Data.Colour.SRGB:transferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 4.7s

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

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

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. Step-by-step derivation

   1. sub-neg 100.0%

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

   2. distribute-rgt1-in 100.0%

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

   3. *-commutative 100.0%

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

   4. associate-+l+ 100.0%

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

   5. neg-mul-1 100.0%

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

   6. distribute-rgt-out 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 62.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-40}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 3650000000000:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+69}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0)
   (* y x)
   (if (<= y 6e-40)
     (- x)
     (if (<= y 3650000000000.0) y (if (<= y 6e+69) (* y x) y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = y * x;
	} else if (y <= 6e-40) {
		tmp = -x;
	} else if (y <= 3650000000000.0) {
		tmp = y;
	} else if (y <= 6e+69) {
		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 <= (-1.0d0)) then
        tmp = y * x
    else if (y <= 6d-40) then
        tmp = -x
    else if (y <= 3650000000000.0d0) then
        tmp = y
    else if (y <= 6d+69) 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 <= -1.0) {
		tmp = y * x;
	} else if (y <= 6e-40) {
		tmp = -x;
	} else if (y <= 3650000000000.0) {
		tmp = y;
	} else if (y <= 6e+69) {
		tmp = y * x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = y * x
	elif y <= 6e-40:
		tmp = -x
	elif y <= 3650000000000.0:
		tmp = y
	elif y <= 6e+69:
		tmp = y * x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = Float64(y * x);
	elseif (y <= 6e-40)
		tmp = Float64(-x);
	elseif (y <= 3650000000000.0)
		tmp = y;
	elseif (y <= 6e+69)
		tmp = Float64(y * x);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.0)
		tmp = y * x;
	elseif (y <= 6e-40)
		tmp = -x;
	elseif (y <= 3650000000000.0)
		tmp = y;
	elseif (y <= 6e+69)
		tmp = y * x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], N[(y * x), $MachinePrecision], If[LessEqual[y, 6e-40], (-x), If[LessEqual[y, 3650000000000.0], y, If[LessEqual[y, 6e+69], N[(y * x), $MachinePrecision], y]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 3.65e12 < y < 5.99999999999999967e69

   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. distribute-rgt1-in 100.0%

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

      3. *-commutative 100.0%

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

      4. associate-+l+ 100.0%

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

      5. neg-mul-1 100.0%

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

      6. distribute-rgt-out 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 99.7%

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

      1. +-commutative 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in x around inf 60.2%

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

      1. *-commutative 60.2%

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

   10. Simplified 60.2%

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

   if -1 < y < 6.00000000000000039e-40

   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. distribute-rgt1-in 100.0%

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

      3. *-commutative 100.0%

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

      4. associate-+l+ 100.0%

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

      5. neg-mul-1 100.0%

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

      6. distribute-rgt-out 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 80.5%

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

      1. neg-mul-1 80.5%

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

   7. Simplified 80.5%

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

   if 6.00000000000000039e-40 < y < 3.65e12 or 5.99999999999999967e69 < y

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. distribute-rgt1-in 100.0%

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

      3. *-commutative 100.0%

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

      4. associate-+l+ 100.0%

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

      5. neg-mul-1 100.0%

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

      6. distribute-rgt-out 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 63.5%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-40}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 3650000000000:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+69}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-21} \lor \neg \left(y \leq 6 \cdot 10^{-32}\right):\\ \;\;\;\;y \cdot \left(x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.4e-21) (not (<= y 6e-32))) (* y (+ x 1.0)) (- x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.4e-21) || !(y <= 6e-32)) {
		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 <= (-1.4d-21)) .or. (.not. (y <= 6d-32))) 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 <= -1.4e-21) || !(y <= 6e-32)) {
		tmp = y * (x + 1.0);
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.4e-21) or not (y <= 6e-32):
		tmp = y * (x + 1.0)
	else:
		tmp = -x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.4e-21) || !(y <= 6e-32))
		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 <= -1.4e-21) || ~((y <= 6e-32)))
		tmp = y * (x + 1.0);
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.4e-21], N[Not[LessEqual[y, 6e-32]], $MachinePrecision]], N[(y * N[(x + 1.0), $MachinePrecision]), $MachinePrecision], (-x)]

Derivation

1. Split input into 2 regimes

2. if y < -1.40000000000000002e-21 or 6.0000000000000001e-32 < y

   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. distribute-rgt1-in 100.0%

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

      3. *-commutative 100.0%

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

      4. associate-+l+ 100.0%

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

      5. neg-mul-1 100.0%

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

      6. distribute-rgt-out 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 97.1%

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

      1. +-commutative 97.1%

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

   7. Simplified 97.1%

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

   if -1.40000000000000002e-21 < y < 6.0000000000000001e-32

   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. distribute-rgt1-in 100.0%

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

      3. *-commutative 100.0%

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

      4. associate-+l+ 100.0%

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

      5. neg-mul-1 100.0%

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

      6. distribute-rgt-out 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 82.2%

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

      1. neg-mul-1 82.2%

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

   7. Simplified 82.2%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-21} \lor \neg \left(y \leq 6 \cdot 10^{-32}\right):\\ \;\;\;\;y \cdot \left(x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{-21}:\\ \;\;\;\;y \cdot \left(x + 1\right)\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-33}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y + y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -6.4e-21) (* y (+ x 1.0)) (if (<= y 5.5e-33) (- x) (+ y (* y x)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -6.4e-21) {
		tmp = y * (x + 1.0);
	} else if (y <= 5.5e-33) {
		tmp = -x;
	} else {
		tmp = y + (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 <= (-6.4d-21)) then
        tmp = y * (x + 1.0d0)
    else if (y <= 5.5d-33) then
        tmp = -x
    else
        tmp = y + (y * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -6.4e-21) {
		tmp = y * (x + 1.0);
	} else if (y <= 5.5e-33) {
		tmp = -x;
	} else {
		tmp = y + (y * x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -6.4e-21:
		tmp = y * (x + 1.0)
	elif y <= 5.5e-33:
		tmp = -x
	else:
		tmp = y + (y * x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -6.4e-21)
		tmp = Float64(y * Float64(x + 1.0));
	elseif (y <= 5.5e-33)
		tmp = Float64(-x);
	else
		tmp = Float64(y + Float64(y * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -6.4e-21)
		tmp = y * (x + 1.0);
	elseif (y <= 5.5e-33)
		tmp = -x;
	else
		tmp = y + (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -6.4e-21], N[(y * N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.5e-33], (-x), N[(y + N[(y * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.4000000000000003e-21

   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. distribute-rgt1-in 100.0%

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

      3. *-commutative 100.0%

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

      4. associate-+l+ 100.0%

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

      5. neg-mul-1 100.0%

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

      6. distribute-rgt-out 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 96.0%

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

      1. +-commutative 96.0%

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

   7. Simplified 96.0%

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

   if -6.4000000000000003e-21 < y < 5.5e-33

   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. distribute-rgt1-in 100.0%

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

      3. *-commutative 100.0%

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

      4. associate-+l+ 100.0%

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

      5. neg-mul-1 100.0%

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

      6. distribute-rgt-out 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 82.2%

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

      1. neg-mul-1 82.2%

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

   7. Simplified 82.2%

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

   if 5.5e-33 < y

   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. distribute-rgt1-in 100.0%

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

      3. *-commutative 100.0%

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

      4. associate-+l+ 100.0%

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

      5. neg-mul-1 100.0%

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

      6. distribute-rgt-out 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 98.2%

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

      1. +-commutative 98.2%

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

   7. Simplified 98.2%

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

      1. distribute-lft-in 98.2%

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

      2. *-rgt-identity 98.2%

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

   9. Applied egg-rr 98.2%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{-21}:\\ \;\;\;\;y \cdot \left(x + 1\right)\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-33}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y + y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -140000:\\ \;\;\;\;y \cdot \left(x + 1\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-32}:\\ \;\;\;\;y \cdot x - x\\ \mathbf{else}:\\ \;\;\;\;y + y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -140000.0)
   (* y (+ x 1.0))
   (if (<= y 5e-32) (- (* y x) x) (+ y (* y x)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -140000.0) {
		tmp = y * (x + 1.0);
	} else if (y <= 5e-32) {
		tmp = (y * x) - x;
	} else {
		tmp = y + (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 <= (-140000.0d0)) then
        tmp = y * (x + 1.0d0)
    else if (y <= 5d-32) then
        tmp = (y * x) - x
    else
        tmp = y + (y * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -140000.0) {
		tmp = y * (x + 1.0);
	} else if (y <= 5e-32) {
		tmp = (y * x) - x;
	} else {
		tmp = y + (y * x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -140000.0:
		tmp = y * (x + 1.0)
	elif y <= 5e-32:
		tmp = (y * x) - x
	else:
		tmp = y + (y * x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -140000.0)
		tmp = Float64(y * Float64(x + 1.0));
	elseif (y <= 5e-32)
		tmp = Float64(Float64(y * x) - x);
	else
		tmp = Float64(y + Float64(y * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -140000.0)
		tmp = y * (x + 1.0);
	elseif (y <= 5e-32)
		tmp = (y * x) - x;
	else
		tmp = y + (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -140000.0], N[(y * N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5e-32], N[(N[(y * x), $MachinePrecision] - x), $MachinePrecision], N[(y + N[(y * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.4e5

   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. distribute-rgt1-in 100.0%

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

      3. *-commutative 100.0%

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

      4. associate-+l+ 100.0%

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

      5. neg-mul-1 100.0%

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

      6. distribute-rgt-out 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 100.0%

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

      1. +-commutative 100.0%

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

   7. Simplified 100.0%

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

   if -1.4e5 < y < 5e-32

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 81.4%

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

   if 5e-32 < y

   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. distribute-rgt1-in 100.0%

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

      3. *-commutative 100.0%

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

      4. associate-+l+ 100.0%

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

      5. neg-mul-1 100.0%

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

      6. distribute-rgt-out 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 98.2%

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

      1. +-commutative 98.2%

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

   7. Simplified 98.2%

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

      1. distribute-lft-in 98.2%

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

      2. *-rgt-identity 98.2%

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

   9. Applied egg-rr 98.2%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -140000:\\ \;\;\;\;y \cdot \left(x + 1\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-32}:\\ \;\;\;\;y \cdot x - x\\ \mathbf{else}:\\ \;\;\;\;y + y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-19}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-33}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -4.2e-19) y (if (<= y 5.2e-33) (- x) y)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -4.2e-19) {
		tmp = y;
	} else if (y <= 5.2e-33) {
		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 <= (-4.2d-19)) then
        tmp = y
    else if (y <= 5.2d-33) 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 <= -4.2e-19) {
		tmp = y;
	} else if (y <= 5.2e-33) {
		tmp = -x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -4.2e-19:
		tmp = y
	elif y <= 5.2e-33:
		tmp = -x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -4.2e-19)
		tmp = y;
	elseif (y <= 5.2e-33)
		tmp = Float64(-x);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -4.2e-19)
		tmp = y;
	elseif (y <= 5.2e-33)
		tmp = -x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -4.2e-19], y, If[LessEqual[y, 5.2e-33], (-x), y]]

Derivation

1. Split input into 2 regimes

2. if y < -4.1999999999999998e-19 or 5.19999999999999988e-33 < y

   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. distribute-rgt1-in 100.0%

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

      3. *-commutative 100.0%

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

      4. associate-+l+ 100.0%

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

      5. neg-mul-1 100.0%

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

      6. distribute-rgt-out 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 49.3%

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

   if -4.1999999999999998e-19 < y < 5.19999999999999988e-33

   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. distribute-rgt1-in 100.0%

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

      3. *-commutative 100.0%

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

      4. associate-+l+ 100.0%

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

      5. neg-mul-1 100.0%

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

      6. distribute-rgt-out 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 82.2%

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

      1. neg-mul-1 82.2%

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

   7. Simplified 82.2%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-19}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-33}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 37.6% 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. Step-by-step derivation

   1. sub-neg 100.0%

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

   2. distribute-rgt1-in 100.0%

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

   3. *-commutative 100.0%

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

   4. associate-+l+ 100.0%

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

   5. neg-mul-1 100.0%

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

   6. distribute-rgt-out 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in x around 0 35.0%

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

6. Final simplification 35.0%

   \[\leadsto y \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024048 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1.0) y) x))