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

Percentage Accurate: 100.0% → 100.0%

Time: 4.9s

Alternatives: 7

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{x - y}{x + y} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y}{x + y} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y}{x + y} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\frac{x - y}{x + y} \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 74.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -1 - \frac{x}{y} \cdot -2\\ \mathbf{if}\;y \leq -1.1 \cdot 10^{+62}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-27}:\\ \;\;\;\;1 + \frac{y \cdot -2}{x}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- -1.0 (* (/ x y) -2.0))))
   (if (<= y -1.1e+62) t_0 (if (<= y 4e-27) (+ 1.0 (/ (* y -2.0) x)) t_0))))

C

double code(double x, double y) {
	double t_0 = -1.0 - ((x / y) * -2.0);
	double tmp;
	if (y <= -1.1e+62) {
		tmp = t_0;
	} else if (y <= 4e-27) {
		tmp = 1.0 + ((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 / y) * (-2.0d0))
    if (y <= (-1.1d+62)) then
        tmp = t_0
    else if (y <= 4d-27) then
        tmp = 1.0d0 + ((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 / y) * -2.0);
	double tmp;
	if (y <= -1.1e+62) {
		tmp = t_0;
	} else if (y <= 4e-27) {
		tmp = 1.0 + ((y * -2.0) / x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = -1.0 - ((x / y) * -2.0)
	tmp = 0
	if y <= -1.1e+62:
		tmp = t_0
	elif y <= 4e-27:
		tmp = 1.0 + ((y * -2.0) / x)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(-1.0 - Float64(Float64(x / y) * -2.0))
	tmp = 0.0
	if (y <= -1.1e+62)
		tmp = t_0;
	elseif (y <= 4e-27)
		tmp = Float64(1.0 + Float64(Float64(y * -2.0) / x));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = -1.0 - ((x / y) * -2.0);
	tmp = 0.0;
	if (y <= -1.1e+62)
		tmp = t_0;
	elseif (y <= 4e-27)
		tmp = 1.0 + ((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[(N[(x / y), $MachinePrecision] * -2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.1e+62], t$95$0, If[LessEqual[y, 4e-27], N[(1.0 + N[(N[(y * -2.0), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.10000000000000007e62 or 4.0000000000000002e-27 < y

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. times-frac N/A

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

      4. *-commutative N/A

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

      5. metadata-eval N/A

         \[\leadsto \frac{x \cdot \left(-1 - 1\right)}{-1 \cdot y} + \left(\mathsf{neg}\left(1\right)\right) \]

      6. distribute-rgt-out-- N/A

         \[\leadsto \frac{-1 \cdot x - 1 \cdot x}{-1 \cdot y} + \left(\mathsf{neg}\left(1\right)\right) \]

      7. *-lft-identity N/A

         \[\leadsto \frac{-1 \cdot x - x}{-1 \cdot y} + \left(\mathsf{neg}\left(1\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto \frac{-1 \cdot x - x}{\mathsf{neg}\left(y\right)} + \left(\mathsf{neg}\left(1\right)\right) \]

      9. distribute-neg-frac2 N/A

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

      10. mul-1-neg N/A

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

      11. metadata-eval N/A

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

      12. +-commutative N/A

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

      13. mul-1-neg N/A

          \[\leadsto -1 + \left(\mathsf{neg}\left(\frac{-1 \cdot x - x}{y}\right)\right) \]

      14. unsub-neg N/A

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

      15. --lowering--.f64 N/A

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

      16. div-sub N/A

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

      17. associate-*r/ N/A

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

      18. sub-neg N/A

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

      19. mul-1-neg N/A

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

      20. distribute-rgt-out N/A

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

      21. metadata-eval N/A

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

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

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

      23. /-lowering-/.f64 83.5%

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

   5. Simplified 83.5%

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

   if -1.10000000000000007e62 < y < 4.0000000000000002e-27

   1. Initial program 99.9%

      \[\frac{x - y}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. div-sub N/A

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

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

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

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

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

      6. *-lft-identity N/A

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

      7. distribute-rgt-out-- N/A

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

      8. metadata-eval N/A

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

      9. *-lowering-*.f64 79.8%

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

   5. Simplified 79.8%

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

Alternative 3: 74.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -1 + \frac{x}{y}\\ \mathbf{if}\;y \leq -1.05 \cdot 10^{+62}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-29}:\\ \;\;\;\;1 + \frac{y \cdot -2}{x}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ -1.0 (/ x y))))
   (if (<= y -1.05e+62) t_0 (if (<= y 3.5e-29) (+ 1.0 (/ (* y -2.0) x)) t_0))))

C

double code(double x, double y) {
	double t_0 = -1.0 + (x / y);
	double tmp;
	if (y <= -1.05e+62) {
		tmp = t_0;
	} else if (y <= 3.5e-29) {
		tmp = 1.0 + ((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 / y)
    if (y <= (-1.05d+62)) then
        tmp = t_0
    else if (y <= 3.5d-29) then
        tmp = 1.0d0 + ((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 / y);
	double tmp;
	if (y <= -1.05e+62) {
		tmp = t_0;
	} else if (y <= 3.5e-29) {
		tmp = 1.0 + ((y * -2.0) / x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = -1.0 + (x / y)
	tmp = 0
	if y <= -1.05e+62:
		tmp = t_0
	elif y <= 3.5e-29:
		tmp = 1.0 + ((y * -2.0) / x)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(-1.0 + Float64(x / y))
	tmp = 0.0
	if (y <= -1.05e+62)
		tmp = t_0;
	elseif (y <= 3.5e-29)
		tmp = Float64(1.0 + Float64(Float64(y * -2.0) / x));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = -1.0 + (x / y);
	tmp = 0.0;
	if (y <= -1.05e+62)
		tmp = t_0;
	elseif (y <= 3.5e-29)
		tmp = 1.0 + ((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 / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.05e+62], t$95$0, If[LessEqual[y, 3.5e-29], N[(1.0 + N[(N[(y * -2.0), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.05e62 or 3.4999999999999997e-29 < y

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Simplified 83.2%

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

      1. div-sub N/A

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

      2. *-inverses N/A

         \[\leadsto \frac{x}{y} - 1 \]

      3. --lowering--.f64 N/A

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

      4. /-lowering-/.f64 83.2%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(x, y\right), 1\right) \]

   7. Applied egg-rr 83.2%

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

   if -1.05e62 < y < 3.4999999999999997e-29

   1. Initial program 99.9%

      \[\frac{x - y}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. div-sub N/A

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

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

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

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

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

      6. *-lft-identity N/A

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

      7. distribute-rgt-out-- N/A

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

      8. metadata-eval N/A

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

      9. *-lowering-*.f64 79.8%

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

   5. Simplified 79.8%

      \[\leadsto \color{blue}{1 + \frac{y \cdot -2}{x}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+62}:\\ \;\;\;\;-1 + \frac{x}{y}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-29}:\\ \;\;\;\;1 + \frac{y \cdot -2}{x}\\ \mathbf{else}:\\ \;\;\;\;-1 + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -1 + \frac{x}{y}\\ \mathbf{if}\;y \leq -8 \cdot 10^{+72}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-26}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ -1.0 (/ x y))))
   (if (<= y -8e+72) t_0 (if (<= y 2.2e-26) (/ x (+ x y)) t_0))))

C

double code(double x, double y) {
	double t_0 = -1.0 + (x / y);
	double tmp;
	if (y <= -8e+72) {
		tmp = t_0;
	} else if (y <= 2.2e-26) {
		tmp = x / (x + 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 = (-1.0d0) + (x / y)
    if (y <= (-8d+72)) then
        tmp = t_0
    else if (y <= 2.2d-26) then
        tmp = x / (x + y)
    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 / y);
	double tmp;
	if (y <= -8e+72) {
		tmp = t_0;
	} else if (y <= 2.2e-26) {
		tmp = x / (x + y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = -1.0 + (x / y)
	tmp = 0
	if y <= -8e+72:
		tmp = t_0
	elif y <= 2.2e-26:
		tmp = x / (x + y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(-1.0 + Float64(x / y))
	tmp = 0.0
	if (y <= -8e+72)
		tmp = t_0;
	elseif (y <= 2.2e-26)
		tmp = Float64(x / Float64(x + y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = -1.0 + (x / y);
	tmp = 0.0;
	if (y <= -8e+72)
		tmp = t_0;
	elseif (y <= 2.2e-26)
		tmp = x / (x + y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(-1.0 + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8e+72], t$95$0, If[LessEqual[y, 2.2e-26], N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -7.99999999999999955e72 or 2.2000000000000001e-26 < y

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Simplified 84.3%

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

      1. div-sub N/A

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

      2. *-inverses N/A

         \[\leadsto \frac{x}{y} - 1 \]

      3. --lowering--.f64 N/A

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

      4. /-lowering-/.f64 84.3%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(x, y\right), 1\right) \]

   7. Applied egg-rr 84.3%

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

   if -7.99999999999999955e72 < y < 2.2000000000000001e-26

   1. Initial program 99.9%

      \[\frac{x - y}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Simplified 78.0%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+72}:\\ \;\;\;\;-1 + \frac{x}{y}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-26}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{else}:\\ \;\;\;\;-1 + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -1 + \frac{x}{y}\\ \mathbf{if}\;y \leq -1.02 \cdot 10^{+62}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-26}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ -1.0 (/ x y))))
   (if (<= y -1.02e+62) t_0 (if (<= y 1.95e-26) 1.0 t_0))))

C

double code(double x, double y) {
	double t_0 = -1.0 + (x / y);
	double tmp;
	if (y <= -1.02e+62) {
		tmp = t_0;
	} else if (y <= 1.95e-26) {
		tmp = 1.0;
	} 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 = (-1.0d0) + (x / y)
    if (y <= (-1.02d+62)) then
        tmp = t_0
    else if (y <= 1.95d-26) then
        tmp = 1.0d0
    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 / y);
	double tmp;
	if (y <= -1.02e+62) {
		tmp = t_0;
	} else if (y <= 1.95e-26) {
		tmp = 1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = -1.0 + (x / y)
	tmp = 0
	if y <= -1.02e+62:
		tmp = t_0
	elif y <= 1.95e-26:
		tmp = 1.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(-1.0 + Float64(x / y))
	tmp = 0.0
	if (y <= -1.02e+62)
		tmp = t_0;
	elseif (y <= 1.95e-26)
		tmp = 1.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = -1.0 + (x / y);
	tmp = 0.0;
	if (y <= -1.02e+62)
		tmp = t_0;
	elseif (y <= 1.95e-26)
		tmp = 1.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(-1.0 + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.02e+62], t$95$0, If[LessEqual[y, 1.95e-26], 1.0, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.02000000000000002e62 or 1.94999999999999993e-26 < y

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Simplified 83.2%

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

      1. div-sub N/A

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

      2. *-inverses N/A

         \[\leadsto \frac{x}{y} - 1 \]

      3. --lowering--.f64 N/A

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

      4. /-lowering-/.f64 83.2%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(x, y\right), 1\right) \]

   7. Applied egg-rr 83.2%

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

   if -1.02000000000000002e62 < y < 1.94999999999999993e-26

   1. Initial program 99.9%

      \[\frac{x - y}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Simplified 78.4%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+62}:\\ \;\;\;\;-1 + \frac{x}{y}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-26}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1 + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+67}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 10^{-28}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.3e+67) -1.0 (if (<= y 1e-28) 1.0 -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.3e+67) {
		tmp = -1.0;
	} else if (y <= 1e-28) {
		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 <= (-1.3d+67)) then
        tmp = -1.0d0
    else if (y <= 1d-28) 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 <= -1.3e+67) {
		tmp = -1.0;
	} else if (y <= 1e-28) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.3e+67:
		tmp = -1.0
	elif y <= 1e-28:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.3e+67)
		tmp = -1.0;
	elseif (y <= 1e-28)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.3e+67)
		tmp = -1.0;
	elseif (y <= 1e-28)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.3e+67], -1.0, If[LessEqual[y, 1e-28], 1.0, -1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.3e67 or 9.99999999999999971e-29 < y

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Simplified 83.3%

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

   if -1.3e67 < y < 9.99999999999999971e-29

   1. Initial program 99.9%

      \[\frac{x - y}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Simplified 78.0%

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

Alternative 7: 49.3% accurate, 7.0× 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%

   \[\frac{x - y}{x + y} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

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

5. Simplified 50.8%

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

Developer Target 1: 100.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \frac{x}{x + y} - \frac{y}{x + y} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024150 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, D"
  :precision binary64

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

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