Data.Colour.RGB:hslsv from colour-2.3.3, C

Percentage Accurate: 100.0% → 100.0%

Time: 6.7s

Alternatives: 6

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{x - y}{2 - \left(x + y\right)} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (- x y) (- 2.0 (+ x y))))

C

double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x - y) / (2.0d0 - (x + y))
end function

Java

public static double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

Python

def code(x, y):
	return (x - y) / (2.0 - (x + y))

Julia

function code(x, y)
	return Float64(Float64(x - y) / Float64(2.0 - Float64(x + y)))
end

MATLAB

function tmp = code(x, y)
	tmp = (x - y) / (2.0 - (x + y));
end

Wolfram

code[x_, y_] := N[(N[(x - y), $MachinePrecision] / N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y}{2 - \left(x + y\right)} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (- x y) (- 2.0 (+ x y))))

C

double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x - y) / (2.0d0 - (x + y))
end function

Java

public static double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

Python

def code(x, y):
	return (x - y) / (2.0 - (x + y))

Julia

function code(x, y)
	return Float64(Float64(x - y) / Float64(2.0 - Float64(x + y)))
end

MATLAB

function tmp = code(x, y)
	tmp = (x - y) / (2.0 - (x + y));
end

Wolfram

code[x_, y_] := N[(N[(x - y), $MachinePrecision] / N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y}{2 - \left(x + y\right)} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (- x y) (- 2.0 (+ x y))))

C

double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x - y) / (2.0d0 - (x + y))
end function

Java

public static double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

Python

def code(x, y):
	return (x - y) / (2.0 - (x + y))

Julia

function code(x, y)
	return Float64(Float64(x - y) / Float64(2.0 - Float64(x + y)))
end

MATLAB

function tmp = code(x, y)
	tmp = (x - y) / (2.0 - (x + y));
end

Wolfram

code[x_, y_] := N[(N[(x - y), $MachinePrecision] / N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{x - y}{2 - \left(x + y\right)} \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 87.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + x \cdot \frac{-2}{y}\\ \mathbf{if}\;y \leq -3.7 \cdot 10^{+43}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{+17}:\\ \;\;\;\;\frac{x - y}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 1.0 (* x (/ -2.0 y)))))
   (if (<= y -3.7e+43) t_0 (if (<= y 1.08e+17) (/ (- x y) (- 2.0 x)) t_0))))

C

double code(double x, double y) {
	double t_0 = 1.0 + (x * (-2.0 / y));
	double tmp;
	if (y <= -3.7e+43) {
		tmp = t_0;
	} else if (y <= 1.08e+17) {
		tmp = (x - y) / (2.0 - x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 + (x * ((-2.0d0) / y))
    if (y <= (-3.7d+43)) then
        tmp = t_0
    else if (y <= 1.08d+17) then
        tmp = (x - y) / (2.0d0 - x)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 1.0 + (x * (-2.0 / y));
	double tmp;
	if (y <= -3.7e+43) {
		tmp = t_0;
	} else if (y <= 1.08e+17) {
		tmp = (x - y) / (2.0 - x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 + (x * (-2.0 / y))
	tmp = 0
	if y <= -3.7e+43:
		tmp = t_0
	elif y <= 1.08e+17:
		tmp = (x - y) / (2.0 - x)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 + Float64(x * Float64(-2.0 / y)))
	tmp = 0.0
	if (y <= -3.7e+43)
		tmp = t_0;
	elseif (y <= 1.08e+17)
		tmp = Float64(Float64(x - y) / Float64(2.0 - x));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 + (x * (-2.0 / y));
	tmp = 0.0;
	if (y <= -3.7e+43)
		tmp = t_0;
	elseif (y <= 1.08e+17)
		tmp = (x - y) / (2.0 - x);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 + N[(x * N[(-2.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.7e+43], t$95$0, If[LessEqual[y, 1.08e+17], N[(N[(x - y), $MachinePrecision] / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.7000000000000001e43 or 1.08e17 < y

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\left(1 + -1 \cdot \frac{x}{y}\right) - -1 \cdot \frac{2 - x}{y}} \]
   4. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto 1 + \color{blue}{\left(-1 \cdot \frac{x}{y} - -1 \cdot \frac{2 - x}{y}\right)} \]

      2. associate-*r/ N/A

         \[\leadsto 1 + \left(\frac{-1 \cdot x}{y} - \color{blue}{-1} \cdot \frac{2 - x}{y}\right) \]

      3. associate-*r/ N/A

         \[\leadsto 1 + \left(\frac{-1 \cdot x}{y} - \frac{-1 \cdot \left(2 - x\right)}{\color{blue}{y}}\right) \]

      4. div-sub N/A

         \[\leadsto 1 + \frac{-1 \cdot x - -1 \cdot \left(2 - x\right)}{\color{blue}{y}} \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{\left(\frac{-1 \cdot x - -1 \cdot \left(2 - x\right)}{y}\right)}\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(-1 \cdot x - -1 \cdot \left(2 - x\right)\right), \color{blue}{y}\right)\right) \]

   5. Simplified 84.0%

      \[\leadsto \color{blue}{1 + \frac{2 + -2 \cdot x}{y}} \]

   6. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{\left(-2 \cdot \frac{x}{y}\right)}\right) \]
   7. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\frac{-2 \cdot x}{\color{blue}{y}}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\frac{x \cdot -2}{y}\right)\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(x \cdot \color{blue}{\frac{-2}{y}}\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(x \cdot \frac{\mathsf{neg}\left(2\right)}{y}\right)\right) \]

      5. distribute-neg-frac N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(x \cdot \left(\mathsf{neg}\left(\frac{2}{y}\right)\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(x \cdot \left(\mathsf{neg}\left(\frac{2 \cdot 1}{y}\right)\right)\right)\right) \]

      7. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(x \cdot \left(\mathsf{neg}\left(2 \cdot \frac{1}{y}\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(2 \cdot \frac{1}{y}\right)\right)}\right)\right) \]

      9. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\frac{2 \cdot 1}{y}\right)\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\frac{2}{y}\right)\right)\right)\right) \]

      11. distribute-neg-frac N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \left(\frac{\mathsf{neg}\left(2\right)}{\color{blue}{y}}\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \left(\frac{-2}{y}\right)\right)\right) \]

      13. /-lowering-/.f64 84.0%

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(-2, \color{blue}{y}\right)\right)\right) \]

   8. Simplified 84.0%

      \[\leadsto 1 + \color{blue}{x \cdot \frac{-2}{y}} \]

   if -3.7000000000000001e43 < y < 1.08e17

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), \mathsf{\_.f64}\left(2, \color{blue}{\left(y \cdot \left(1 + \frac{x}{y}\right)\right)}\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), \mathsf{\_.f64}\left(2, \mathsf{*.f64}\left(y, \color{blue}{\left(1 + \frac{x}{y}\right)}\right)\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), \mathsf{\_.f64}\left(2, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \color{blue}{\left(\frac{x}{y}\right)}\right)\right)\right)\right) \]

      3. /-lowering-/.f64 72.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), \mathsf{\_.f64}\left(2, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(x, \color{blue}{y}\right)\right)\right)\right)\right) \]

   5. Simplified 72.3%

      \[\leadsto \frac{x - y}{2 - \color{blue}{y \cdot \left(1 + \frac{x}{y}\right)}} \]

   6. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), \color{blue}{\left(2 - x\right)}\right) \]
   7. Step-by-step derivation

      1. --lowering--.f64 95.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), \mathsf{\_.f64}\left(2, \color{blue}{x}\right)\right) \]

   8. Simplified 95.3%

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

Alternative 3: 73.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{y + -2}\\ \mathbf{if}\;y \leq -8.6 \cdot 10^{-23}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-58}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ y (+ y -2.0))))
   (if (<= y -8.6e-23) t_0 (if (<= y 4.8e-58) (/ x (- 2.0 x)) t_0))))

C

double code(double x, double y) {
	double t_0 = y / (y + -2.0);
	double tmp;
	if (y <= -8.6e-23) {
		tmp = t_0;
	} else if (y <= 4.8e-58) {
		tmp = x / (2.0 - x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y / (y + (-2.0d0))
    if (y <= (-8.6d-23)) then
        tmp = t_0
    else if (y <= 4.8d-58) then
        tmp = x / (2.0d0 - x)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = y / (y + -2.0);
	double tmp;
	if (y <= -8.6e-23) {
		tmp = t_0;
	} else if (y <= 4.8e-58) {
		tmp = x / (2.0 - x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = y / (y + -2.0)
	tmp = 0
	if y <= -8.6e-23:
		tmp = t_0
	elif y <= 4.8e-58:
		tmp = x / (2.0 - x)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(y / Float64(y + -2.0))
	tmp = 0.0
	if (y <= -8.6e-23)
		tmp = t_0;
	elseif (y <= 4.8e-58)
		tmp = Float64(x / Float64(2.0 - x));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = y / (y + -2.0);
	tmp = 0.0;
	if (y <= -8.6e-23)
		tmp = t_0;
	elseif (y <= 4.8e-58)
		tmp = x / (2.0 - x);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.6e-23], t$95$0, If[LessEqual[y, 4.8e-58], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -8.60000000000000004e-23 or 4.8000000000000001e-58 < y

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-1 \cdot \frac{y}{2 - y}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(\frac{y}{2 - y}\right) \]

      2. distribute-neg-frac2 N/A

         \[\leadsto \frac{y}{\color{blue}{\mathsf{neg}\left(\left(2 - y\right)\right)}} \]

      3. mul-1-neg N/A

         \[\leadsto \frac{y}{-1 \cdot \color{blue}{\left(2 - y\right)}} \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(y, \color{blue}{\left(-1 \cdot \left(2 - y\right)\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(y, \left(\mathsf{neg}\left(\left(2 - y\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(y, \left(\mathsf{neg}\left(\left(2 + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(y, \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(y\right)\right) + 2\right)\right)\right)\right) \]

      8. distribute-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(y, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(y, \left(-1 \cdot \left(\mathsf{neg}\left(y\right)\right) + \left(\mathsf{neg}\left(\color{blue}{2}\right)\right)\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{/.f64}\left(y, \left(-1 \cdot \left(-1 \cdot y\right) + \left(\mathsf{neg}\left(2\right)\right)\right)\right) \]

      11. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(y, \left(\left(-1 \cdot -1\right) \cdot y + \left(\mathsf{neg}\left(\color{blue}{2}\right)\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(y, \left(1 \cdot y + \left(\mathsf{neg}\left(2\right)\right)\right)\right) \]

      13. *-lft-identity N/A

          \[\leadsto \mathsf{/.f64}\left(y, \left(y + \left(\mathsf{neg}\left(\color{blue}{2}\right)\right)\right)\right) \]

      14. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(y, \mathsf{+.f64}\left(y, \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right) \]

      15. metadata-eval 79.7%

          \[\leadsto \mathsf{/.f64}\left(y, \mathsf{+.f64}\left(y, -2\right)\right) \]

   5. Simplified 79.7%

      \[\leadsto \color{blue}{\frac{y}{y + -2}} \]

   if -8.60000000000000004e-23 < y < 4.8000000000000001e-58

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{x}{2 - x}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(2 - x\right)}\right) \]

      2. --lowering--.f64 84.4%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(2, \color{blue}{x}\right)\right) \]

   5. Simplified 84.4%

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

Alternative 4: 73.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{+45}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+59}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.06e+45) 1.0 (if (<= y 6.5e+59) (/ x (- 2.0 x)) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.06e+45) {
		tmp = 1.0;
	} else if (y <= 6.5e+59) {
		tmp = x / (2.0 - x);
	} else {
		tmp = 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 <= (-1.06d+45)) then
        tmp = 1.0d0
    else if (y <= 6.5d+59) then
        tmp = x / (2.0d0 - x)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.06e+45) {
		tmp = 1.0;
	} else if (y <= 6.5e+59) {
		tmp = x / (2.0 - x);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.06e+45:
		tmp = 1.0
	elif y <= 6.5e+59:
		tmp = x / (2.0 - x)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.06e+45)
		tmp = 1.0;
	elseif (y <= 6.5e+59)
		tmp = Float64(x / Float64(2.0 - x));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.06e+45)
		tmp = 1.0;
	elseif (y <= 6.5e+59)
		tmp = x / (2.0 - x);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.06e+45], 1.0, If[LessEqual[y, 6.5e+59], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.06e45 or 6.50000000000000021e59 < y

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Simplified 85.6%

      \[\leadsto \color{blue}{1} \]

   if -1.06e45 < y < 6.50000000000000021e59

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{x}{2 - x}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(2 - x\right)}\right) \]

      2. --lowering--.f64 76.5%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(2, \color{blue}{x}\right)\right) \]

   5. Simplified 76.5%

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

Alternative 5: 62.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+40}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+17}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1e+40) 1.0 (if (<= y 1.4e+17) -1.0 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1e+40) {
		tmp = 1.0;
	} else if (y <= 1.4e+17) {
		tmp = -1.0;
	} else {
		tmp = 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 <= (-1d+40)) then
        tmp = 1.0d0
    else if (y <= 1.4d+17) then
        tmp = -1.0d0
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1e+40) {
		tmp = 1.0;
	} else if (y <= 1.4e+17) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1e+40:
		tmp = 1.0
	elif y <= 1.4e+17:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1e+40)
		tmp = 1.0;
	elseif (y <= 1.4e+17)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1e+40)
		tmp = 1.0;
	elseif (y <= 1.4e+17)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1e+40], 1.0, If[LessEqual[y, 1.4e+17], -1.0, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.00000000000000003e40 or 1.4e17 < y

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Simplified 82.8%

      \[\leadsto \color{blue}{1} \]

   if -1.00000000000000003e40 < y < 1.4e17

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{-1} \]
   4. Step-by-step derivation

   5. Simplified 58.5%

      \[\leadsto \color{blue}{-1} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 38.3% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ -1 \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return -1.0

Julia

function code(x, y)
	return -1.0
end

MATLAB

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

Wolfram

code[x_, y_] := -1.0

Derivation

1. Initial program 100.0%

   \[\frac{x - y}{2 - \left(x + y\right)} \]
2. Add Preprocessing

3. Taylor expanded in x around inf

   \[\leadsto \color{blue}{-1} \]
4. Step-by-step derivation

5. Simplified 38.1%

   \[\leadsto \color{blue}{-1} \]
6. Add Preprocessing

Developer Target 1: 100.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 2 - \left(x + y\right)\\ \frac{x}{t\_0} - \frac{y}{t\_0} \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- 2.0 (+ x y)))) (- (/ x t_0) (/ y t_0))))

C

double code(double x, double y) {
	double t_0 = 2.0 - (x + y);
	return (x / t_0) - (y / t_0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    t_0 = 2.0d0 - (x + y)
    code = (x / t_0) - (y / t_0)
end function

Java

public static double code(double x, double y) {
	double t_0 = 2.0 - (x + y);
	return (x / t_0) - (y / t_0);
}

Python

def code(x, y):
	t_0 = 2.0 - (x + y)
	return (x / t_0) - (y / t_0)

Julia

function code(x, y)
	t_0 = Float64(2.0 - Float64(x + y))
	return Float64(Float64(x / t_0) - Float64(y / t_0))
end

MATLAB

function tmp = code(x, y)
	t_0 = 2.0 - (x + y);
	tmp = (x / t_0) - (y / t_0);
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]}, N[(N[(x / t$95$0), $MachinePrecision] - N[(y / t$95$0), $MachinePrecision]), $MachinePrecision]]

Reproduce

herbie shell --seed 2024140 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, C"
  :precision binary64

  :alt
  (! :herbie-platform default (- (/ x (- 2 (+ x y))) (/ y (- 2 (+ x y)))))

  (/ (- x y) (- 2.0 (+ x y))))