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

Percentage Accurate: 100.0% → 100.0%

Time: 6.8s

Alternatives: 8

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: 85.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{2 - \left(x + y\right)}\\ \mathbf{if}\;x \leq -8.9 \cdot 10^{+77}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+76}:\\ \;\;\;\;\frac{x - y}{2 - y}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (- 2.0 (+ x y)))))
   (if (<= x -8.9e+77) t_0 (if (<= x 1.5e+76) (/ (- x y) (- 2.0 y)) t_0))))

C

double code(double x, double y) {
	double t_0 = x / (2.0 - (x + y));
	double tmp;
	if (x <= -8.9e+77) {
		tmp = t_0;
	} else if (x <= 1.5e+76) {
		tmp = (x - y) / (2.0 - y);
	} 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 = x / (2.0d0 - (x + y))
    if (x <= (-8.9d+77)) then
        tmp = t_0
    else if (x <= 1.5d+76) then
        tmp = (x - y) / (2.0d0 - y)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x / (2.0 - (x + y));
	double tmp;
	if (x <= -8.9e+77) {
		tmp = t_0;
	} else if (x <= 1.5e+76) {
		tmp = (x - y) / (2.0 - y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (2.0 - (x + y))
	tmp = 0
	if x <= -8.9e+77:
		tmp = t_0
	elif x <= 1.5e+76:
		tmp = (x - y) / (2.0 - y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(2.0 - Float64(x + y)))
	tmp = 0.0
	if (x <= -8.9e+77)
		tmp = t_0;
	elseif (x <= 1.5e+76)
		tmp = Float64(Float64(x - y) / Float64(2.0 - y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x / (2.0 - (x + y));
	tmp = 0.0;
	if (x <= -8.9e+77)
		tmp = t_0;
	elseif (x <= 1.5e+76)
		tmp = (x - y) / (2.0 - y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8.9e+77], t$95$0, If[LessEqual[x, 1.5e+76], N[(N[(x - y), $MachinePrecision] / N[(2.0 - y), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -8.8999999999999998e77 or 1.4999999999999999e76 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 80.8%

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

   if -8.8999999999999998e77 < x < 1.4999999999999999e76

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. --lowering--.f64 91.7%

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

   5. Simplified 91.7%

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

Alternative 3: 73.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{2 - \left(x + y\right)}\\ \mathbf{if}\;x \leq -1.2 \cdot 10^{-7}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+75}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (- 2.0 (+ x y)))))
   (if (<= x -1.2e-7) t_0 (if (<= x 1.9e+75) (/ y (+ y -2.0)) t_0))))

C

double code(double x, double y) {
	double t_0 = x / (2.0 - (x + y));
	double tmp;
	if (x <= -1.2e-7) {
		tmp = t_0;
	} else if (x <= 1.9e+75) {
		tmp = y / (y + -2.0);
	} 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 = x / (2.0d0 - (x + y))
    if (x <= (-1.2d-7)) then
        tmp = t_0
    else if (x <= 1.9d+75) then
        tmp = y / (y + (-2.0d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x / (2.0 - (x + y));
	double tmp;
	if (x <= -1.2e-7) {
		tmp = t_0;
	} else if (x <= 1.9e+75) {
		tmp = y / (y + -2.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (2.0 - (x + y))
	tmp = 0
	if x <= -1.2e-7:
		tmp = t_0
	elif x <= 1.9e+75:
		tmp = y / (y + -2.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(2.0 - Float64(x + y)))
	tmp = 0.0
	if (x <= -1.2e-7)
		tmp = t_0;
	elseif (x <= 1.9e+75)
		tmp = Float64(y / Float64(y + -2.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x / (2.0 - (x + y));
	tmp = 0.0;
	if (x <= -1.2e-7)
		tmp = t_0;
	elseif (x <= 1.9e+75)
		tmp = y / (y + -2.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.2e-7], t$95$0, If[LessEqual[x, 1.9e+75], N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.19999999999999989e-7 or 1.9000000000000001e75 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 76.8%

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

   if -1.19999999999999989e-7 < x < 1.9000000000000001e75

   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 77.6%

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

   5. Simplified 77.6%

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

Alternative 4: 73.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{-7}:\\ \;\;\;\;\frac{1}{\frac{2}{x} + -1}\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+74}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -4.3e-7)
   (/ 1.0 (+ (/ 2.0 x) -1.0))
   (if (<= x 3.5e+74) (/ y (+ y -2.0)) (/ x (- 2.0 x)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -4.3e-7) {
		tmp = 1.0 / ((2.0 / x) + -1.0);
	} else if (x <= 3.5e+74) {
		tmp = y / (y + -2.0);
	} else {
		tmp = x / (2.0 - 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 <= (-4.3d-7)) then
        tmp = 1.0d0 / ((2.0d0 / x) + (-1.0d0))
    else if (x <= 3.5d+74) then
        tmp = y / (y + (-2.0d0))
    else
        tmp = x / (2.0d0 - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -4.3e-7) {
		tmp = 1.0 / ((2.0 / x) + -1.0);
	} else if (x <= 3.5e+74) {
		tmp = y / (y + -2.0);
	} else {
		tmp = x / (2.0 - x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -4.3e-7:
		tmp = 1.0 / ((2.0 / x) + -1.0)
	elif x <= 3.5e+74:
		tmp = y / (y + -2.0)
	else:
		tmp = x / (2.0 - x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -4.3e-7)
		tmp = Float64(1.0 / Float64(Float64(2.0 / x) + -1.0));
	elseif (x <= 3.5e+74)
		tmp = Float64(y / Float64(y + -2.0));
	else
		tmp = Float64(x / Float64(2.0 - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -4.3e-7)
		tmp = 1.0 / ((2.0 / x) + -1.0);
	elseif (x <= 3.5e+74)
		tmp = y / (y + -2.0);
	else
		tmp = x / (2.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -4.3e-7], N[(1.0 / N[(N[(2.0 / x), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.5e+74], N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.3000000000000001e-7

   1. Initial program 99.9%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   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 71.4%

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

   5. Simplified 71.4%

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

      1. clear-num N/A

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

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

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. *-inverses N/A

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

      6. metadata-eval N/A

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

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

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

      8. /-lowering-/.f64 71.4%

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

   7. Applied egg-rr 71.4%

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

   if -4.3000000000000001e-7 < x < 3.50000000000000014e74

   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 77.6%

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

   5. Simplified 77.6%

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

   if 3.50000000000000014e74 < x

   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 81.5%

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

   5. Simplified 81.5%

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

Alternative 5: 73.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{2 - x}\\ \mathbf{if}\;x \leq -2.85 \cdot 10^{-7}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+71}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (- 2.0 x))))
   (if (<= x -2.85e-7) t_0 (if (<= x 7.2e+71) (/ y (+ y -2.0)) t_0))))

C

double code(double x, double y) {
	double t_0 = x / (2.0 - x);
	double tmp;
	if (x <= -2.85e-7) {
		tmp = t_0;
	} else if (x <= 7.2e+71) {
		tmp = y / (y + -2.0);
	} 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 = x / (2.0d0 - x)
    if (x <= (-2.85d-7)) then
        tmp = t_0
    else if (x <= 7.2d+71) then
        tmp = y / (y + (-2.0d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x / (2.0 - x);
	double tmp;
	if (x <= -2.85e-7) {
		tmp = t_0;
	} else if (x <= 7.2e+71) {
		tmp = y / (y + -2.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (2.0 - x)
	tmp = 0
	if x <= -2.85e-7:
		tmp = t_0
	elif x <= 7.2e+71:
		tmp = y / (y + -2.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(2.0 - x))
	tmp = 0.0
	if (x <= -2.85e-7)
		tmp = t_0;
	elseif (x <= 7.2e+71)
		tmp = Float64(y / Float64(y + -2.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x / (2.0 - x);
	tmp = 0.0;
	if (x <= -2.85e-7)
		tmp = t_0;
	elseif (x <= 7.2e+71)
		tmp = y / (y + -2.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.85e-7], t$95$0, If[LessEqual[x, 7.2e+71], N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.8500000000000002e-7 or 7.1999999999999999e71 < x

   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 76.0%

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

   5. Simplified 76.0%

      \[\leadsto \color{blue}{\frac{x}{2 - x}} \]

   if -2.8500000000000002e-7 < x < 7.1999999999999999e71

   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 77.6%

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

   5. Simplified 77.6%

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

Alternative 6: 74.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+19}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{+51}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.6e+19) 1.0 (if (<= y 2.55e+51) (/ x (- 2.0 x)) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.6e+19) {
		tmp = 1.0;
	} else if (y <= 2.55e+51) {
		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 <= (-2.6d+19)) then
        tmp = 1.0d0
    else if (y <= 2.55d+51) 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 <= -2.6e+19) {
		tmp = 1.0;
	} else if (y <= 2.55e+51) {
		tmp = x / (2.0 - x);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.6e+19:
		tmp = 1.0
	elif y <= 2.55e+51:
		tmp = x / (2.0 - x)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.6e+19)
		tmp = 1.0;
	elseif (y <= 2.55e+51)
		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 <= -2.6e+19)
		tmp = 1.0;
	elseif (y <= 2.55e+51)
		tmp = x / (2.0 - x);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.6e+19], 1.0, If[LessEqual[y, 2.55e+51], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -2.6e19 or 2.55000000000000005e51 < 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 78.8%

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

   if -2.6e19 < y < 2.55000000000000005e51

   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 74.1%

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

   5. Simplified 74.1%

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

Alternative 7: 60.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{+78}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{+70}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.95e+78) -1.0 (if (<= x 4.1e+70) 1.0 -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.95e+78) {
		tmp = -1.0;
	} else if (x <= 4.1e+70) {
		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 (x <= (-1.95d+78)) then
        tmp = -1.0d0
    else if (x <= 4.1d+70) 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 (x <= -1.95e+78) {
		tmp = -1.0;
	} else if (x <= 4.1e+70) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.95e+78:
		tmp = -1.0
	elif x <= 4.1e+70:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.95e+78)
		tmp = -1.0;
	elseif (x <= 4.1e+70)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.95e+78)
		tmp = -1.0;
	elseif (x <= 4.1e+70)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.95e+78], -1.0, If[LessEqual[x, 4.1e+70], 1.0, -1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -1.9500000000000002e78 or 4.1000000000000002e70 < x

   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 80.2%

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

   if -1.9500000000000002e78 < x < 4.1000000000000002e70

   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 55.3%

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

Alternative 8: 38.4% 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 35.6%

   \[\leadsto \color{blue}{-1} \]
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 2024161 
(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))))