Data.Colour.SRGB:transferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 3.1s

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

\[\begin{array}{l} \\ \mathsf{fma}\left(x, y, y - x\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (fma x y (- y x)))

C

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

Julia

function code(x, y)
	return fma(x, y, Float64(y - x))
end

Wolfram

code[x_, y_] := N[(x * y + N[(y - x), $MachinePrecision]), $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. *-commutative 100.0%

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

   3. distribute-lft1-in 100.0%

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

   4. associate--l+ 100.0%

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

   5. fma-def 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 60.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{+163}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -3.15 \cdot 10^{+59}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq -25000000:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -2.05 \cdot 10^{-108}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 0.125:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+143}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.25e+163)
   (* x y)
   (if (<= x -3.15e+59)
     (- x)
     (if (<= x -25000000.0)
       (* x y)
       (if (<= x -2.05e-108)
         (- x)
         (if (<= x 0.125) y (if (<= x 7e+143) (* x y) (- x))))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.25e+163) {
		tmp = x * y;
	} else if (x <= -3.15e+59) {
		tmp = -x;
	} else if (x <= -25000000.0) {
		tmp = x * y;
	} else if (x <= -2.05e-108) {
		tmp = -x;
	} else if (x <= 0.125) {
		tmp = y;
	} else if (x <= 7e+143) {
		tmp = x * y;
	} 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 (x <= (-2.25d+163)) then
        tmp = x * y
    else if (x <= (-3.15d+59)) then
        tmp = -x
    else if (x <= (-25000000.0d0)) then
        tmp = x * y
    else if (x <= (-2.05d-108)) then
        tmp = -x
    else if (x <= 0.125d0) then
        tmp = y
    else if (x <= 7d+143) then
        tmp = x * y
    else
        tmp = -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2.25e+163) {
		tmp = x * y;
	} else if (x <= -3.15e+59) {
		tmp = -x;
	} else if (x <= -25000000.0) {
		tmp = x * y;
	} else if (x <= -2.05e-108) {
		tmp = -x;
	} else if (x <= 0.125) {
		tmp = y;
	} else if (x <= 7e+143) {
		tmp = x * y;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.25e+163:
		tmp = x * y
	elif x <= -3.15e+59:
		tmp = -x
	elif x <= -25000000.0:
		tmp = x * y
	elif x <= -2.05e-108:
		tmp = -x
	elif x <= 0.125:
		tmp = y
	elif x <= 7e+143:
		tmp = x * y
	else:
		tmp = -x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.25e+163)
		tmp = Float64(x * y);
	elseif (x <= -3.15e+59)
		tmp = Float64(-x);
	elseif (x <= -25000000.0)
		tmp = Float64(x * y);
	elseif (x <= -2.05e-108)
		tmp = Float64(-x);
	elseif (x <= 0.125)
		tmp = y;
	elseif (x <= 7e+143)
		tmp = Float64(x * y);
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.25e+163)
		tmp = x * y;
	elseif (x <= -3.15e+59)
		tmp = -x;
	elseif (x <= -25000000.0)
		tmp = x * y;
	elseif (x <= -2.05e-108)
		tmp = -x;
	elseif (x <= 0.125)
		tmp = y;
	elseif (x <= 7e+143)
		tmp = x * y;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.25e+163], N[(x * y), $MachinePrecision], If[LessEqual[x, -3.15e+59], (-x), If[LessEqual[x, -25000000.0], N[(x * y), $MachinePrecision], If[LessEqual[x, -2.05e-108], (-x), If[LessEqual[x, 0.125], y, If[LessEqual[x, 7e+143], N[(x * y), $MachinePrecision], (-x)]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.24999999999999994e163 or -3.15e59 < x < -2.5e7 or 0.125 < x < 7.00000000000000017e143

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 97.7%

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

   3. Taylor expanded in y around inf 69.1%

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

   if -2.24999999999999994e163 < x < -3.15e59 or -2.5e7 < x < -2.05000000000000018e-108 or 7.00000000000000017e143 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 63.8%

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

      1. neg-mul-1 63.8%

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

   4. Simplified 63.8%

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

   if -2.05000000000000018e-108 < x < 0.125

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 81.8%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{+163}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -3.15 \cdot 10^{+59}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq -25000000:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -2.05 \cdot 10^{-108}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 0.125:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+143}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 3: 84.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.05 \cdot 10^{-108} \lor \neg \left(x \leq 1.8 \cdot 10^{-65}\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -2.05e-108) (not (<= x 1.8e-65))) (* x (+ y -1.0)) y))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -2.05e-108) || !(x <= 1.8e-65)) {
		tmp = x * (y + -1.0);
	} 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 <= (-2.05d-108)) .or. (.not. (x <= 1.8d-65))) then
        tmp = x * (y + (-1.0d0))
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -2.05e-108) || !(x <= 1.8e-65)) {
		tmp = x * (y + -1.0);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -2.05e-108) or not (x <= 1.8e-65):
		tmp = x * (y + -1.0)
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -2.05e-108) || !(x <= 1.8e-65))
		tmp = Float64(x * Float64(y + -1.0));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -2.05e-108) || ~((x <= 1.8e-65)))
		tmp = x * (y + -1.0);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -2.05e-108], N[Not[LessEqual[x, 1.8e-65]], $MachinePrecision]], N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision], y]

Derivation

1. Split input into 2 regimes

2. if x < -2.05000000000000018e-108 or 1.7999999999999999e-65 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 89.5%

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

   if -2.05000000000000018e-108 < x < 1.7999999999999999e-65

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 87.2%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.05 \cdot 10^{-108} \lor \neg \left(x \leq 1.8 \cdot 10^{-65}\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 4: 85.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-13} \lor \neg \left(y \leq 1.8 \cdot 10^{-112}\right):\\ \;\;\;\;y \cdot \left(x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.9e-13) (not (<= y 1.8e-112)))
   (* y (+ x 1.0))
   (* x (+ y -1.0))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.9e-13) || !(y <= 1.8e-112)) {
		tmp = y * (x + 1.0);
	} else {
		tmp = x * (y + -1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-1.9d-13)) .or. (.not. (y <= 1.8d-112))) then
        tmp = y * (x + 1.0d0)
    else
        tmp = x * (y + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.9e-13) || !(y <= 1.8e-112)) {
		tmp = y * (x + 1.0);
	} else {
		tmp = x * (y + -1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.9e-13) or not (y <= 1.8e-112):
		tmp = y * (x + 1.0)
	else:
		tmp = x * (y + -1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.9e-13) || !(y <= 1.8e-112))
		tmp = Float64(y * Float64(x + 1.0));
	else
		tmp = Float64(x * Float64(y + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.9e-13) || ~((y <= 1.8e-112)))
		tmp = y * (x + 1.0);
	else
		tmp = x * (y + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.9e-13], N[Not[LessEqual[y, 1.8e-112]], $MachinePrecision]], N[(y * N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.9e-13 or 1.8e-112 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 93.1%

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

   if -1.9e-13 < y < 1.8e-112

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 82.7%

      \[\leadsto \color{blue}{x \cdot \left(y - 1\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-13} \lor \neg \left(y \leq 1.8 \cdot 10^{-112}\right):\\ \;\;\;\;y \cdot \left(x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \end{array} \]

Alternative 5: 85.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-13} \lor \neg \left(y \leq 1.8 \cdot 10^{-112}\right):\\ \;\;\;\;y \cdot \left(x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.3e-13) (not (<= y 1.8e-112))) (* y (+ x 1.0)) (- (* x y) x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.3e-13) || !(y <= 1.8e-112)) {
		tmp = y * (x + 1.0);
	} else {
		tmp = (x * 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 <= (-1.3d-13)) .or. (.not. (y <= 1.8d-112))) then
        tmp = y * (x + 1.0d0)
    else
        tmp = (x * y) - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.3e-13) || !(y <= 1.8e-112)) {
		tmp = y * (x + 1.0);
	} else {
		tmp = (x * y) - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.3e-13) or not (y <= 1.8e-112):
		tmp = y * (x + 1.0)
	else:
		tmp = (x * y) - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.3e-13) || !(y <= 1.8e-112))
		tmp = Float64(y * Float64(x + 1.0));
	else
		tmp = Float64(Float64(x * y) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.3e-13) || ~((y <= 1.8e-112)))
		tmp = y * (x + 1.0);
	else
		tmp = (x * y) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.3e-13], N[Not[LessEqual[y, 1.8e-112]], $MachinePrecision]], N[(y * N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.3e-13 or 1.8e-112 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 93.1%

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

   if -1.3e-13 < y < 1.8e-112

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 82.7%

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

      1. distribute-rgt-out-- 82.7%

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

      2. *-lft-identity 82.7%

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

   4. Simplified 82.7%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-13} \lor \neg \left(y \leq 1.8 \cdot 10^{-112}\right):\\ \;\;\;\;y \cdot \left(x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - x\\ \end{array} \]

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. Final simplification 100.0%

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

Alternative 7: 61.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-13}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-112}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.8e-13) y (if (<= y 1.8e-112) (- x) y)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.8e-13) {
		tmp = y;
	} else if (y <= 1.8e-112) {
		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 <= (-1.8d-13)) then
        tmp = y
    else if (y <= 1.8d-112) 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 <= -1.8e-13) {
		tmp = y;
	} else if (y <= 1.8e-112) {
		tmp = -x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.8e-13:
		tmp = y
	elif y <= 1.8e-112:
		tmp = -x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.8e-13)
		tmp = y;
	elseif (y <= 1.8e-112)
		tmp = Float64(-x);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.8e-13)
		tmp = y;
	elseif (y <= 1.8e-112)
		tmp = -x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.8e-13], y, If[LessEqual[y, 1.8e-112], (-x), y]]

Derivation

1. Split input into 2 regimes

2. if y < -1.7999999999999999e-13 or 1.8e-112 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 51.1%

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

   if -1.7999999999999999e-13 < y < 1.8e-112

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 82.5%

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

      1. neg-mul-1 82.5%

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

   4. Simplified 82.5%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-13}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-112}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 8: 38.8% 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 38.4%

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

3. Final simplification 38.4%

   \[\leadsto y \]

Reproduce

herbie shell --seed 2023271 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1.0) y) x))