

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

   2. distribute-lft-in 100.0%

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

   3. *-commutative 100.0%

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

   4. *-un-lft-identity 100.0%

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

4. Applied egg-rr 100.0%

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

5. Taylor expanded in x around 0 39.4%

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

Reproduce

herbie shell --seed 2024084 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1.0) y) x))