Data.Colour.SRGB:transferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 5.1s

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, 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%

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

   3. *-commutative 100.0%

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

   4. distribute-rgt-in 100.0%

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

   5. associate-+r+ 100.0%

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

   6. +-commutative 100.0%

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

   7. neg-mul-1 100.0%

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

   8. *-commutative 100.0%

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

   9. distribute-lft-out 100.0%

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

   10. *-lft-identity 100.0%

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

   11. fma-def 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. Final simplification 100.0%

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

Alternative 2: 74.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+238}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+62}:\\ \;\;\;\;y - x\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+126}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.3e+238)
   (* x y)
   (if (<= y 1.1e+62) (- y x) (if (<= y 1.15e+126) (* x y) y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.3e+238) {
		tmp = x * y;
	} else if (y <= 1.1e+62) {
		tmp = y - x;
	} else if (y <= 1.15e+126) {
		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+238)) then
        tmp = x * y
    else if (y <= 1.1d+62) then
        tmp = y - x
    else if (y <= 1.15d+126) 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+238) {
		tmp = x * y;
	} else if (y <= 1.1e+62) {
		tmp = y - x;
	} else if (y <= 1.15e+126) {
		tmp = x * y;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.3e+238:
		tmp = x * y
	elif y <= 1.1e+62:
		tmp = y - x
	elif y <= 1.15e+126:
		tmp = x * y
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.3e+238)
		tmp = Float64(x * y);
	elseif (y <= 1.1e+62)
		tmp = Float64(y - x);
	elseif (y <= 1.15e+126)
		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+238)
		tmp = x * y;
	elseif (y <= 1.1e+62)
		tmp = y - x;
	elseif (y <= 1.15e+126)
		tmp = x * y;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.3e+238], N[(x * y), $MachinePrecision], If[LessEqual[y, 1.1e+62], N[(y - x), $MachinePrecision], If[LessEqual[y, 1.15e+126], N[(x * y), $MachinePrecision], y]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.30000000000000003e238 or 1.10000000000000007e62 < y < 1.15e126

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. distribute-rgt-in 100.0%

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

      3. *-un-lft-identity 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in y around inf 100.0%

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

   5. Taylor expanded in x around inf 73.0%

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

      1. *-commutative 73.0%

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

   7. Simplified 73.0%

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

   if -2.30000000000000003e238 < y < 1.10000000000000007e62

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]

   2. Taylor expanded in x around 0 84.7%

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

   if 1.15e126 < y

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. distribute-rgt-in 100.0%

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

      3. *-un-lft-identity 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in x around 0 55.6%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+238}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+62}:\\ \;\;\;\;y - x\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+126}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 3: 98.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 0.075\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.0) (not (<= x 0.075))) (* x (+ y -1.0)) (- y x)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.0) || !(x <= 0.075)) {
		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 <= 0.075d0))) 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 <= 0.075)) {
		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 <= 0.075):
		tmp = x * (y + -1.0)
	else:
		tmp = y - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.0) || !(x <= 0.075))
		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 <= 0.075)))
		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, 0.075]], $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 0.0749999999999999972 < x

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]

   2. Taylor expanded in x around inf 99.6%

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

   if -1 < x < 0.0749999999999999972

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]

   2. Taylor expanded in x around 0 98.0%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 0.075\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \]

Alternative 4: 62.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+238}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -33000000000:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-11}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.6e+238)
   (* x y)
   (if (<= y -33000000000.0) y (if (<= y 2.7e-11) (- x) y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.6e+238) {
		tmp = x * y;
	} else if (y <= -33000000000.0) {
		tmp = y;
	} else if (y <= 2.7e-11) {
		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 <= (-2.6d+238)) then
        tmp = x * y
    else if (y <= (-33000000000.0d0)) then
        tmp = y
    else if (y <= 2.7d-11) 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 <= -2.6e+238) {
		tmp = x * y;
	} else if (y <= -33000000000.0) {
		tmp = y;
	} else if (y <= 2.7e-11) {
		tmp = -x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.6e+238:
		tmp = x * y
	elif y <= -33000000000.0:
		tmp = y
	elif y <= 2.7e-11:
		tmp = -x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.6e+238)
		tmp = Float64(x * y);
	elseif (y <= -33000000000.0)
		tmp = y;
	elseif (y <= 2.7e-11)
		tmp = Float64(-x);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -2.6e+238)
		tmp = x * y;
	elseif (y <= -33000000000.0)
		tmp = y;
	elseif (y <= 2.7e-11)
		tmp = -x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.6e+238], N[(x * y), $MachinePrecision], If[LessEqual[y, -33000000000.0], y, If[LessEqual[y, 2.7e-11], (-x), y]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.6e238

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. distribute-rgt-in 100.0%

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

      3. *-un-lft-identity 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in y around inf 100.0%

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

   5. Taylor expanded in x around inf 77.9%

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

      1. *-commutative 77.9%

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

   7. Simplified 77.9%

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

   if -2.6e238 < y < -3.3e10 or 2.70000000000000005e-11 < y

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. distribute-rgt-in 100.0%

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

      3. *-un-lft-identity 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in x around 0 54.6%

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

   if -3.3e10 < y < 2.70000000000000005e-11

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]

   2. Taylor expanded in y around 0 76.6%

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

      1. mul-1-neg 76.6%

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

   4. Simplified 76.6%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+238}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -33000000000:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-11}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 5: 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. Final simplification 100.0%

   \[\leadsto y \cdot \left(x + 1\right) - x \]

Alternative 6: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. *-commutative 100.0%

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

   2. distribute-rgt-in 100.0%

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

   3. *-un-lft-identity 100.0%

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

3. Applied egg-rr 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \left(y + x \cdot y\right) - x \]

Alternative 7: 62.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -33000000000:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-15}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -33000000000.0) y (if (<= y 5.5e-15) (- x) y)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -33000000000.0) {
		tmp = y;
	} else if (y <= 5.5e-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 (y <= (-33000000000.0d0)) then
        tmp = y
    else if (y <= 5.5d-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 (y <= -33000000000.0) {
		tmp = y;
	} else if (y <= 5.5e-15) {
		tmp = -x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -33000000000.0:
		tmp = y
	elif y <= 5.5e-15:
		tmp = -x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -33000000000.0)
		tmp = y;
	elseif (y <= 5.5e-15)
		tmp = Float64(-x);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -33000000000.0)
		tmp = y;
	elseif (y <= 5.5e-15)
		tmp = -x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -33000000000.0], y, If[LessEqual[y, 5.5e-15], (-x), y]]

Derivation

1. Split input into 2 regimes

2. if y < -3.3e10 or 5.5000000000000002e-15 < y

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. distribute-rgt-in 100.0%

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

      3. *-un-lft-identity 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in x around 0 50.3%

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

   if -3.3e10 < y < 5.5000000000000002e-15

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]

   2. Taylor expanded in y around 0 76.6%

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

      1. mul-1-neg 76.6%

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

   4. Simplified 76.6%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -33000000000:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-15}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

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. Step-by-step derivation

   1. *-commutative 100.0%

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

   2. distribute-rgt-in 100.0%

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

   3. *-un-lft-identity 100.0%

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

3. Applied egg-rr 100.0%

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

4. Taylor expanded in x around 0 38.5%

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

5. Final simplification 38.5%

   \[\leadsto y \]

Reproduce

herbie shell --seed 2023326 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1.0) y) x))