Data.Colour.SRGB:transferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 5.1s

Alternatives: 9

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. distribute-rgt1-in 100.0%

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

   3. +-commutative 100.0%

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

   4. associate-+l+ 100.0%

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

   5. *-commutative 100.0%

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

   6. +-commutative 100.0%

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

   7. associate-+r+ 100.0%

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

   8. neg-mul-1 100.0%

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

   9. distribute-rgt-out 100.0%

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

   10. 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: 62.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-42}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+62}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.0)
   (* x y)
   (if (<= x 4.8e-42) y (if (<= x 2.4e+62) (- x) (* x y)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.0) {
		tmp = x * y;
	} else if (x <= 4.8e-42) {
		tmp = y;
	} else if (x <= 2.4e+62) {
		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 <= (-1.0d0)) then
        tmp = x * y
    else if (x <= 4.8d-42) then
        tmp = y
    else if (x <= 2.4d+62) 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 <= -1.0) {
		tmp = x * y;
	} else if (x <= 4.8e-42) {
		tmp = y;
	} else if (x <= 2.4e+62) {
		tmp = -x;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.0:
		tmp = x * y
	elif x <= 4.8e-42:
		tmp = y
	elif x <= 2.4e+62:
		tmp = -x
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.0)
		tmp = Float64(x * y);
	elseif (x <= 4.8e-42)
		tmp = y;
	elseif (x <= 2.4e+62)
		tmp = Float64(-x);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.0)
		tmp = x * y;
	elseif (x <= 4.8e-42)
		tmp = y;
	elseif (x <= 2.4e+62)
		tmp = -x;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.0], N[(x * y), $MachinePrecision], If[LessEqual[x, 4.8e-42], y, If[LessEqual[x, 2.4e+62], (-x), N[(x * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1 or 2.4e62 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 59.8%

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

      1. distribute-lft-in 59.8%

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

      2. *-rgt-identity 59.8%

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

      3. +-commutative 59.8%

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

   4. Applied egg-rr 59.8%

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

   5. Taylor expanded in x around inf 59.8%

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

   if -1 < x < 4.80000000000000005e-42

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 76.1%

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

   if 4.80000000000000005e-42 < x < 2.4e62

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 64.4%

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

      1. neg-mul-1 64.4%

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

   4. Simplified 64.4%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-42}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+62}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 3: 86.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{-92} \lor \neg \left(x \leq 8.6 \cdot 10^{-40}\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -4.2e-92) (not (<= x 8.6e-40))) (* x (+ y -1.0)) y))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -4.2e-92) || !(x <= 8.6e-40)) {
		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 <= (-4.2d-92)) .or. (.not. (x <= 8.6d-40))) 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 <= -4.2e-92) || !(x <= 8.6e-40)) {
		tmp = x * (y + -1.0);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -4.2e-92) or not (x <= 8.6e-40):
		tmp = x * (y + -1.0)
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -4.2e-92) || !(x <= 8.6e-40))
		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 <= -4.2e-92) || ~((x <= 8.6e-40)))
		tmp = x * (y + -1.0);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -4.2e-92], N[Not[LessEqual[x, 8.6e-40]], $MachinePrecision]], N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision], y]

Derivation

1. Split input into 2 regimes

2. if x < -4.2e-92 or 8.6000000000000005e-40 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 91.3%

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

   if -4.2e-92 < x < 8.6000000000000005e-40

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 84.6%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{-92} \lor \neg \left(x \leq 8.6 \cdot 10^{-40}\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 4: 86.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-65} \lor \neg \left(y \leq 45000000\right):\\ \;\;\;\;y \cdot \left(x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -4e-65) (not (<= y 45000000.0)))
   (* y (+ x 1.0))
   (* x (+ y -1.0))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -4e-65) || !(y <= 45000000.0)) {
		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 <= (-4d-65)) .or. (.not. (y <= 45000000.0d0))) 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 <= -4e-65) || !(y <= 45000000.0)) {
		tmp = y * (x + 1.0);
	} else {
		tmp = x * (y + -1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -4e-65) or not (y <= 45000000.0):
		tmp = y * (x + 1.0)
	else:
		tmp = x * (y + -1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -4e-65) || !(y <= 45000000.0))
		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 <= -4e-65) || ~((y <= 45000000.0)))
		tmp = y * (x + 1.0);
	else
		tmp = x * (y + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -4e-65], N[Not[LessEqual[y, 45000000.0]], $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 < -3.99999999999999969e-65 or 4.5e7 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 95.7%

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

   if -3.99999999999999969e-65 < y < 4.5e7

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 76.8%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-65} \lor \neg \left(y \leq 45000000\right):\\ \;\;\;\;y \cdot \left(x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \end{array} \]

Alternative 5: 86.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-65}:\\ \;\;\;\;y + x \cdot y\\ \mathbf{elif}\;y \leq 38000000:\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -4e-65)
   (+ y (* x y))
   (if (<= y 38000000.0) (* x (+ y -1.0)) (* y (+ x 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -4e-65) {
		tmp = y + (x * y);
	} else if (y <= 38000000.0) {
		tmp = x * (y + -1.0);
	} else {
		tmp = y * (x + 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 <= (-4d-65)) then
        tmp = y + (x * y)
    else if (y <= 38000000.0d0) then
        tmp = x * (y + (-1.0d0))
    else
        tmp = y * (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -4e-65) {
		tmp = y + (x * y);
	} else if (y <= 38000000.0) {
		tmp = x * (y + -1.0);
	} else {
		tmp = y * (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -4e-65:
		tmp = y + (x * y)
	elif y <= 38000000.0:
		tmp = x * (y + -1.0)
	else:
		tmp = y * (x + 1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -4e-65)
		tmp = Float64(y + Float64(x * y));
	elseif (y <= 38000000.0)
		tmp = Float64(x * Float64(y + -1.0));
	else
		tmp = Float64(y * Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -4e-65)
		tmp = y + (x * y);
	elseif (y <= 38000000.0)
		tmp = x * (y + -1.0);
	else
		tmp = y * (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -4e-65], N[(y + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 38000000.0], N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision], N[(y * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.99999999999999969e-65

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 93.2%

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

      1. distribute-lft-in 93.2%

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

      2. *-rgt-identity 93.2%

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

      3. +-commutative 93.2%

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

   4. Applied egg-rr 93.2%

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

   if -3.99999999999999969e-65 < y < 3.8e7

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 76.8%

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

   if 3.8e7 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 98.8%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-65}:\\ \;\;\;\;y + x \cdot y\\ \mathbf{elif}\;y \leq 38000000:\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + 1\right)\\ \end{array} \]

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: 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-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%

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

3. Applied egg-rr 100.0%

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

4. Final simplification 100.0%

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

Alternative 8: 61.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-94} \lor \neg \left(x \leq 8.5 \cdot 10^{-40}\right):\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -6e-94) (not (<= x 8.5e-40))) (- x) y))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -6e-94) || !(x <= 8.5e-40)) {
		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 <= (-6d-94)) .or. (.not. (x <= 8.5d-40))) 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 <= -6e-94) || !(x <= 8.5e-40)) {
		tmp = -x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -6e-94) or not (x <= 8.5e-40):
		tmp = -x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -6e-94) || !(x <= 8.5e-40))
		tmp = Float64(-x);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -6e-94) || ~((x <= 8.5e-40)))
		tmp = -x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -6e-94], N[Not[LessEqual[x, 8.5e-40]], $MachinePrecision]], (-x), y]

Derivation

1. Split input into 2 regimes

2. if x < -6.0000000000000003e-94 or 8.4999999999999998e-40 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 44.1%

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

      1. neg-mul-1 44.1%

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

   4. Simplified 44.1%

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

   if -6.0000000000000003e-94 < x < 8.4999999999999998e-40

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 84.6%

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

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-94} \lor \neg \left(x \leq 8.5 \cdot 10^{-40}\right):\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 9: 38.9% 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 38.6%

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

3. Final simplification 38.6%

   \[\leadsto y \]

Reproduce

herbie shell --seed 2023320 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1.0) y) x))