Data.Colour.SRGB:transferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 2.8s

Alternatives: 7

Speedup: N/A×

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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in x around 0 100.0%

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

3. Final simplification 100.0%

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

Alternative 2: 59.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -23:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -6.3 \cdot 10^{-31}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-63}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-137}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -23.0)
   y
   (if (<= y -6.3e-31)
     (- x)
     (if (<= y -2.1e-63) y (if (<= y 1.4e-137) (- x) y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -23.0) {
		tmp = y;
	} else if (y <= -6.3e-31) {
		tmp = -x;
	} else if (y <= -2.1e-63) {
		tmp = y;
	} else if (y <= 1.4e-137) {
		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 <= (-23.0d0)) then
        tmp = y
    else if (y <= (-6.3d-31)) then
        tmp = -x
    else if (y <= (-2.1d-63)) then
        tmp = y
    else if (y <= 1.4d-137) 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 <= -23.0) {
		tmp = y;
	} else if (y <= -6.3e-31) {
		tmp = -x;
	} else if (y <= -2.1e-63) {
		tmp = y;
	} else if (y <= 1.4e-137) {
		tmp = -x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -23.0:
		tmp = y
	elif y <= -6.3e-31:
		tmp = -x
	elif y <= -2.1e-63:
		tmp = y
	elif y <= 1.4e-137:
		tmp = -x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -23.0)
		tmp = y;
	elseif (y <= -6.3e-31)
		tmp = Float64(-x);
	elseif (y <= -2.1e-63)
		tmp = y;
	elseif (y <= 1.4e-137)
		tmp = Float64(-x);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -23.0)
		tmp = y;
	elseif (y <= -6.3e-31)
		tmp = -x;
	elseif (y <= -2.1e-63)
		tmp = y;
	elseif (y <= 1.4e-137)
		tmp = -x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -23.0], y, If[LessEqual[y, -6.3e-31], (-x), If[LessEqual[y, -2.1e-63], y, If[LessEqual[y, 1.4e-137], (-x), y]]]]

Derivation

1. Split input into 2 regimes

2. if y < -23 or -6.3000000000000002e-31 < y < -2.1e-63 or 1.3999999999999999e-137 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 100.0%

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

   3. Taylor expanded in x around 0 56.2%

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

   if -23 < y < -6.3000000000000002e-31 or -2.1e-63 < y < 1.3999999999999999e-137

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 85.8%

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

      1. neg-mul-1 85.8%

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

   4. Simplified 85.8%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -23:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -6.3 \cdot 10^{-31}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-63}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-137}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 3: 63.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.66 \cdot 10^{-7}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-27}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+27}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.66e-7)
   (* y x)
   (if (<= x 5.2e-27) y (if (<= x 1.55e+27) (- x) (* y x)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.66e-7) {
		tmp = y * x;
	} else if (x <= 5.2e-27) {
		tmp = y;
	} else if (x <= 1.55e+27) {
		tmp = -x;
	} 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 <= (-1.66d-7)) then
        tmp = y * x
    else if (x <= 5.2d-27) then
        tmp = y
    else if (x <= 1.55d+27) then
        tmp = -x
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.66e-7) {
		tmp = y * x;
	} else if (x <= 5.2e-27) {
		tmp = y;
	} else if (x <= 1.55e+27) {
		tmp = -x;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.66e-7:
		tmp = y * x
	elif x <= 5.2e-27:
		tmp = y
	elif x <= 1.55e+27:
		tmp = -x
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.66e-7)
		tmp = Float64(y * x);
	elseif (x <= 5.2e-27)
		tmp = y;
	elseif (x <= 1.55e+27)
		tmp = Float64(-x);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.66e-7)
		tmp = y * x;
	elseif (x <= 5.2e-27)
		tmp = y;
	elseif (x <= 1.55e+27)
		tmp = -x;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.66e-7], N[(y * x), $MachinePrecision], If[LessEqual[x, 5.2e-27], y, If[LessEqual[x, 1.55e+27], (-x), N[(y * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.66000000000000004e-7 or 1.54999999999999998e27 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 100.0%

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

   3. Taylor expanded in y around inf 58.0%

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

      1. +-commutative 58.0%

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

      2. distribute-rgt1-in 58.0%

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

   5. Simplified 58.0%

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

   6. Taylor expanded in x around inf 57.5%

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

   if -1.66000000000000004e-7 < x < 5.20000000000000034e-27

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 100.0%

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

   3. Taylor expanded in x around 0 75.0%

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

   if 5.20000000000000034e-27 < x < 1.54999999999999998e27

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 74.0%

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

      1. neg-mul-1 74.0%

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

   4. Simplified 74.0%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.66 \cdot 10^{-7}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-27}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+27}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 4: 98.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 8 \cdot 10^{-26}\right):\\ \;\;\;\;\left(y - 1\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.0) (not (<= x 8e-26))) (* (- y 1.0) x) (- y x)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.0) || !(x <= 8e-26)) {
		tmp = (y - 1.0) * x;
	} 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 <= 8d-26))) then
        tmp = (y - 1.0d0) * x
    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 <= 8e-26)) {
		tmp = (y - 1.0) * x;
	} else {
		tmp = y - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.0) or not (x <= 8e-26):
		tmp = (y - 1.0) * x
	else:
		tmp = y - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.0) || !(x <= 8e-26))
		tmp = Float64(Float64(y - 1.0) * x);
	else
		tmp = Float64(y - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.0) || ~((x <= 8e-26)))
		tmp = (y - 1.0) * x;
	else
		tmp = y - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.0], N[Not[LessEqual[x, 8e-26]], $MachinePrecision]], N[(N[(y - 1.0), $MachinePrecision] * x), $MachinePrecision], N[(y - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1 or 8.0000000000000003e-26 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 99.0%

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

   if -1 < x < 8.0000000000000003e-26

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 99.8%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 8 \cdot 10^{-26}\right):\\ \;\;\;\;\left(y - 1\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \]

Alternative 5: 99.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.00072\right):\\ \;\;\;\;y + y \cdot x\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 0.00072))) (+ y (* y x)) (- y x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 0.00072)) {
		tmp = y + (y * x);
	} 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 <= (-1.0d0)) .or. (.not. (y <= 0.00072d0))) then
        tmp = y + (y * x)
    else
        tmp = y - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 0.00072)) {
		tmp = y + (y * x);
	} else {
		tmp = y - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.0) or not (y <= 0.00072):
		tmp = y + (y * x)
	else:
		tmp = y - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 0.00072))
		tmp = Float64(y + Float64(y * x));
	else
		tmp = Float64(y - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.0) || ~((y <= 0.00072)))
		tmp = y + (y * x);
	else
		tmp = y - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 0.00072]], $MachinePrecision]], N[(y + N[(y * x), $MachinePrecision]), $MachinePrecision], N[(y - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 7.20000000000000045e-4 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 100.0%

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

   3. Taylor expanded in y around inf 99.3%

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

      1. +-commutative 99.3%

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

      2. distribute-rgt1-in 99.3%

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

   5. Simplified 99.3%

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

   if -1 < y < 7.20000000000000045e-4

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 100.0%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.00072\right):\\ \;\;\;\;y + y \cdot x\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \]

Alternative 6: 75.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.7 \cdot 10^{+15}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+32}:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -5.7e+15) (* y x) (if (<= x 2.7e+32) (- y x) (* y x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -5.7e+15) {
		tmp = y * x;
	} else if (x <= 2.7e+32) {
		tmp = y - x;
	} 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 <= (-5.7d+15)) then
        tmp = y * x
    else if (x <= 2.7d+32) then
        tmp = y - x
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -5.7e+15) {
		tmp = y * x;
	} else if (x <= 2.7e+32) {
		tmp = y - x;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -5.7e+15:
		tmp = y * x
	elif x <= 2.7e+32:
		tmp = y - x
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -5.7e+15)
		tmp = Float64(y * x);
	elseif (x <= 2.7e+32)
		tmp = Float64(y - x);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -5.7e+15)
		tmp = y * x;
	elseif (x <= 2.7e+32)
		tmp = y - x;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -5.7e+15], N[(y * x), $MachinePrecision], If[LessEqual[x, 2.7e+32], N[(y - x), $MachinePrecision], N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.7e15 or 2.70000000000000013e32 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 100.0%

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

   3. Taylor expanded in y around inf 59.4%

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

      1. +-commutative 59.4%

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

      2. distribute-rgt1-in 59.4%

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

   5. Simplified 59.4%

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

   6. Taylor expanded in x around inf 59.4%

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

   if -5.7e15 < x < 2.70000000000000013e32

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 97.4%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.7 \cdot 10^{+15}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+32}:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

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. Taylor expanded in x around 0 100.0%

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

3. Taylor expanded in x around 0 41.5%

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

4. Final simplification 41.5%

   \[\leadsto y \]

Reproduce

herbie shell --seed 2023214 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1.0) y) x))