Data.Colour.SRGB:transferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 4.1s

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. *-commutative 100.0%

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

   3. +-commutative 100.0%

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

   4. distribute-lft-in 100.0%

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

   5. *-rgt-identity 100.0%

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

   6. associate-+l+ 100.0%

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

   7. *-commutative 100.0%

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

   8. +-commutative 100.0%

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

   9. *-commutative 100.0%

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

   10. neg-mul-1 100.0%

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

   11. distribute-rgt-out 100.0%

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

   12. 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: 62.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+270}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{+210}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{+48}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{-58}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-29}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+32} \lor \neg \left(x \leq 4.9 \cdot 10^{+182}\right) \land x \leq 1.85 \cdot 10^{+203}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -4e+270)
   (* x y)
   (if (<= x -3.6e+210)
     (- x)
     (if (<= x -2.8e+48)
       (* x y)
       (if (<= x -2.2e-58)
         (- x)
         (if (<= x 3.9e-29)
           y
           (if (or (<= x 2.9e+32) (and (not (<= x 4.9e+182)) (<= x 1.85e+203)))
             (- x)
             (* x y))))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -4e+270) {
		tmp = x * y;
	} else if (x <= -3.6e+210) {
		tmp = -x;
	} else if (x <= -2.8e+48) {
		tmp = x * y;
	} else if (x <= -2.2e-58) {
		tmp = -x;
	} else if (x <= 3.9e-29) {
		tmp = y;
	} else if ((x <= 2.9e+32) || (!(x <= 4.9e+182) && (x <= 1.85e+203))) {
		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 <= (-4d+270)) then
        tmp = x * y
    else if (x <= (-3.6d+210)) then
        tmp = -x
    else if (x <= (-2.8d+48)) then
        tmp = x * y
    else if (x <= (-2.2d-58)) then
        tmp = -x
    else if (x <= 3.9d-29) then
        tmp = y
    else if ((x <= 2.9d+32) .or. (.not. (x <= 4.9d+182)) .and. (x <= 1.85d+203)) 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 <= -4e+270) {
		tmp = x * y;
	} else if (x <= -3.6e+210) {
		tmp = -x;
	} else if (x <= -2.8e+48) {
		tmp = x * y;
	} else if (x <= -2.2e-58) {
		tmp = -x;
	} else if (x <= 3.9e-29) {
		tmp = y;
	} else if ((x <= 2.9e+32) || (!(x <= 4.9e+182) && (x <= 1.85e+203))) {
		tmp = -x;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -4e+270:
		tmp = x * y
	elif x <= -3.6e+210:
		tmp = -x
	elif x <= -2.8e+48:
		tmp = x * y
	elif x <= -2.2e-58:
		tmp = -x
	elif x <= 3.9e-29:
		tmp = y
	elif (x <= 2.9e+32) or (not (x <= 4.9e+182) and (x <= 1.85e+203)):
		tmp = -x
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -4e+270)
		tmp = Float64(x * y);
	elseif (x <= -3.6e+210)
		tmp = Float64(-x);
	elseif (x <= -2.8e+48)
		tmp = Float64(x * y);
	elseif (x <= -2.2e-58)
		tmp = Float64(-x);
	elseif (x <= 3.9e-29)
		tmp = y;
	elseif ((x <= 2.9e+32) || (!(x <= 4.9e+182) && (x <= 1.85e+203)))
		tmp = Float64(-x);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -4e+270)
		tmp = x * y;
	elseif (x <= -3.6e+210)
		tmp = -x;
	elseif (x <= -2.8e+48)
		tmp = x * y;
	elseif (x <= -2.2e-58)
		tmp = -x;
	elseif (x <= 3.9e-29)
		tmp = y;
	elseif ((x <= 2.9e+32) || (~((x <= 4.9e+182)) && (x <= 1.85e+203)))
		tmp = -x;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -4e+270], N[(x * y), $MachinePrecision], If[LessEqual[x, -3.6e+210], (-x), If[LessEqual[x, -2.8e+48], N[(x * y), $MachinePrecision], If[LessEqual[x, -2.2e-58], (-x), If[LessEqual[x, 3.9e-29], y, If[Or[LessEqual[x, 2.9e+32], And[N[Not[LessEqual[x, 4.9e+182]], $MachinePrecision], LessEqual[x, 1.85e+203]]], (-x), N[(x * y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.0000000000000002e270 or -3.6000000000000003e210 < x < -2.80000000000000012e48 or 2.90000000000000003e32 < x < 4.9e182 or 1.85e203 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 64.5%

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

      1. distribute-lft-in 64.5%

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

      2. *-rgt-identity 64.5%

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

      3. +-commutative 64.5%

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

   5. Applied egg-rr 64.5%

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

   6. Taylor expanded in x around inf 64.5%

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

      1. *-commutative 64.5%

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

   8. Simplified 64.5%

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

   if -4.0000000000000002e270 < x < -3.6000000000000003e210 or -2.80000000000000012e48 < x < -2.20000000000000006e-58 or 3.8999999999999998e-29 < x < 2.90000000000000003e32 or 4.9e182 < x < 1.85e203

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 63.5%

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

      1. neg-mul-1 63.5%

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

   5. Simplified 63.5%

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

   if -2.20000000000000006e-58 < x < 3.8999999999999998e-29

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 88.8%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+270}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{+210}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{+48}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{-58}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-29}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+32} \lor \neg \left(x \leq 4.9 \cdot 10^{+182}\right) \land x \leq 1.85 \cdot 10^{+203}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+205}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{+163}:\\ \;\;\;\;y - x\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{+145}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -4 \cdot 10^{+118}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -1 \cdot 10^{+85} \lor \neg \left(y \leq 1.06 \cdot 10^{+54}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -5.8e+205)
   (* x y)
   (if (<= y -1.05e+163)
     (- y x)
     (if (<= y -2.1e+145)
       (* x y)
       (if (<= y -4e+118)
         y
         (if (or (<= y -1e+85) (not (<= y 1.06e+54))) (* x y) (- y x)))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -5.8e+205) {
		tmp = x * y;
	} else if (y <= -1.05e+163) {
		tmp = y - x;
	} else if (y <= -2.1e+145) {
		tmp = x * y;
	} else if (y <= -4e+118) {
		tmp = y;
	} else if ((y <= -1e+85) || !(y <= 1.06e+54)) {
		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 <= (-5.8d+205)) then
        tmp = x * y
    else if (y <= (-1.05d+163)) then
        tmp = y - x
    else if (y <= (-2.1d+145)) then
        tmp = x * y
    else if (y <= (-4d+118)) then
        tmp = y
    else if ((y <= (-1d+85)) .or. (.not. (y <= 1.06d+54))) 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 <= -5.8e+205) {
		tmp = x * y;
	} else if (y <= -1.05e+163) {
		tmp = y - x;
	} else if (y <= -2.1e+145) {
		tmp = x * y;
	} else if (y <= -4e+118) {
		tmp = y;
	} else if ((y <= -1e+85) || !(y <= 1.06e+54)) {
		tmp = x * y;
	} else {
		tmp = y - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -5.8e+205:
		tmp = x * y
	elif y <= -1.05e+163:
		tmp = y - x
	elif y <= -2.1e+145:
		tmp = x * y
	elif y <= -4e+118:
		tmp = y
	elif (y <= -1e+85) or not (y <= 1.06e+54):
		tmp = x * y
	else:
		tmp = y - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -5.8e+205)
		tmp = Float64(x * y);
	elseif (y <= -1.05e+163)
		tmp = Float64(y - x);
	elseif (y <= -2.1e+145)
		tmp = Float64(x * y);
	elseif (y <= -4e+118)
		tmp = y;
	elseif ((y <= -1e+85) || !(y <= 1.06e+54))
		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 <= -5.8e+205)
		tmp = x * y;
	elseif (y <= -1.05e+163)
		tmp = y - x;
	elseif (y <= -2.1e+145)
		tmp = x * y;
	elseif (y <= -4e+118)
		tmp = y;
	elseif ((y <= -1e+85) || ~((y <= 1.06e+54)))
		tmp = x * y;
	else
		tmp = y - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -5.8e+205], N[(x * y), $MachinePrecision], If[LessEqual[y, -1.05e+163], N[(y - x), $MachinePrecision], If[LessEqual[y, -2.1e+145], N[(x * y), $MachinePrecision], If[LessEqual[y, -4e+118], y, If[Or[LessEqual[y, -1e+85], N[Not[LessEqual[y, 1.06e+54]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(y - x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.8000000000000003e205 or -1.05e163 < y < -2.09999999999999989e145 or -3.99999999999999987e118 < y < -1e85 or 1.06e54 < 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. Step-by-step derivation

      1. distribute-lft-in 100.0%

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

      2. *-rgt-identity 100.0%

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

      3. +-commutative 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in x around inf 62.7%

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

      1. *-commutative 62.7%

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

   8. Simplified 62.7%

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

   if -5.8000000000000003e205 < y < -1.05e163 or -1e85 < y < 1.06e54

   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 89.9%

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

   if -2.09999999999999989e145 < y < -3.99999999999999987e118

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 85.2%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+205}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{+163}:\\ \;\;\;\;y - x\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{+145}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -4 \cdot 10^{+118}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -1 \cdot 10^{+85} \lor \neg \left(y \leq 1.06 \cdot 10^{+54}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -360000000000 \lor \neg \left(x \leq 8.6 \cdot 10^{-30}\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -360000000000.0) (not (<= x 8.6e-30)))
   (* x (+ y -1.0))
   (- y x)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -360000000000.0) || !(x <= 8.6e-30)) {
		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 <= (-360000000000.0d0)) .or. (.not. (x <= 8.6d-30))) 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 <= -360000000000.0) || !(x <= 8.6e-30)) {
		tmp = x * (y + -1.0);
	} else {
		tmp = y - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -360000000000.0) or not (x <= 8.6e-30):
		tmp = x * (y + -1.0)
	else:
		tmp = y - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -360000000000.0) || !(x <= 8.6e-30))
		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 <= -360000000000.0) || ~((x <= 8.6e-30)))
		tmp = x * (y + -1.0);
	else
		tmp = y - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -360000000000.0], N[Not[LessEqual[x, 8.6e-30]], $MachinePrecision]], N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision], N[(y - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.6e11 or 8.59999999999999932e-30 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 97.4%

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

   if -3.6e11 < x < 8.59999999999999932e-30

   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 98.3%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -360000000000 \lor \neg \left(x \leq 8.6 \cdot 10^{-30}\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 63.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.65 \cdot 10^{-34} \lor \neg \left(x \leq 3.5 \cdot 10^{-30}\right):\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -2.65e-34) (not (<= x 3.5e-30))) (- x) y))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -2.65e-34) || !(x <= 3.5e-30)) {
		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 <= (-2.65d-34)) .or. (.not. (x <= 3.5d-30))) 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 <= -2.65e-34) || !(x <= 3.5e-30)) {
		tmp = -x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -2.65e-34) or not (x <= 3.5e-30):
		tmp = -x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -2.65e-34) || !(x <= 3.5e-30))
		tmp = Float64(-x);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -2.65e-34) || ~((x <= 3.5e-30)))
		tmp = -x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -2.65e-34], N[Not[LessEqual[x, 3.5e-30]], $MachinePrecision]], (-x), y]

Derivation

1. Split input into 2 regimes

2. if x < -2.6499999999999998e-34 or 3.5000000000000003e-30 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 45.3%

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

      1. neg-mul-1 45.3%

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

   5. Simplified 45.3%

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

   if -2.6499999999999998e-34 < x < 3.5000000000000003e-30

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 87.1%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.65 \cdot 10^{-34} \lor \neg \left(x \leq 3.5 \cdot 10^{-30}\right):\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. 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: 38.5% 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 39.2%

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

Reproduce

herbie shell --seed 2024107 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1.0) y) x))